Related papers: Lattice-Spring Analogy for Isotropic Elasticity
The transformation theory of optics and acoustics is developed for the equations of linear anisotropic elasticity. The transformed equations correspond to non-unique material properties that can be varied for a given transformation by…
Developing a unified theory describing both ductile and brittle yielding constitutes a fundamental challenge of non-equilibrium statistical physics. Recently, it has been proposed that the nature of the yielding transition is controlled by…
One of the main theoretical issues in developing a theory of anisotropic viscoelastic media at finite strains lies in the proper definition of the material symmetry group and its evolution with time. In this paper the matter is discussed…
Given the success of Large Language Models (LLMs), there has been considerable interest in studying the properties of model activations. The literature overwhelmingly agrees that LLM representations are dominated by a few "outlier…
The fcc Lennard-Jones crystal is used as a generic model of solid to study the elastic properties of thin films as a function of thickness and temperature. The Monte Carlo algorithm is used to calculate the average deformations along the…
The mechanical response of isotropic elastoplastic materials containing random distributions of initially spherical voids is investigated computationally based on Fast Fourier Transform simulations. Numerical limit-analysis simulations at…
The quasistatic, Prandtl-Reuss perfect plasticity at small strains is combined with a gradient, reversible (i.e. admitting healing) damage which influences both the elastic moduli and the yield stress. Existence of weak solutions of the…
Auxetic materials are characterized by a negative Poisson's ratio, $\mathrm{\nu}$. As the Poisson's ratio becomes negative and approaches the lower isotropic mechanical limit of $\mathrm{\nu = -1}$, materials show enhanced resistance to…
The lattice Boltzmann method has become a widely adopted approach in computational fluid dynamics, offering unique advantages in mesoscopic kinetic modeling, intrinsic parallelism, and simple treatment of boundary conditions. However, its…
An inhomogeneous random recursive lattice was constructed from the multi-branched Husimi square lattice. The number of repeating units connected on one vertex was randomly set to be 2 or 3 with a quenched ratio $P_2$ or $P_3$ with…
The classical continuous mixed formulation of linear elasticity with pointwise symmetric stresses allows for a conforming finite element discretization with piecewise polynomials of degree at least three. Symmetric stress approximations of…
Additively manufactured auxetic structures offer desirable qualities like lightweight, good energy absorption, excellent indentation resistance, high shear stiffness and fracture toughness among others. A wide range of materials from…
The numerical approximation of 2D elasticity problems is considered, in the framework of the small strain theory and in connection with the mixed Hellinger-Reissner variational formulation. A low-order Virtual Element Method (VEM) with…
This contribution investigates the extension of the microplane formulation to the description of transversely isotropic materials such as shale rock, foams, unidirectional composites, and ceramics. Two possible approaches are considered: 1)…
Addressing the intricate challenges in plane elasticity, especially with non-vanishing traction and complex geometries, requires innovative methods. This paper offers a novel approach, drawing inspiration from the Neumann problem for the…
A refined a priori error analysis of the lowest order (linear) Virtual Element Method (VEM) is developed for approximating a model two dimensional Poisson problem. A set of new geometric assumptions is proposed on shape regularity of…
Intergranular normal stresses (INS) are critical in the initiation and evolution of grain boundary damage in polycrystalline materials. To model the effects of such microstructural damage on a macroscopic scale, knowledge of INS is usually…
We present a study of the isospin-breaking (IB) corrections to pseudoscalar (PS) meson masses using the gauge configurations produced by the ETM Collaboration with $N_f=2+1+1$ dynamical quarks at three lattice spacings varying from 0.089 to…
We study a generalized Blume-Capel model on the simple cubic lattice. In addition to the nearest neighbor coupling there is a next to next to nearest neighbor coupling. In order to quantify spatial anisotropy, we determine the correlation…
Aiming at the study of critical phenomena in the presence of boundaries with a non-trivial shape we discuss how lattices with an adaptive lattice spacing can be implemented. Since the parameters of the Hamiltonian transform non-trivially…