Related papers: Investigating elastic constants across diverse str…

Analytical method for the second-order homogenization of two-phase composites within Mindlin-Toupin strain gradient elasticity theory is proposed. Direct approach and self-consistent approximation are used to reduce the homogenization…

Using the density functional formalism we derive expression for the distortion free energy for systems with continuous broken symmetry and use it to derive expression for the elastic constants of smectic phases in which director is tilted…

We introduce models for viscoelastic materials, both solids and fluids, based on logarithmic stresses to capture the elastic contribution to the material response. The matrix logarithm allows to link the measures of strain, that naturally…

The multi-scale nature of architectured materials raises the need for advanced experimental methods suitable for the identification of their effective properties, especially when their size is finite and they undergo extreme deformations.…

Plastic deformation of micron-scale crystalline solids exhibits stress-strain curves with significant sample-to-sample variations. It is a pertinent question if this variability is purely random or to some extent predictable. Here we show,…

Spatial heterogeneity in the elastic properties of soft random solids is investigated via a two-pronged approach. First, a nonlocal phenomenological model for the elastic free energy is examined. This features a quenched random kernel,…

A system of partial differential equations (PDEs) is derived to compute the full-field stress from an observed kinematic field when the flow rule governing the plastic deformation is unknown. These equations generalize previously proposed…

The purpose of the present article is to make a model using analytical equations, based on elasticity theory of continuous media for small deformations, with the aim of completely characterizing the material in their mechanical properties…

The stress-strain curve of two-dimensional frictional dispersed grains interacting with a harmonic potential without considering the dynamical slip under a finite strain is determined by using eigenvalue analysis of the Hessian matrix.…

Colloidal magnetic particles embedded in an elastic polymer matrix constitute a smart material called ferrogel. It responds to an applied external magnetic field by changes in elastic properties, which can be exploited for various…

The classical Oseen-Frank theory of liquid crystal elasticity is based on the experimentally verified fact that there are three independent modes of distortion, each with its associated elastic constant. On the other hand, the arguably more…

Disordered network materials abound in both nature and synthetic situations while rigorous analysis of their nonlinear mechanical behaviors still is very challenging. The purpose of this paper is to connect the mathematical framework of…

Synchrotron Laue microdiffraction and Digital Image Correlation measurements were coupled to track the elastic strain field (or stress field) and the total strain field near a general grain boundary in a bent bicrystal. A 316L stainless…

This paper introduces a simple framework for accurately predicting the fatigue lifetime of notched components by employing various machine learning algorithms applied to a wide range of materials, loading conditions, notch geometries, and…

We propose a robust elastic net (REN) model for high-dimensional sparse regression and give its performance guarantees (both the statistical error bound and the optimization bound). A simple idea of trimming the inner product is applied to…

Randomly textured polycrystalline materials of constituents with highly anisotropic nature of grains can be considered globally isotropic. In order to determine the isotropic properties, like elasticity or conductivity, we propose a theory…

Liquid crystal elastomers are special cross-linked polymer materials combining the large elastic deformability of elastomers with the orientational orders of liquid crystals. This model exhibits markedly different phenomena than the liquid…

This work provides an efficient virtual element scheme for the modeling of nonlinear elastodynamics undergoing large deformations. The virtual element method (VEM) has been applied to various engineering problems such as elasto-plasticity,…

Hooke's law states that the forces or stresses experienced by an elastic object are proportional to the applied deformations or strains. The number of coefficients of proportionality between stress and strain, i.e., the elastic moduli, is…

We propose a framework to model elastic properties of polycrystals by coupling crystal orientational degrees of freedom with elastic strains. Our model encodes crystal symmetries and takes into account explicitly the strain compatibility…