MechanicsArXiv
type: channel
description: Welcome to MechanicsArXiv. This repository provides a platform for researchers to share early-stage research, working or completed papers, technical reports, reviews, and tutorials in the broadly defined field of solid mechanics. Our mission is to accelerate the dissemination of scholarly work, foster collaboration, and provide open access to the latest innovations across mechanics.
language: en-US
publication name: MechanicsArXiv
items: A new perspective in linear Cauchy Elasticity: variational minimum principles for statics, dynamics, and heterogeneous materials
items: Driven Odd Elasticity in Passive Mechanical Metamaterials
items: Conformal Mechanics of Serpentine Meshes for Millimeter-Scale Neural Probes
items: Thermo-elastic properties of hydrated epoxy-graphene nanocomposites from ensemble-based molecular dynamics simulations
items: First-Order Compatible-Strain Mixed Quadrilateral Finite Elements for $2$D Nonlinear Elasticity
items: Interpenetrating Gyroid Lattice - Foam Composites with Synergistically Enhanced Stiffness and Energy Absorption for Impact Mitigation
items: Why is the strength of an elastomeric polymer network so low?
items: Inward buckling of spiral layered structures subject to volumetric expansion and external constraint
items: Crack-Parallel Tension Effects on Fracture of Soft Knitted Polymer Composites deduced from Gap Tests via Microplane Triads
items: A closed-form correction for three-point bend testing of functionally graded beams, with application to endovascular devices
items: Nonlinear Anisotropic Visco-Anelasticity
items: Harnessing Functional Gradients for Enhanced Shock Absorption in Foam Materials
items: Analysis of Stress Wave Interaction with a 180° Bend Junction Between Two Square Bars
items: Universal deformations and universal residual stresses in incompressible isotropic Cauchy elasticity
items: On the stability of Euler’s elastica with natural curvature: Out-of-plane bifurcation with twisting
items: Sequential prediction of transverse crack paths in CFRP composites via a deep learning approach
items: In-Plane Wave Homogenization and the Emergent Electromomentum Tensor
items: Nonlinear dynamics of miniaturized dielectric elastomer actuators with surface effects
items: A Unified Stiffness Evolution Model and Its Application to 3D-Printed Regular and Re-Entrant Honeycombs
items: Universal Displacements in Linear Strain-Gradient Elasticity
items: Finite Element Investigation of Optimal Reinforced Concrete Shear Wall Placement for Vibration Mitigation in Adjacent Buildings with Open-Trench Isolation
items: Inverse Design of Metamaterials with Adaptable Force-Displacement Characteristics
items: Phase-field model for mesoscale simulation of crystallization morphology evolution in 3D printing of thermoplastic composite
items: Compatibility Conditions for Singular Strain Fields on Linear Shells
items: Competitive Hardening Dynamics in Viscoplastic Materials with Evolving Threshold Stress
items: Thermoviscoelasticity of polydomain liquid crystal elastomers regulated by soft elasticity
items: Fractional Calculus based Elasticity obtained from Homogenization
items: Contact loss in all solid-state Li-ion batteries via deposition of impurities
items: Finite-width adiabatic shear banding and dislocation patterning in mesoscale polycrystalline aggregates
items: Dynamic micromagnetism a la Ericksen-Leslie, and the constrained polar continuum mechanics of hard magnetic soft materials

A new perspective in linear Cauchy Elasticity: variational minimum principles for statics, dynamics, and heterogeneous materials
type: item
description: A variational minimum principle for linear elastodynamics of a possibly heterogeneous material without a stored energy function is developed. It involves a change of variables to dual fields, and results in a degenerate elliptic Euler-Lagrange system, even when the primal elastodynamics is hyperbolic. Uniqueness assertions for the dual dynamic and static problems and implications of the degenerate ellipticity are sketched. Some implications pertaining to heterogeneous materials and ones with indefinite elastic moduli are discussed.
subject: Preprints
  topic: section
creator: Amit Acharya
rights: Copyright (c) 2026 MechanicsArXiv
date: 2026-06-23
publication date: 2026-06-23

Driven Odd Elasticity in Passive Mechanical Metamaterials
type: item
description: We present a mechanical mechanism leveraging passive mechanical components, i.e. chiral gears and a square lattice metamaterial, to demonstrate driven odd elasticity in a mechanical metamaterial. The mechanism couples tension and shear in a non-reciprocal way, resulting in an odd shear modulus. The emergence of this odd shear modulus enables non-conservative work in a standard quasistatic strain cycle, and further enables the non-Hermitian skin effect in dynamics. Our results demonstrate that odd elasticity can be achieved in mechanical structures using passive elements without electronic components coupled with feedback or robotic control systems.
subject: Preprints
  topic: section
subject: Odd Elasticity Metamaterial non-Hermitian
  topic: keywords
creator: Mohamad Rahimi
creator: Harold Park
rights: Copyright (c) 2026 MechanicsArXiv
date: 2026-06-22
publication date: 2026-06-22

Conformal Mechanics of Serpentine Meshes for Millimeter-Scale Neural Probes
type: item
description: The mechanical reliability of implantable neural probes depends on their ability to accommodate large deformations during implantation and chronic operation while limiting stress concentrations within conductive interconnects. Despite extensive studies of serpentine interconnects in stretchable electronics, their mechanics under loading conditions relevant to cylindrical neural probes remain poorly understood. This work investigates the mechanics of two stretchable neural interface architectures, Single Serpentine Traces and Interconnected Mesh networks, designed with gold (Au) interconnects encapsulated in polyimide (PI) and embedded within a soft elastomeric substrate. Finite element analysis and experiments are used to characterize their response under stretching, conformal wrapping onto cylindrical neural probes, and bending of the wrapped structure. Deformation in both architectures is accommodated primarily through bending and rotation of the serpentine segments, with localized metal yielding initiating at strains of approximately 5.5–8.25% depending on loading direction and topology. During conformal wrapping onto probes with radii as small as 0.4 mm, the Single Serpentine Traces architecture remains below the Au yield stress, reaching a maximum stress of 145 MPa, whereas the Interconnected Mesh develops localized yielding at interconnection junctions with peak stresses exceeding 215 MPa. Subsequent bending produces only modest stress amplification, although the Interconnected Mesh exhibits approximately twofold greater stress sensitivity than the Single Serpentine Traces. The results demonstrate that rotational compliance governs stress redistribution, while geometric constraints at interconnection junctions control failure initiation. These findings reveal a fundamental tradeoff between electrical connectivity and stress concentrations and provide mechanics guidelines for conformal neural probes and related stretchable bioelectronic systems.
subject: Preprints
  topic: section
subject: stretchable neural probes
  topic: keywords
subject: serpentine interconnects
  topic: keywords
subject: mesh electronics
  topic: keywords
subject: conformal mechanics
  topic: keywords
subject: finite element analysis
  topic: keywords
creator: Sagidolla Batay
creator: Yulin Zhou
creator: Priyan V. Pathirana
creator: John P. Seymour
creator: Raudel Avila
rights: Copyright (c) 2026 MechanicsArXiv
date: 2026-06-19
publication date: 2026-06-19

Thermo-elastic properties of hydrated epoxy-graphene nanocomposites from ensemble-based molecular dynamics simulations
type: item
description: Epoxy-based materials are inherently hygroscopic, absorbing moisture from the environment, which can significantly alter their short and long-term performance. The presence of graphene is often considered as a potential candidate to act as a microscopic barrier, mitigating the adverse effects of hydration on the matrix. This study investigates the impact of hydration on the glass transition and elastic mechanical properties of epoxy resins and their graphene nanocomposites, focusing on water content up to 5 wt%. Using large-ensemble molecular dynamics simulations, we analyze the temperature-driven glass transition and mechanical response of both neat epoxy and epoxy-graphene systems under varying hydration levels. Our results reveal a distinct threshold at 3 wt% water content: below this, hydration primarily reduces the glass transition temperature, while mechanical properties remain unaffected. Beyond 3 wt%, however, the mechanical properties deteriorate, highlighting a non-linear sensitivity to water uptake. Furthermore, we emphasize the critical role of ensemble size in ensuring the reliability of molecular dynamics predictions for such heterogeneous systems. Our simulations demonstrate that ensembles substantially larger than current state-of-the-art standards are necessary to achieve converged distributions of the predicted mechanical properties, particularly in highly heterogeneous hydrated epoxy-graphene nanocomposites. These findings provide novel insights into the hydration behavior of epoxy-based materials and underscore the potential of graphene to enhance their environmental resistance. This work also advances the understanding of structure-property relationships in polymer nanocomposites, offering guidance for the design of more robust materials in humid environments.
subject: Preprints
  topic: section
subject: mechanical behavior
  topic: keywords
subject: hydration
  topic: keywords
subject: molecular dynamics
  topic: keywords
subject: epoxy resin
  topic: keywords
subject: graphene
  topic: keywords
creator: Maxime Vassaux
creator: Werner A. Müller
creator: James L. Suter
creator: Alexandros Anastasiou
creator: Martin Simmons
creator: David Tilbrook
creator: Peter V. Coveney
rights: Copyright (c) 2026 MechanicsArXiv
date: 2026-06-19
publication date: 2026-06-19

First-Order Compatible-Strain Mixed Quadrilateral Finite Elements for $2$D Nonlinear Elasticity
type: item
description: Compatible-strain mixed finite elements (CSMFEs) use the differential complex of nonlinear elasticity to construct discretizations that preserve the underlying topological structure. Existing developments of CSMFEs have focused on simplicial meshes, for which efficient formulations have been developed for first- and second-order elements and successfully applied to compressible and incompressible nonlinear elasticity problems. In this paper, we develop two compatible-strain mixed formulations for quadrilateral elements applicable to compressible and incompressible nonlinear elasticity. For quadrilateral elements, the Piola transformation preserves vector fields tangent and normal to element edges only for special classes of elements, such as rectangles, parallelograms, and trapezoids. Consequently, it cannot be used to construct compatible shape functions for general quadrilateral elements. To overcome this limitation, the shape functions are computed directly in the physical space using numerical integration. N\'ed\'elec shape functions of the first kind are used to construct the interpolation of the displacement gradient. We also introduce a new class of shape functions for the stress tensor that is compatible with the displacement and displacement-gradient discretizations. The formulation for compressible elasticity follows the framework previously developed for first- and second-order simplicial CSMFEs, whereas a new formulation is proposed for incompressible elasticity. The incompressible formulation employs element-level condensation of the pressure field and therefore does not increase the number of global degrees of freedom relative to the corresponding compressible formulation. These developments extend the compatible-strain mixed finite element framework from simplicial to general quadrilateral meshes for both compressible and incompressible nonlinear elasticity. Numerical examples demonstrate that the proposed quadrilateral elements can successfully solve…
subject: Preprints
  topic: section
creator: Mohsen Jahanshahi
creator: Damiano Pasini
creator: Arash Yavari
rights: Copyright (c) 2026 MechanicsArXiv
date: 2026-06-18
publication date: 2026-06-18

Interpenetrating Gyroid Lattice - Foam Composites with Synergistically Enhanced Stiffness and Energy Absorption for Impact Mitigation
type: item
description: Advanced lightweight structural materials require both high stiffness and energy-absorption capacity for demanding protective applications. Low-density polymer foams offer excellent specific energy absorption but have inadequate stiffness and structural stability for load-bearing applications. Stiff structural materials, on the other hand, provide load-bearing capacity at the expense of deformability and energy absorption capacity. Here, we overcome this trade-off by creating lattice–foam interpenetrating phase composites (IPCs) via in-situ foaming that integrate stochastic polymeric foam with elastomeric gyroid lattices featuring robust interfacial integration and precisely controlled architecture and density profile. This hybrid design couples the high specific energy absorption of foam with the tunable stiffness and structural integrity of architected lattices, leading to synergistically improved mechanical performance that neither standalone constituent achieves. Introducing a density gradient to IPC enables spatially programmed deformation and gradient-governed load transfer. Under impact loading, the IPCs exhibit dynamic synergy beyond the response of each individual component, markedly reducing transmitted peak stress and acceleration while simultaneously increasing energy absorption at low strain levels. The gyroid lattice–foam IPCs offer a versatile strategy for designing lightweight structural materials that integrate load-bearing capacity with impact-mitigation capability.
subject: Preprints
  topic: section
creator: Jizhe Cai
creator: Bhanugoban Maheswaran
creator: Emmanuel Dada
creator: Hridyesh Tewani
creator: Pavana Prabhakar
creator: Ramathasan Thevamaran
rights: Copyright (c) 2026 MechanicsArXiv
date: 2026-06-16
publication date: 2026-06-16

Why is the strength of an elastomeric polymer network so low?
type: item
description: Experiments have long shown that a polymer network of covalent bonds commonly ruptures at a stress that is orders of magnitude lower than the strength of the covalent bonds. Here we investigate this large reduction in strength by coarse-grained molecular dynamics simulations. We show that the network ruptures by sequentially breaking only a small fraction of bonds, and that each broken bond lies on a path belonging to the left-tail of the “shortest paths” distribution. A shortest path is the path of the fewest bonds that connect two monomers at the opposite ends of the network. As the network is stretched, the strands along these left-tail shortest paths straighten and bear high tension set by covalent bonds, while most strands off these paths deform via entropic elasticity. After a bond on one of the left-tail shortest paths breaks, the load shifts to other left-tail shortest paths and the process repeats. As the network is stretched and bonds are broken, the scatter in lengths of the shortest paths first narrows, causing stress to rise, and then broadens, causing stress to decline. This sequential breaking of a small fraction of bonds causes the network to rupture at a stress that is orders of magnitude below the strength of the covalent bonds.
subject: Preprints
  topic: section
creator: Shaswat Mohanty
creator: Zhigang Suo
creator: Jose Blanchet
creator: Wei Cai
rights: Copyright (c) 2026 MechanicsArXiv
date: 2026-06-18
publication date: 2026-06-18

Inward buckling of spiral layered structures subject to volumetric expansion and external constraint
type: item
description: Spiral layered structures subjected to thermal or diffusion-induced expansion often develop inward collapse, yet predictive models that connect geometry, confinement, and contact remain limited. Here we formulate a planar beam-based theory for an Archimedean spiral confined by a rigid circular ring, in which eigenstrain is converted into compressive circumferential resultants through kinematic constraint and unilateral contact. Using a variational framework, we derive spiral-path Föppl–von Kármán–type governing equations including a one-sided Winkler penalty representation of wall contact. A Rayleigh–Ritz energy estimate is then used to obtain closed-form scaling relations for the onset of instability. As an analytical benchmark, we reduce the spiral to the zero-pitch limit and recover a circular ring model, yielding mode-dependent critical compressive resultants for detached and fully contacting pre-buckling states. Complementary Dynamic/Explicit finite-element simulations under prescribed thermal expansion validate the theory and provide robust onset identification via internal-energy release, kinetic-energy bursts, and Fourier-mode growth. Finally, we study physically realistic multi-turn spirals, where turn-to-turn self-contact produces intrinsic kinematic locking without artificial end constraints, and we nondimensionalize the parameter space using the inner radius as the reference length to characterize the response in terms of thickness and turn number. The results establish a unified eigenstrain-to-compression mechanism for inward buckling, quantify the roles of confinement and contact state, and provide dimensionless design trends for layered spiral structures.
subject: Preprints
  topic: section
subject: Archimedean spirals
  topic: keywords
subject: layered structures
  topic: keywords
subject: volumetric expansion
  topic: keywords
subject: Rayleigh--Ritz method
  topic: keywords
subject: buckling instability
  topic: keywords
creator: Xinran Shi
creator: Juner Zhu
rights: Copyright (c) 2026 MechanicsArXiv
date: 2026-06-15
publication date: 2026-06-15

Crack-Parallel Tension Effects on Fracture of Soft Knitted Polymer Composites deduced from Gap Tests via Microplane Triads
type: item
description: Soft composites are increasingly used in wearable and soft robotic systems as advances in material architecture enable greater damage tolerance under large deformation. In these mesoscale architectures, the crack-parallel stresses bias geometric rearrangements of reinforcement fibers, modifying the crack initiation and growth beyond the opening-mode fracture. Here, we introduce a tensile gap test to quantify how the crack-parallel stress affects the onset and trajectory of damage localization, as well as the load- and energy-based fracture responses. We also develop and experimentally validate a continuum model that captures nonlinear behavior and progressive damage of knitted composites, using an ensemble of oriented microplane triads aligned with the yarn direction, capturing the axial load-transfer mechanisms while incorporating the transverse and shear effects. Together, the experiments and the computational model provide a tool to predict fracture under realistic stress states and to guide the rational design of soft composites in engineering applications.
subject: Preprints
  topic: section
subject: fracture and damage
  topic: keywords
subject: large strain
  topic: keywords
subject: knitted fiber composites
  topic: keywords
subject: silicone elastomers
  topic: keywords
subject: microplane triad model
  topic: keywords
subject: finite element analysis
  topic: keywords
creator: Xiaoxiao Ding
creator: Yanzhao Niu
creator: Yang Zhao
creator: Hongshun Chen
creator: Chanhyeong Bae
creator: Anh T. Nguyen
creator: Horacio D. Espinosa
creator: Zdeněk P. Bažant
creator: Jian Cao
rights: Copyright (c) 2026 MechanicsArXiv
date: 2026-06-12
publication date: 2026-06-12

A closed-form correction for three-point bend testing of functionally graded beams, with application to endovascular devices
type: item
description: Three-point bend testing offers simple, non-destructive quantification of the flexural rigidity of a slender structure, but the single apparent stiffness that it returns misrepresents the true local properties if flexural rigidity varies along the span. The error can be severe in structures with deliberately engineered stiffness gradients, such as endovascular catheters and guidewires whose graded transition zones govern clinical performance, and which are thus the regions most in need of accurate characterization. We solve the Euler-Bernoulli bending of a linearly graded beam in closed form and show that the true midspan rigidity exceeds the apparent value by a correction factor with the compact expansion W = 1 + m2/10 + O(m4), where m is the dimensionless change in stiffness across the support span. The leading measurement error term therefore grows quadratically with the local gradient. To recover m from discrete, noisy data we estimate the local gradient by windowed linear regression with optional Gaussian pre-smoothing, and identify the sampling and smoothing needed for stable inversion. On synthetic profiles spanning the gradient range of real devices, the correction reduces transition-zone error from as much as 10% to a fraction of a percent; applied to a commercial graded long sheath it removes a systematic transition-zone bias of order 1%. We further distinguish where the correction helps and where standard three-point testing already suffices, yielding a simple decision rule for the recovery of local properties from bending of any functionally graded beam.
subject: Preprints
  topic: section
creator: Charles Suskin
creator: Juan Becerra-García
creator: Yosef Granillo
creator: Michael Qiu
creator: Yuxuan Huang
creator: Mohamed Zayed
creator: Joshua Osbun
creator: Guy Genin
rights: Copyright (c) 2026 MechanicsArXiv
date: 2026-06-12
publication date: 2026-06-12

Nonlinear Anisotropic Visco-Anelasticity
type: item
description: We formulate a nonlinear geometric theory of visco-anelasticity that unifies viscoelastic and anelastic responses within a single thermodynamic framework. At each material point, the total deformation gradient is multiplicatively decomposed into elastic, viscous, and anelastic distortions, thereby generalizing the Bilby-Kr\"oner-Lee decomposition to visco-anelasticity. The theory explicitly incorporates the material metric, which encodes the evolving natural configuration of the solid, the transformed structural tensors, and provides a consistent formulation of the constitutive equations, the balance laws, the thermodynamic potentials, and the kinetic equations. The first and second laws of thermodynamics are systematically applied to derive the constitutive and evolution equations without invoking observer invariance. Anisotropy is treated in full generality through structural tensors. As illustrative examples, we specialize the general framework to isotropic and transversely isotropic visco-anelastic solids. Two examples within the class of universal deformations, which admit closed or partially closed form solutions, show how the proposed framework can be used to model the coupled viscous and anelastic response of incompressible anisotropic solids with distributed eigenstrains and the associated residual stresses. This geometric framework unifies nonlinear viscoelasticity and anelasticity by coupling time-dependent and eigenstrain-driven effects within a single, fully consistent geometric formulation. In particular, the proposed framework clarifies the geometric structure of the elastic, viscous, and anelastic distortions and resolves ambiguities associated with intermediate configurations in existing formulations of nonlinear viscoelasticity and viscoplasticity.
subject: Preprints
  topic: section
creator: Souhayl Sadik
creator: Arash Yavari
rights: Copyright (c) 2026 MechanicsArXiv
date: 2026-06-10
publication date: 2026-06-10

Harnessing Functional Gradients for Enhanced Shock Absorption in Foam Materials
type: item
description: Shock generating high-velocity impacts produce intense, stress waves and rapid accelerations—unlike low-velocity impacts that deform materials under dynamic equilibrium—posing severe risks to human organs, structures, and sensitive equipment. Functionally graded protective foams are promising candidates for shock mitigation due to their spatially tunable density and constitutive profile. However, limited mechanistic understanding of energy absorption and stress attenuation during compaction shock formation in graded foams may hinder their application-specific design. Here, in an integrated experimental and theoretical study, we investigate the compaction shock characteristics of graded foams using intrinsically graded vertically aligned carbon nanotube (VACNT) foams as a model system. Our analysis shows that while energy absorption is governed by compaction shock evolution from impact to the protected boundary, transmitted dynamic stress is primarily dictated by local material impedance. Using our generalizable shock modeling framework applicable to diverse functionally graded foam types, we demonstrate how density and density-dependent constitutive gradation dictate compaction shock characteristics. By selecting appropriate foam types and tailoring functional gradients, simultaneous optimization of energy absorption and transmitted stress attenuation can be achieved, facilitating designs for application-specific shock-mitigation.
subject: Preprints
  topic: section
subject: Functionally graded materials
  topic: keywords
subject: Dynamic compression
  topic: keywords
subject: Shock mitigation
  topic: keywords
subject: Carbon nanotube foams
  topic: keywords
subject: Shock model
  topic: keywords
creator: Bhanugoban Maheswaran
creator: Komal Chawla
creator: Ramathasan Thevamaran
rights: Copyright (c) 2026 MechanicsArXiv
date: 2026-06-09
publication date: 2026-06-09

Analysis of Stress Wave Interaction with a 180° Bend Junction Between Two Square Bars
type: item
description: An analytical model for wave propagation through an unrestrained 180° bend junction connecting two long bars of rectangular cross-section is developed and the results are validated using experimental and numerical analyses. Upon arrival of a longitudinal stress wave, the bend junction is assumed to undergo rigid translation followed by rotation. By analyzing the normal and shear forces as well as the bending moments acting at the intersection of the bend junction, a set of 15 equations consisting of fifteen variables has been derived. Solving the system of equations in Laplace domain leads to transfer functions that relate the incident pulse to reflected and transmitted wave characteristics, as well as to the translation and rotation of the bend junction. These results in Laplace domain are converted back to time domain using the convolution integral. Concurrently, finite element analysis and experimental validation of the bend junction behavior were carried out to verify the results obtained from the analytical model. In addition to revealing the influence of individual parameters explicitly, the model revealed that the efficiency of the unrestrained bend junction for transmission of the longitudinal waves is at most ∼70% for a long duration stress pulse. This limitation is a result of the rotation of the bend junction which emanates flexural waves into both the bars. Thus, further increase in transmission efficiency of longitudinal wave is possible if the bend junction is restrained to move only in the axial direction with no rotation.
subject: Preprints
  topic: section
subject: wave mechanics
  topic: keywords
subject: wave propagation
  topic: keywords
subject: waveguide
  topic: keywords
subject: transfer function
  topic: keywords
subject: DIC
  topic: keywords
creator: Salil Bavdekar
creator: Joaquin Garcia
creator: Amith Cheenady
creator: Andres Bernardo
creator: Ghatu Subhash
rights: Copyright (c) 2026 MechanicsArXiv
date: 2026-06-09
publication date: 2026-06-09

Universal deformations and universal residual stresses in incompressible isotropic Cauchy elasticity
type: item
description: We study universal deformations in incompressible isotropic Cauchy elastic solids with residual stress, without assuming any specific origin for the residual stress. Starting from the constitutive representation of the Cauchy stress as an isotropic tensor-valued function of strain and residual stress, we derive the universality constraints for residually-stressed incompressible isotropic Cauchy elastic solids. We show that for the six known families of universal deformations the set of universal deformations is identical to that of incompressible isotropic elasticity in the absence of residual stress. We also show that residual stress does not enlarge the space of universal deformations. We then determine the universal residual stress fields corresponding to the six known families of universal deformations. Assuming that the residual stress field has the same symmetry as the corresponding universal deformation, the universality constraints reduce to systems of ordinary differential equations that can be solved explicitly. The resulting universal residual stress fields are characterized and discussed for each family.
subject: Preprints
  topic: section
creator: Arash Yavari
rights: Copyright (c) 2026 MechanicsArXiv
date: 2026-06-05
publication date: 2026-06-05

On the stability of Euler’s elastica with natural curvature: Out-of-plane bifurcation with twisting
type: item
description: Elastic rods can exhibit distinct buckling behavior in the presence of natural curvature due to the induced prestress. Recent work has shown that prestressed, clamped rods can undergo a secondary bifurcation from in-plane Euler buckling and subsequently exhibit twisting or snapping under axial compression. In this work, a bifurcation analysis for the secondary out-of-plane bifurcation of Euler’s elastica is performed based on Kirchhoff’s three-dimensional theory of inextensional rods. The critical end-shortening, critical load, and associated eigenmode at the onset of bifurcation are determined, and the role of natural curvature in the out-of-plane bifurcation from the Euler solution is systematically examined. It is found that the effect of natural curvature depends on the bending direction of Euler buckling. When the Euler buckling direction is consistent with the rod’s naturally curved direction, the critical end-shortening decreases as the natural curvature increases, and vice versa. The imperfection sensitivity of the out-of-plane bifurcation is further investigated. The results reveal that the primary role of in-plane imperfections is to select the in-plane Euler buckling direction, which in turn has a major effect in the presence of substantial natural curvature. By contrast, the primary role of out-of-plane imperfections is to trigger the out-of-plane bifurcation and induce three-dimensional twisting or snapping.
subject: Preprints
  topic: section
subject: The elastica; Euler buckling; Out-of-plane bifurcation; Natural curvature; Imperfection
  topic: keywords
creator: Lu Lu
creator: Sophie Leanza
creator: Ruike Renee Zhao
creator: John Hutchinson
rights: Copyright (c) 2026 MechanicsArXiv
date: 2026-06-04
publication date: 2026-06-04

Sequential prediction of transverse crack paths in CFRP composites via a deep learning approach
type: item
description: Transverse cracking is one of the earliest damage modes in carbon fiber-reinforced polymer (CFRP) composites under transverse or complex loading, leading to stiffness degradation and reduced fatigue life. Its initiation and early propagation occur at the microscale and are strongly influenced by random fiber distributions and local streconcentrations. However, transverse crack propagation cannot be fully characterized within a single microstructural window, owing to the combined effects of the local fiber arrangement and crack state inheritance from the preceding region. To address this challenge, a physics guided deep learning framework is developed for sequential prediction of transverse crack paths in CFRP composites. Specifically, the framework directly predicts crack paths from microstructural images and incorporates the predicted crack segment as the initial crack information for the subsequent prediction window, thereby enabling sequential prediction across neighboring regions. An attention enhanced encoder decoder network is employed to capture multiscale features of crack evolution, while physical guidance derived from phase-field fracture analysis is incorporated to improve the consistency of the predicted paths. Compared with phase-field model results, the proposed framework accurately reconstructs transverse crack paths in extended microstructural regions with a prediction accuracy of 93.8%. This study provides an efficient surrogate model for sequential transverse crack path prediction and multiscale damage analysis of CFRP composites.
subject: Preprints
  topic: section
subject: deeplearning, composites, crack propogation
  topic: keywords
creator: Xin Yan
rights: Copyright (c) 2026 MechanicsArXiv
date: 2026-05-28
publication date: 2026-05-28

In-Plane Wave Homogenization and the Emergent Electromomentum Tensor
type: item
description: The electromomentum coupling is a macroscopic interaction between momentum density and electric field in piezoelectric composites, absent from the response of their constituents. Existing works have focused mainly on its analysis scalar mechanical settings. Here, we develop and apply homogenization scheme for the vectorial settings of in-plane motions of periodic composites, where two wave polarizations coexist. The method defines macroscopic fields by ensemble averaging and uses driving sources to obtain a unique effective model for arbitrary frequency and wavevector excitations. Numerical examples for composites with circular and circular-sector fibers show that the homogenized model recovers the Bloch dispersion of the underlying microstructure while satisfying physical restrictions, whereas equivalent models that suppress electromomentum coupling may violate these restrictions. The structure of the effective properties distinguishes mesoscale effects, present even for axisymmetric cells at finite wavelengths, from symmetry-breaking contributions that persist in the local response of asymmetric cells. Time-domain scattering simulations further demonstrate that the local effective medium reproduces the macroscopic reflected and transmitted response of the underlying composite for the excitations considered. These results advance the modeling and analysis of electromomentum metamaterials, towards their integration in future wave-control applications.
subject: Preprints
  topic: section
subject: Dynamic homogenization
  topic: keywords
subject: Willis coupling
  topic: keywords
subject: Electromomentum coupling
  topic: keywords
subject: Composites
  topic: keywords
subject: metamaterials
  topic: keywords
subject: Piezoelectricity
  topic: keywords
subject: Bloch Waves
  topic: keywords
creator: Paramveer Sharma
creator: Gal Shmuel
rights: Copyright (c) 2026 MechanicsArXiv
date: 2026-05-28
publication date: 2026-05-28

Nonlinear dynamics of miniaturized dielectric elastomer actuators with surface effects
type: item
description: Dielectric elastomer actuators (DEAs) have attracted considerable attention for applications requiring lightweight, compliant, and large-strain electromechanical transduction. However, the reduction of operating voltage through miniaturization introduces pronounced surface and interfacial effects that can significantly alter the dynamic response and stability characteristics of these systems. In this work, a dynamic electromechanical framework is developed to investigate the nonlinear dynamics of miniaturized dielectric elastomer actuators while explicitly incorporating surface elasticity, intrinsic surface energy, and surface tension. The dielectric elastomer is modeled as an incompressible neo-Hookean ideal dielectric, and the governing nonlinear equation of motion is derived using an Euler-Lagrange formulation under finite deformation. An energy-based approach is further employed to predict the onset of dynamic pull-in instability and the associated critical conditions. The dynamic response under both DC and AC voltage excitations is examined through transient time-history analysis, phase portraits, Poincaré maps, and frequency-response characteristics. Particular attention is devoted to dynamic pull-in instability and its dependence on surface parameters. The predictions of critical instability parameters are verified through direct numerical integration of the nonlinear governing equation, showing close agreement. A comprehensive parametric study reveals how surface elasticity, intrinsic surface energy, and surface tension modify the effective stiffness, resonance behavior, and critical instability thresholds of miniaturized DEAs. The results demonstrate that surface effects substantially shift dynamic pull-in voltages and alter nonlinear oscillatory characteristics, highlighting their critical role in the design and development of miniaturized dielectric elastomer actuators operating under transient electromechanical loading.
subject: Preprints
  topic: section
creator: Akhil Pratap Singh
creator: Gal Shmuel
creator: ATUL KUMAR SHARMA
rights: Copyright (c) 2026 MechanicsArXiv
date: 2026-05-28
publication date: 2026-05-28

A Unified Stiffness Evolution Model and Its Application to 3D-Printed Regular and Re-Entrant Honeycombs
type: item
description: The evolution of the elastic modulus in cellular materials involves both post-yield stiffness degradation and densification-induced recovery, yet a unified theoretical framework to describe this non-monotonic behavior remains lacking. This study investigates the stiffness evolution and deformation mechanisms of regular hexagonal (HC) and re-entrant (NHC) honeycombs under quasi-static uniaxial compression. Specimens with varied wall thicknesses were fabricated using fused deposition modeling, and incremental loading–unloading tests were performed along two orthogonal in-plane directions. A stiffness evolution model was developed to describe the complete non-monotonic variation of the global modulus, incorporating a linear elastic pre-yield response within a modified rigid–plastic hardening framework. The model captures both stiffness degradation induced by localized collapse and subsequent recovery driven by structural compaction, outperforming conventional approaches that neglect modulus rebound. Pronounced anisotropy in modulus evolution is observed, governed by direction-dependent collapse mechanisms. Bending-dominated deformation in the 1-direction leads to progressive compaction and earlier stiffness recovery as wall thickness increases. In contrast, fracture-dominated crushing in the 2-direction delays the modulus rebound in thicker specimens due to enhanced structural strength and toughness. These results reveal that wall thickness not only scales the stiffness magnitude but also modulates its evolution path: thicker walls accelerate compaction in bending-dominated modes while delaying it in fracture-dominated modes. The proposed framework provides a robust theoretical foundation for the optimized design of honeycombs and offers predictive insights into the interplay between geometry, thickness, and performance evolution in architected materials.
subject: Preprints
  topic: section
subject: 3D printing
  topic: keywords
subject: Honeycomb structure
  topic: keywords
subject: Stiffness evolution
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subject: Incremental cyclic compression
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subject: Anisotropy
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subject: Collapse mechanism
  topic: keywords
creator: Shaohua Wang
rights: Copyright (c) 2026 MechanicsArXiv
date: 2026-05-24
publication date: 2026-05-24

Universal Displacements in Linear Strain-Gradient Elasticity
type: item
description: We study universal displacement fields in three-dimensional linear strain-gradient elasticity within the Toupin-Mindlin first strain-gradient theory. Building on the approach of Yavari (2020), we derive, for each material symmetry class, the universality PDEs obtained by requiring the equilibrium equations (in the absence of body forces) to hold for any material in that class, and we determine the complete set of universal displacements. Using the full symmetry classification together with compact matrix representations of the elasticity tensors, we provide explicit characterizations for all 48 strain-gradient symmetry classes, including centrosymmetric and chiral classes. For several high-symmetry classes, the strain-gradient universality PDEs impose no additional restrictions beyond the classical ones, so the universal displacement families coincide with those of classical linear elasticity (for example, the isotropic classes SO(3) and O(3)). For lower symmetry classes, the strain-gradient universality PDEs can be stricter than their classical counterparts, so the universal displacements form proper subsets of the classical universal displacement families due to additional higher-order differential conditions.
subject: Preprints
  topic: section
creator: Dimitris Sfyris
creator: Arash Yavari
rights: Copyright (c) 2026 MechanicsArXiv
date: 2026-05-23
publication date: 2026-05-23

Finite Element Investigation of Optimal Reinforced Concrete Shear Wall Placement for Vibration Mitigation in Adjacent Buildings with Open-Trench Isolation
type: item
description: Vibration transmission in coupled soil--structure systems remains a fundamental challenge in the serviceability and resilience assessment of reinforced concrete (RC) buildings subjected to external dynamic excitations. Among the various sources of ground-borne vibration, railway-induced excitation constitutes a particularly significant engineering concern due to the continuing expansion of urban rail transportation networks and the increasing proximity of buildings to railway infrastructure. Motivated by this practical problem, the present study investigates the combined effectiveness of open-trench wave barriers and optimized shear wall placement for vibration mitigation in RC buildings subjected to railway-generated ground motion. A two-dimensional plane-strain finite element framework was developed in ABAQUS to simulate the fully coupled soil--track--structure interaction problem. The computational model consists of a six-story RC frame structure founded on layered soil, a railway embankment subjected to dynamic excitation, and a 3~m-deep open trench positioned between the vibration source and the structure. To examine the influence of stiffness redistribution on structural vibration characteristics, four structural configurations were considered, including a reference model without a shear wall and three additional cases incorporating a 0.30~m-thick RC shear wall located in the first, second, and third structural spans, respectively. The numerical framework was verified against established benchmark studies for ground-borne wave propagation and dynamic soil--structure interaction. Structural vibration response was evaluated at multiple roof-level monitoring locations using peak particle velocity (PPV), root mean square velocity (RMS), and vibration decibel level (VdB). The results demonstrate that the open trench effectively attenuates incident wave energy before interaction with the structure, while the incorporation of strategically positioned shear walls furt…
subject: Preprints
  topic: section
creator: Mohammad Torabi Yazdi
creator: Mohsen Farsiani
rights: Copyright (c) 2026 MechanicsArXiv
date: 2026-05-21
publication date: 2026-05-21

Inverse Design of Metamaterials with Adaptable Force-Displacement Characteristics
type: item
description: Metamaterials with tailored force-displacement characteristics hold significant promise for applications ranging from soft robotics and energy dissipation to biomedical devices such as prosthetic sockets, where distinct regions of a structure must simultaneously satisfy fundamentally different mechanical requirements. Existing inverse design frameworks, however, are restricted to single loading conditions and homogeneous desired behaviors, limiting their utility in real-world scenarios where complex, spatially varying mechanical demands must be met within a single continuous material. We present an inverse design method that closes this gap by combining finite element simulation, surrogate optimization, and machine learning within a unified framework. Starting from a fixed unit cell topology governed by eleven geometric shape parameters, we first construct a surrogate model that replaces each unit cell with a polynomial energy density, reducing the metamaterial-scale inverse problem to a tractable optimization over polynomial coefficients. A multi-output multilayer perceptron trained on finite element simulations then maps any required unit cell force-displacement response back to the corresponding shape parameters. We extend the formulation to multi-surface loading, enabling two qualitatively distinct force-displacement targets to be achieved simultaneously in different regions of the same structure. Fabricated prototypes tested under prescribed displacements confirm that the predicted responses, spanning superelastic, bistable, and constant-force behaviors, are reproduced with high fidelity. These results demonstrate a flexible and computationally efficient route to multifunctional metamaterial design under realistic, multi-condition loading environments.
subject: Preprints
  topic: section
subject: mechanics
  topic: keywords
subject: metamaterials
  topic: keywords
subject: mechanical metamaterials
  topic: keywords
subject: inverse design
  topic: keywords
creator: Hatice Gokcen Guner
creator: Kaushik Dayal
creator: Alexandra Ion
rights: Copyright (c) 2026 MechanicsArXiv
date: 2026-05-21
publication date: 2026-05-21

Phase-field model for mesoscale simulation of crystallization morphology evolution in 3D printing of thermoplastic composite
type: item
description: 3D printing has enabled the production of continuous fiber-reinforced thermoplastic composites (CFRTPCs) with exceptional mechanical properties and design flexibility. The crystalline morphological evolution during 3D printing of CFRTPCs, particularly the transcrystalline layer (TCL) that is critical for the mechanical performance, remains poorly modeled and understood. Herein, we develop a non-isothermal phase-field model (PFM) for mesoscale simulating the crystallization process and morphology evolution during the 3D printing of thermoplastic composites.The PFM is derived by constructing a free energy density functional incorporating order parameters to characterize the crystallization process, with the phase-field evolution equations being intrinsically coupled to heat transfer. In particular, the fiber-crystalline melt contact angle-dependent sporadic nucleation processes are integrated into the PFM using an explicit nucleation algorithm. Phase-field simulations of crystallization behavior in isotactic polypropylene (iPP) under conditions emulating 3D printing are demonstrated to verify the PFM capability. The influence of contact angle (θ), convective coefficient (h), and fiber spacing (D) on non-isothermal crystallization is comprehensively examined. It is found that TCL thickness increases with decreasing θ, smaller h, and larger D, until it reaches saturation. Slower cooling during 3D printing could significantly amplify the effects of both contact angle and fiber spacing on the TCL evolution. The proposed PFM could enable mesoscale simulation of 3D-printed thermoplastics and help optimization of crystallization and printing parameters.
subject: Preprints
  topic: section
creator: Xin Yan
rights: Copyright (c) 2026 MechanicsArXiv
date: 2026-05-20
publication date: 2026-05-20

Compatibility Conditions for Singular Strain Fields on Linear Shells
type: item
description: Strain compatibility conditions are derived for orientable linear shells with strain fields which are piecewise smooth and develop concentrations along curves and junctions on the shell surface. The concentrations in strain fields appear due to folds, fold dipoles, and tears in the shell. The compatibility equations include local conditions in the bulk of the shell surface, local equations at the singular curves in terms of jump in strain fields (and their gradients) and strain concentrations, local equations at the junction of singular curves, and global conditions for every family of irreducible curves on the shell surface. These equations couple shell kinematics with the geometry and topology of the shell surface. The applicability of the framework is illustrated assuming the bulk strains to be elastic and the strain concentrations to be plastic. The compatibility equations then lead to a boundary value problem for the determination of stresses and moments in an elastic surface in response to the incompatibility induced by the plastic strains.
subject: Preprints
  topic: section
creator: Animesh Pandey
creator: Anurag Gupta
rights: Copyright (c) 2026 MechanicsArXiv
date: 2026-05-19
publication date: 2026-05-19

Competitive Hardening Dynamics in Viscoplastic Materials with Evolving Threshold Stress
type: item
description: Conventional viscoplasticity frameworks treat the threshold stress as either a material constant or a quantity evolving solely with accumulated plastic strain. Since microstructural evolution — whether precipitation, phase transformation, or solute redistribution — may proceed concurrently with deformation, such a treatment is often inadequate. The present work formulates a constitutive framework, derived from the Clausius–Duhem inequality and Perzyna-type overstress viscoplasticity, in which the threshold stress evolves autonomously with physical time through microstructural kinetics, independently of accumulated strain. Modified Armstrong–Frederick kinematic hardening with static recovery is incorporated, so that back stress develops only during active inelastic flow. The interaction between time-driven threshold evolution and strain-driven back-stress development gives rise to three behavioural regimes: (I) a purely elastic response, (II) flow arrest, in which inelastic flow initiates but subsequently ceases as the threshold overtakes the effective stress, and (III) continuous flow. A constructive Lyapunov function is employed to prove that flow arrest is asymptotically stable, a result not previously established at the material-point level in the viscoplastic creep literature. It is further shown that back-stress development reduces the time to arrest through a kinematic hardening acceleration effect. A physics-informed neural network employing smooth Macaulay bracket approximation with curriculum learning reproduces all three regimes within a single trained surrogate. The framework is validated against experimental data using the creep-ageing and back-stress test (CABT), which provides independent measurements of inelastic strain and back-stress evolution.
subject: Preprints
  topic: section
creator: Yo-Lun Yang
rights: Copyright (c) 2026 MechanicsArXiv
date: 2026-06-07
publication date: 2026-06-07

Thermoviscoelasticity of polydomain liquid crystal elastomers regulated by soft elasticity
type: item
description: Liquid crystal elastomers (LCEs) are elastomeric networks with rod-like mesogens that reorient under load. In polydomain LCEs, this reorientation drives a polydomain-to-monodomain transition that produces a soft-elastic plateau. The intricate coupling between this soft elasticity and the polymer-network viscoelasticity gives rise to a path-dependent thermoviscoelastic response, central to applications of polydomain LCEs in damping, impact protection, and tough adhesives. However, the physics governing this response under complex thermomechanical histories remains insufficiently studied. In this work, we present a combined experimental and theoretical study of polydomain LCEs under three uniaxial loading protocols: single-cycle loading-unloading, stress-free recovery from various pre-stretches, and multi-cycle loading with progressively increasing amplitude. We develop a finite-deformation constitutive model that combines two parallel mechanisms: rate-independent, temperature-dependent soft elasticity from mesogen reorientation, and time- and temperature-dependent viscoelasticity from various sources. Calibrated with a single parameter set, the model quantitatively reproduces all three protocols and resolves the individual contribution of each mechanism. Across the three protocols, a temperature-dependent soft-elastic limit governs the low-rate response and the long-time recovered stretch, while polymer-network viscoelasticity controls the rate-dependent deviation and the cycle-wise accumulation of residual stretch away from this low-rate limit. A thermal recovery test above the nematic-isotropic transition temperature confirms that all hysteresis and residual deformation are reversible, ruling out irreversible internal damage. The combined experimental-theoretical framework provides mechanistic understanding and a predictive basis for the design of polydomain LCE components under complex thermomechanical histories.
subject: Preprints
  topic: section
creator: Ruobing Bai
rights: Copyright (c) 2026 MechanicsArXiv
date: 2026-05-12
publication date: 2026-05-12

Fractional Calculus based Elasticity obtained from Homogenization
type: item
description: Anomalous phenomena, such as diffusion in biological systems, scale-dependent plasticity in thin films, and electromagnetic wave propagation in complex media, often defy explanation by conventional theories rooted in integer-order calculus. Models based on fractional calculus have proven effective in capturing such behaviors, yet the fractional exponents they employ are typically introduced as empirical fitting parameters without grounding in the underlying physics. In this work, we propose that fractional differential equations can emerge naturally through homogenization of materials with complex microstructures, which are themselves the source of the anomalous behavior that necessitates a fractional description. Focusing on linear elasticity, we identify precise microstructural conditions that give rise to emergent fractional behavior. In the static regime, homogenization reveals that the order of the fractional derivative is directly linked to the power-law exponent of the microstructure’s autocovariance function. By connecting microscale structural variation to macroscale material response, our study opens new avenues for designing architectured materials with tailored anomalous properties. The implications of thiswork extend broadly across physics, biology, materials science, and beyond.
subject: Preprints
  topic: section
subject: fractional calculus
  topic: keywords
subject: homogenization
  topic: keywords
creator: Kshiteej Deshmukh
creator: Liping Liu
creator: Pradeep Sharma
rights: Copyright (c) 2026 MechanicsArXiv
date: 2026-05-11
publication date: 2026-05-11

Contact loss in all solid-state Li-ion batteries via deposition of impurities
type: item
description: Solid-state batteries promise high energy storage with enhanced safety but suffer from contact loss at the lithium (Li) metal anode-solid electrolyte interface as Li is stripped into the ionically conducting solid electrolyte. Our measurements demonstrate that, in cells with garnet electrolytes, an important but overlooked mechanism for contact loss arises from the deposition of insulating impurities from within the Li electrode onto the interface. These impurities form a porous layer, and an imposed stack pressure is required for Li to creep through this layer. Insufficient stack pressure results in empty pores between the impurity particles and these pores resemble inter-connected nano to micro-scale voids. This proposed mechanism is supported by our direct observations of the interface and by our finding that contact loss persists at stack pressures which are sufficiently high to collapse any voids in the Li that are not mechanically supported by the skeleton of impurity particles. Theoretical models developed using the impurity deposition mechanism are in excellent agreement with measurements. This finding has significant implications for improving the design of all solid-state batteries including the development of anode-free cells for which impurities within the electrode are expected to be substantially reduced.
subject: Preprints
  topic: section
subject: Lithium metal
  topic: keywords
subject: solid electrolyte
  topic: keywords
subject: contact loss
  topic: keywords
subject: impurities
  topic: keywords
subject: voids
  topic: keywords
creator: Sundeep Vema
creator: James Gott
creator: Hao Yin
creator: Ashley Roach
creator: Geoff West
creator: Norman Fleck
creator: Vikram Deshpande
creator: Clare Grey
rights: Copyright (c) 2026 MechanicsArXiv
date: 2026-05-08
publication date: 2026-05-08

Finite-width adiabatic shear banding and dislocation patterning in mesoscale polycrystalline aggregates
type: item
description: Dynamic shear banding under adiabatic conditions in a mesoscale polycrystalline aggregate is studied using a model of mesoscale dislocation mechanics and experiments. The model involves a length scale related to hardening induced by excess/polar/geometrically necessary dislocation (GND) density, and utilizes a simple classical crystal plasticity model with isotropic Voce law hardening. Simulations of statistically representative volume elements of a polycrystal determined from experimental samples are conducted. Studies in 2-d (section) and 3-d capture the experimentally observed finite-width shear bands and the formation of low-angle subgrain boundaries even in the absence of heat conduction in the model, as well as size-dependent strengthening for grain sizes from 1 to 20μm. The 2-d and large-scale 3-d simulations, the latter involving 1 million finite elements, provide access to the progressive evolution of material strength, stress state, and temperature in the course of large deformations. GND distributions accumulate at grain boundaries and form patterned structures within grain interiors, offering insight into the microstructural changes that precede failure in adiabatic shear bands. Mesh-converged, delocalized and localized plastic flow to very large deformations without softening is observed for a significant range of parameters, reflecting a competition between GND hardening and thermal softening in setting the non-softening steady state in the absence of other ductile damage mechanisms in the model.
subject: Preprints
  topic: section
creator: Siddharth Singh
creator: Rajat Arora
creator: Janith Wanni
creator: Charles Adkins
creator: Raymond Rasmussen
creator: Noah Schmelzer
creator: Dan Thoma
creator: Curt Bronkhorst
creator: Amit Acharya
rights: Copyright (c) 2026 MechanicsArXiv
date: 2026-05-08
publication date: 2026-05-08

Dynamic micromagnetism a la Ericksen-Leslie, and the constrained polar continuum mechanics of hard magnetic soft materials
type: item
description: A model of dissipative micromagnetics coupled to (visco-)elasticity is explored, following the procedures of the Ericksen-Leslie theory of nematic liquid crystals allowing for angular momentum due to magnetization. An outcome is the Landau-Lifshitz-Gilbert theory coupled to material spin. A further power-less augmentation to the angular momentum of the theory with classical kinetic energy density is also considered, with a preliminary exploration of its potential in representing the Einstein-de Haas and Barnett effects within continuum mechanics. A treatment of the continuum mechanics of hard magnetic soft materials as a constrained polar material is presented. The models of DeSimone and James (2002) and Zhao et al. (2019) are discussed as two different, namely energetically and kinematically, constrained models of magnetoelasticity encompassed within the overall framework.
subject: Preprints
  topic: section
creator: Amit Acharya
creator: Siladitya Pal
rights: Copyright (c) 2026 MechanicsArXiv
date: 2026-05-06
publication date: 2026-05-06