Related papers: First-principles calculation of higher-order elast…
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…
In this work the linear elastic properties of materials containing spherical voids are calculated and compared using finite element simulations. The focus is on homogeneous solid materials with spherical, empty voids of equal size. The…
A method for the calculation of elastic constants in the NVT ensamble, using molecular dynamics (MD) simulation with a realistic many-body embedded-atom-model (EAM) potential, is studied in detail. It is shown that in such NVT MD…
In this work we present a formalism for the calculation of the local elastic constants in inhomogeneous systems based on a method of planes. Unlike previous work, this formalism does not require the partitioning of the system into a set of…
A general Monte Carlo simulation method of calculating the elastic constants of polydisperse hard-sphere colloidal crystal was developed. The elastic constants of a size polydisperse hard sphere fcc crystal is calculated. The pressure and…
We present details of our effective computational methods based on the real-space finite-difference formalism to elucidate electronic and magnetic properties of the two-dimensional (2D) materials within the framework of the density…
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…
A novel approach was derived to compute the elastic displacement field from a measured elastic deformation field (i.e., deformation gradient or strain). The method is based on integrating the deformation field using Finite Element…
We present stable mixed finite elements for planar linear elasticity on general quadrilateral meshes. The symmetry of the stress tensor is imposed weakly and so there are three primary variables, the stress tensor, the displacement vector…
We present a theoretical method for deriving the stress tensor and elastic response of ordered systems within a Ginzburg-Landau type density field theory in the linear regime. This is based on spatially coarse graining the microscopic…
Despite of some progresses in investigating the roles of the higher-order strain gradients on elastic stabilities of solids, the physical nature on the higher-order elastic instabilities of crystals, especially under extreme strain rates,…
The Discrete elastic rod method (Bergou et al., 2008) is a numerical method for simulating slender elastic bodies. It works by representing the center-line as a polygonal chain, attaching two perpendicular directors to each segment, and…
Dynamic models, particularly rate-dependent models, have proven effective in capturing the key phenomenological features of frictional processes, whilst also possessing important mathematical properties that facilitate the design of control…
We show that the vibrational response of a glassy liquid at finite frequencies can be described by continuum mechanics despite the vast degeneracy of the vibrational ground state; standard continuum elasticity assumes a unique ground state.…
In this paper, we review some recent work on amorphous materials using current "first principles" electronic structure/molecular dynamics techniques. The main theme of the paper is to emphasize new directions in the use of such ab initio…
When the nonconvex problem is complicated by stochasticity, the sample complexity of stochastic first-order methods may depend linearly on the problem dimension, which is undesirable for large-scale problems. To alleviate this linear…
We consider Cauchy's equation of motion for hyperelastic materials. The solution of this nonlinear initial-boundary value problem is the vector field which discribes the displacement which a particle of this material perceives when exposed…
In this work we propose and analyze a novel Hybrid High-Order discretization of a class of (linear and) nonlinear elasticity models in the small deformation regime which are of common use in solid mechanics. The proposed method is valid in…
Fluctuations of the instantaneous local Lagrangian strain $\epsilon_{ij}(\bf{r},t)$, measured with respect to a static ``reference'' lattice, are used to obtain accurate estimates of the elastic constants of model solids from atomistic…
Real-world solids, such as rocks, soft tissues, and engineering materials, are often under some form of stress. Most real materials are also, to some degree, anisotropic due to their microstructure, a characteristic often called the…