Related papers: New Nonconforming Elements for Linear Strain Gradi…
Second-order partial differential equations in non-divergence form are considered. Equations of this kind typically arise as subproblems for the solution of Hamilton-Jacobi-Bellman equations in the context of stochastic optimal control, or…
The lowest order nonconforming rectangular element in three dimensions involves 54 degrees of freedom for the stress and 12 degrees of freedom for the displacement. With a modest increase in the number of degrees of freedom (24 for the…
Recently there has been interest in studying a new class of elastic materials, which is described by implicit constitutive relations. Under some basic assumption for elasticity constants, the system of governing equations of motion for this…
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…
Usual introductions of the concept of motion are not well adapted to a subsequent, strictly tensorial, theory of elasticity. The consideration of arbitrary coordinate systems for the representation of both, the points in the laboratory, and…
This paper analyzes rectangular finite element methods for fourth order elliptic singular perturbation problems. We show that the non-$C^0$ rectangular Morley element is uniformly convergent in the energy norm with respect to the…
The usual approach to the development of new nonlinear dielectric materials focuses on the search for materials in which the components possess an inherently large nonlinear dielectric response. In contrast, based on thermodynamics, we have…
We investigate non-linear elastic deformations in the phase field crystal model and derived amplitude equations formulations. Two sources of non-linearity are found, one of them based on geometric non-linearity expressed through a finite…
This study addresses the modelling of elastic bodies, particularly when the relaxed configuration is unknown or non-existent. We adopt the theory of initially stressed materials, incorporating the deformation gradient and stress state of…
This article introduces continuous $H^2$-nonconforming finite elements in two and three space dimensions which satisfy a strong discrete Miranda--Talenti inequality in the sense that the global $L^2$ norm of the piecewise Hessian is bounded…
This short note shows the superconvergence of an $H(\mathrm{grad}\,\mathrm{curl})$-nonconforming brick element very recently introduced in [17] for the quad-curl problem. The supercloseness is based on proper modifications for both the…
We introduce and analyze a new mixed finite element method with reduced symmetry for the standard linear model in viscoelasticity. Following a previous approach employed for linear elastodynamics, the present problem is formulated as a…
The strain-energy formulation of nonlinear elasticity can be extended to the case of significant compression by modulating suitable strain energy terms by a function of relative volume. For isotropic materials this can be accomplished by…
Optimal convergence rates of adaptive finite element methods are well understood in terms of the axioms of adaptivity. One key ingredient is the discrete reliability of a residual-based a posteriori error estimator, which controls the error…
We investigate the elastic properties of selected zincblende III-V semiconductors. Using hybrid functional density functional theory we calculate the second and third order elastic constants, and first and second-order internal strain…
In order to enhance the modeling of metallic materials behavior in non proportional loadings, a modification of the classical elastic-plastic models including distortion of the yield surface is proposed. The new yield criterion uses the…
In the presented research, the intergranular elastic interaction and the second-order plastic incompatibility stress in textured ferritic and austenitic steels were investigated by means of diffraction. The lattice strains were measured…
The work reported in ``Granular micromechanics-based identification of isotropic strain gradient parameters for elastic geometrically nonlinear deformations" misidentified key terms in the grain-pair objective relative displacement when…
We propose a complement to constitutive modeling that augments neural networks with material principles to capture anisotropy and inelasticity at finite strains. The key element is a dual potential that governs dissipation, consistently…
Elastic constants and their derived properties of various cubic Heusler compounds were calculated using first-principles density functional theory. To begin with, Cu$_2$MnAl is used as a case study to explain the interpretation of the basic…