Related papers: A Remark on stress of a spatially uniform dislocat…
We investigate the possibility of projecting low dimensional chaos from spatiotemporal dynamics of a model for a kind of plastic instability observed under constant strain rate deformation conditions. We first discuss the relationship…
We demonstrate that irreversible structural reorganization is not necessary for the observation of yield behaviour in an amorphous solid. While the majority of solids strained to their yield point do indeed undergo an irreversible…
In recent work, it was shown that elasticity theory can break down in amorphous solids subjected to nonuniform {\em static} loads. The elastic fields are screened by geometric dipoles; these stem from gradients of the quadrupole field…
We present a complete analytical solution for the stress field inside a homogeneous, inside a homogeneous, linearly elastic solid sphere subjected to a concentrated normal load applied on its surface. Starting from the three-dimensional…
A recently proposed generalised continuum theory of curved dislocations describes the spatial and temporal evolution of statistically stored and geometrically necessary dislocation densities as well as the curvature. The dynamics follow…
The foundation of continuum elasticity theory is based on two general principles: (i) the force felt by a small volume element from its surrounding acts only through its surface (the Cauchy principle, justified by the fact that interactions…
For a given class of materials, \emph{universal deformations} are those deformations that can be maintained in the absence of body forces and by applying solely boundary tractions. For inhomogeneous bodies, in addition to the universality…
The mechanical response of naturally abundant amorphous solids such as gels, jammed grains, and biological tissues are not described by the conventional paradigm of broken symmetry that defines crystalline elasticity. In contrast, the…
Amorphous solids display numerous universal features in their mechanics, structure, and response. Current models assume heterogeneity in mesoscale elastic properties, but require fine-tuning in order to quantitatively explain vibrational…
We present the foundations of a projective geometric theory of elasticity, as well as outline a few possible application possibilities. We give the description of the Cauchy stress and infinitesimal strain tensors compatible with coordinate…
A novel, concurrent multiscale approach to meso/macroscale plasticity is demonstrated. It utilizes a carefully designed coupling of a partial differential equation (pde) based theory of dislocation mediated crystal plasticity with…
Unlike classical elasticity, where stresses arise from deformations relative to a stress-free reference configuration, rigidity in amorphous systems is maintained by disordered force networks that generate internal prestress. Previously, we…
The equations of stress equilibrium and strain compatibility/incompatibility are discussed for fields with point singularities in a planar domain. The sufficiency (or insufficiency) of the smooth maps, obtained by restricting the singular…
This paper investigates the stress and displacement distribution in a two-dimensional elastic hollow disk subjected to distributed diametric loading, extending our previous analysis of concentrated loading [Okamura et al. Strength Mater.…
The distribution of internal shear stresses in a 2D dislocation system is investigated when external shear stress is applied. This problem serves as a natural continuation of the previous work of Csikor and Groma (Csikor F F and Groma I…
The transmission of stress is analysed for static periodic arrays of rigid grains, with perfect and zero friction. For minimal coordination number (which is sensitive to friction, sphericity and dimensionality), the stress distribution is…
Crystal plasticity theory is often employed to predict the mesoscopic states of polycrystalline metals, and is well-known to be costly to simulate. Using a neural network with convolutional layers encoding correlations in time and space, we…
The vertex model is widely used to simulate the mechanical properties of confluent epithelia and other multicellular tissues. This inherently discrete framework allows a Cauchy stress to be attributed to each cell, and its symmetric…
The present paper studies non-uniform plastic deformations of crystals undergoing anti-plane constrained shear. The asymptotically exact energy density of crystals containing a moderately large density of excess dislocations is found by the…
The similarity in mechanical properties of dense active matter and sheared amorphous solids has been noted in recent years without a rigorous examination of the underlying mechanism. We develop a mean-field model that predicts that their…