arXiv subjects

John D. Clayton

Publications and source records attributed to John D. Clayton.

11 recordsLinked to original sources

arXiv2026

Compressive Splitting in Brittle Solids: The Inverse of Wrinkling in Sheets

Axial splitting is the dominant failure mode of brittle solids under compression, yet its mechanical origin remains unclear. We show that clamped loading platens suppress lateral Poisson expansion, generating boundary-induced tensile stresses at the specimen interior -- the compressive analog of wrinkling in stretched sheets. This mechanism provides a predictive strength law, relating axial splitting to tensile strength, geometry, and confinement pressure. This is validated against diverse materials ranging from rocks to ceramics, establishing axial splitting as a geometry-controlled elastic process rather than a stochastic flaw problem.

cond-mat.mtrl-sci↗

arXiv2026

Stress Asymmetry in Hard Magnetic Soft Materials

Hard magnetic soft materials -- soft polymers embedded with hard magnetic particles -- are modeled using continuum magnetomechanical formulations in which the deformation and the magnetization field are the primary kinematic variables. A recent question in such formulations is whether the Cauchy stress is symmetric, which is directly related to frame invariance and angular momentum balance. This note discusses energetically equivalent formulations, related by a change of variables between referential and current descriptions of the magnetization, and shows that they generally yield different Cauchy stresses, including a change in their symmetry. Specifically, the formulation based on a referential magnetization produces a symmetric Cauchy stress, while that based on a current magnetization generally yields an asymmetric Cauchy stress. We highlight that when the internal variable (magnetization field) is at the energy-minimizing equilibrium configuration, the divergences of these stresses are the same, and both stresses are symmetric.

cond-mat.mtrl-sci↗

arXiv2026

Constitutive theory for mechanics of amorphous thermoplastic polymers under extreme dynamic loading

A geometrically nonlinear continuum mechanical theory is formulated for deformation and failure behaviors of amorphous polymers. The model seeks to capture material response over a range of loading rates, temperatures, and stress states encompassing shock compression, inelasticity, melting, decomposition, and spallation. Thermoelasticity, viscoelasticity, viscoplasticity, ductile failure with localized shear yielding, and brittle fracture with crazing can all emerge under this ensemble of intense loading conditions. Known prior theories have considered one or more, but not all, such physical mechanisms. The present coherent formulation invokes thermodynamics with internal state variables for dynamic molecular and network configurational changes affecting viscoelasticity and plastic deformation, and it uses order parameters for more abrupt structural changes across state-dependent glass-transition and shock-decomposition thresholds. A phase-field order parameter captures material degradation from ductile or brittle fracture, including evolving porosity from crazing. The theory is applied toward polymethyl methacrylate (PMMA) under intense dynamic loading. The high-pressure equilibrium response, with shear strength and temperature over known ranges, is well represented along the principal Hugoniot to pressures far exceeding shock decomposition. Predicted release wave velocities agree with experiment. A semi-analytical solution for steady waves describes the relatively lower-pressure viscoelastic setting, providing insight into relaxation times. One-dimensional calculations assess suitability of the model for representing spall fracture strengths seen in experiments over a range of initial temperatures and loading rates.

cond-mat.mtrl-sci↗

arXiv2025

Modeling dynamic impact, shock waves, and injury in liver tissue with a constrained mixture theory

A nonlinear continuum theory is advanced for high-rate mechanics and thermodynamics of liver parenchyma. The homogenized continuum is idealized as a solid-fluid mixture of dense viscoelastic tissue and liquid blood. The solid consists of a matrix material comprising the liver lobules and a collagenous fiber network. Under high loading rates pertinent to impact and blast, the velocity difference between solid and fluid is assumed negligible, leading to a constrained mixture theory. The model captures nonlinear isotropic elasticity, viscoelasticity, temperature changes from thermoelasticity and dissipation, and tissue damage, the latter via a scale-free phase-field representation. Effects of blood volume and initial constituent pressures are included. The model is implemented in 3-D finite element software. Analytical and numerical solutions for planar shock loading are compared with observations of liver trauma from shock-tube experiments. Finite-element simulations of dynamic impact are compared with cylinder drop-weight experiments. Model results, including matrix damage exceeding fiber damage at high rates and reduced mechanical stiffness with higher perfused blood volume, agree with experimental trends. Viscoelasticity is important at modest impact speeds.

cond-mat.soft↗

arXiv2025

Analytical shear-band process zone model incorporating nonlinear viscous effects and initial defects

Experimental, theoretical, and numerical studies of adiabatic shear in ductile metals suggest initial defects such as pores or material imperfections increase shear-band susceptibility. Conversely, viscous effects manifesting macroscopically as strain-rate sensitivity inhibit localization. The analytical shear-band process zone model due to D.E. Grady, in turn based on a rigid-plastic solution for stress release by N.F. Mott, is advanced to account for these phenomena. The material contains an average defect measure (e.g., porosity) and a concentrated defect measure at a spatial location where shear banding is most likely to initiate after an instability threshold is attained. Shearing resistance and certain physical properties are reduced commensurately with local defect concentration. Non-Newtonian viscosity increases dissipative resistance. Viscous dissipation, if strong enough, is shown to prevent an infinitesimal-width shear band even in a non-conductor. Here, a pseudo-quadratic viscosity widens the band similarly to heat conduction, and akin to quadratic shock viscosity often used to resolve widths of planar shock waves. The model captures simulation data showing reduced localization strain and shear band width with increasing maximum initial pore size in additively manufactured titanium and HY-100 steel. Predictions for shear band width, local strain, and temperature are more accurate versus data on steel than prior analytical modeling. A quantitative framework is established by which processing defects can be related to shear-banding characteristics.

cond-mat.mtrl-sci↗

arXiv2025

Analysis of adiabatic shear coupled to ductile fracture and melting in viscoplastic metals

Material failure by adiabatic shear is analyzed in viscoplastic metals that can demonstrate up to three distinct softening mechanisms: thermal softening, ductile fracture, and melting. An analytical framework is constructed for studying simple shear deformation with superposed static pressure. A continuum power-law viscoplastic formulation is coupled to a ductile damage model and a solid-liquid phase transition model in a thermodynamically consistent manner. Criteria for localization to a band of infinite shear strain are discussed. An analytical-numerical method for determining the critical average shear strain for localization and commensurate stress decay is devised. Averaged results for a high-strength steel agree reasonably well with experimental dynamic torsion data. Calculations probe possible effects of ductile fracture and melting on shear banding, and vice-versa, including influences of cohesive energy, equilibrium melting temperature, and initial defects. A threshold energy density for localization onset is positively correlated to critical strain and inversely correlated to initial defect severity. Tensile pressure accelerates damage softening and increases defect sensitivity, promoting shear failure. In the present steel, melting is precluded by ductile fracture for loading conditions and material properties within realistic protocols. If heat conduction, fracture, and damage softening are artificially suppressed, melting is confined to a narrow region in the core of the band.

cond-mat.mtrl-sci↗

arXiv2024

Nonlinear soft-tissue elasticity, remodeling, and degradation described by an extended Finsler geometry

A continuum mechanical theory incorporating an extension of Finsler geometry is formulated for fibrous soft solids. Especially if of biologic origin, such solids are nonlinear elastic with evolving microstructures. For example, elongated cells or collagen fibers can stretch and rotate independently of motions of their embedding matrix. Here, a director vector or internal state vector, not always of unit length, in generalized Finsler space relates to a physical mechanism, with possible preferred direction and intensity, in the microstructure. Classical Finsler geometry is extended to accommodate multiple director vectors (i.e., multiple fibers in both a differential-geometric and physical sense) at each point on the base manifold. A metric tensor can depend on the ensemble of director vector fields. Residual or remnant strains from biologic growth, remodeling, and degradation manifest as non-affine fiber and matrix stretches. These remnant stretch fields are quantified by internal state vectors and a corresponding, generally non-Euclidean, metric tensor. Euler-Lagrange equations derived from a variational principle yield equilibrium configurations satisfying balances of forces from elastic energy, remodeling and cohesive energies, and external chemical-biological interactions. Given certain assumptions, the model can reduce to a representation in Riemannian geometry. Residual stresses that emerge from a non-Euclidean material metric in the Riemannian setting are implicitly included in the Finslerian setting. The theory is used to study stress and damage in the ventricle (heart muscle) expanding or contracting under internal and external pressure. Remnant strains from remodeling can reduce stress concentrations and mitigate tissue damage under severe loading.

cond-mat.soft↗

arXiv2024

Generalized Finsler geometry and the anisotropic tearing of skin

A continuum mechanical theory with foundations in generalized Finsler geometry describes the complex anisotropic behavior of skin. A fiber bundle approach, encompassing total spaces with assigned linear and nonlinear connections, geometrically characterizes evolving configurations of a deformable body with microstructure. An internal state vector is introduced on each configuration, describing subscale physics. A generalized Finsler metric depends on position and the state vector, where the latter dependence allows for both direction (i.e., as in Finsler geometry) as well as magnitude. Equilibrium equations are derived using a variational method, extending concepts of finite-strain hyperelasticity coupled to phase-field mechanics to generalized Finsler space. For application to skin tearing, state vector components represent microscopic damage processes (e.g., fiber rearrangements and ruptures) in different directions with respect to intrinsic orientations (e.g., parallel or perpendicular to Langer's lines). Nonlinear potentials, motivated from soft-tissue mechanics and phase-field fracture theories, are assigned with orthotropic material symmetry pertinent to properties of skin. Governing equations are derived for one- and two-dimensional base manifolds. Analytical solutions capture experimental force-stretch data, toughness, and observations on evolving microstructure, in a more geometrically and physically descriptive way than prior phenomenological models.

cond-mat.soft↗

arXiv2024

Analysis of shear localization in viscoplastic solids with pressure-sensitive structural transformations

Localization, in the form of adiabatic shear, is analyzed in viscoplastic solids that may undergo structural transformation driven by pressure, shear stress, temperature, and magnetic field. As pertinent to polycrystalline metals, transformations may include solid-solid phase transitions, twinning, and dynamic recrystallization. A finite-strain constitutive framework for isotropic metals is used to solve a boundary value problem involving simple shearing with superposed hydrostatic pressure and constant external magnetic field. Three-dimensional theory is reduced to a formulation simple enough to facilitate approximate analytical solutions yet sophisticated enough to maintain the salient physics. Ranges of constitutive parameters (e.g., strain hardening, strain-rate sensitivity, thermal softening, and strain-driven structure transformation limits influenced by pressure and magnetic field) are obtained for which localization to infinite shear strain is possible. Motivated by experimental and theoretical studies suggesting a non-negligible role of shear on phase transformations in iron (Fe), the model is used to understand influences of pressure and phase transitions on applied strains for which localization should occur in pure Fe and a high-strength steel. Results show, among other trends for these two materials, that shear localization in conjunction with phase transformation is promoted when the transformed phase is softer than the parent phase. Localization that would occur in the isolated parent phase can be mitigated if the strain hardening or thermal softening tendencies of the transformed phase are sufficiently increased or reduced, respectively.

cond-mat.mtrl-sci↗

arXiv2024

A universal phase-field mixture representation of thermodynamics and shock wave mechanics in porous soft biologic continua

A continuum mixture theory is formulated for large deformations, thermal effects, phase interactions, and degradation of soft biologic tissues. Such tissues consist of one or more solid and fluid phases and can demonstrate nonlinear anisotropic elastic, viscoelastic, thermoelastic, and poroelastic physics. Under extremely large or rapid deformations, for example impact or shock loading, tissues may fracture, tear, or rupture. Mechanisms are encompassed in a universal, thermodynamically consistent formulation that combines the continuum theory of mixtures with phase-field mechanics of fracture. A metric tensor of generalized Finsler space supplies geometric insight on effects rearrangements of microstructure, for example degrading collagen fibers. Governing equations are derived, and energy potentials and kinetic laws posited, for generic soft porous tissues with solid and liquid or gas phases. Shock waves are modeled as singular surfaces; Hugoniot states and shock decay are studied analytically. Suitability of the framework for representing blood, skeletal muscle, and liver is demonstrated. Insight into physics presently unresolved by experiments is obtained.

cond-mat.soft↗

arXiv2020

Laplace Stretch: Eulerian and Lagrangian Formulations

Two triangular factorizations of the deformation gradient tensor are studied. The first, termed the Lagrangian formulation, consists of an upper-triangular stretch premultiplied by a rotation tensor. The second, termed the Eulerian formulation, consists of a lower-triangular stretch postmultiplied by a different rotation tensor. The corresponding stretch tensors are denoted as the Lagrangian and Eulerian Laplace stretches, respectively. Kinematics (with physical interpretations) and work conjugate stress measures are analyzed and compared for each formulation. While the Lagrangian formulation has been used in prior work for constitutive modeling of anisotropic and hyper\-elastic materials, the Eulerian formulation, which may be advantageous for modeling isotropic solids and fluids with no physically identifiable reference configuration, does not seem to have been used elsewhere in a continuum mechanical setting.

physics.class-ph↗