Related papers: First-principles calculation of higher-order elast…
A method to retrieve the elastic constants of rectangular wooden plates is presented, relying on the measurement of a set of eigenfrequencies and the identification of the corresponding mode shapes, and belonging to the more general…
In contrast with the diffusion equation which smoothens the initial data to $C^\infty$ for $t>0$ (away from the corners/edges of the domain), the subdiffusion equation only exhibits limited spatial regularity. As a result, one generally…
The method of many body Green's functions is used to derive algebraic expressions for the different elastic and thermodynamical quantities such as the free energy, internal energy, entropy, heat capacity, elastic constants (adiabatic and…
This book is organized into eight chapters. The first three gently introduce the basic principles of hybrid high-order methods on a linear diffusion problem, the key ideas underlying the mathematical analysis, and some useful variants of…
We introduce a new class of mixed finite element methods for 2D and 3D compressible nonlinear elasticity. The independent unknowns of these conformal methods are displacement, displacement gradient, and the first Piola-Kirchhoff stress…
This paper derives a posteriori error estimators for the nonlinear first-order optimality conditions associated with the electrically and flexoelectrically coupled Frank-Oseen model of liquid crystals, building on the results of [14] for…
A general force-perturbation-based criterion for solid instability is proposed, which can predict instability including crease without priori knowledge of instability configuration. The crease instability is analyzed in detail, we found…
Multicomponent nitrides are a hot research topic in the search of hard coatings. The effect of substitutions on the phase stabilities, magnetic, and elastic properties of $Al_{1-x-y}Cr_{x}Ti_{y}N$ $(0\leq x,y\leq1)$ was studied using first…
We study a fully discrete finite element method for variable-order time-fractional diffusion equations with a time-dependent variable order. Optimal convergence estimates are proved with the first-order accuracy in time (and second order…
First-principles alloy theory is used to establish the $\gamma$-surface of Fe-Cr-Ni alloys as function of chemical composition and temperature. The theoretical stacking fault energy (SFE) versus chemistry and temperature trends agree well…
To reduce reliance on experimental fitting data within the crystal plasticity finite element method (CPFEM), an approached is proposed that integrates first-principles calculations based on density functional theory (DFT) to predict the…
This article is a description of elasticity theory for readers with mathematical background. The first sections are an abridgment of parts of the book by Marsden and Hughes, including a compact identification of the equations of motion as…
A theory is developed for evaluation of nonlinear elastic moduli of composite materials with nonlinear inclusions dispersed in another nonlinear material (matrix). We elaborate a method aimed for determination of elastic parameters of a…
Recent developments in imaging techniques and correlation algorithms enable measurement of strain fields on a deforming material at high spatial and temporal resolution. In such cases, the computation of the stress field from the known…
Anisotropic ideal strength is a fundamental and important plasticity parameter in scaling the intrinsic strength of strong crystalline materials, and is a potential descriptor in searching and designing novel hard/superhard materials.…
A covariant formulation of the virtual power principle based on Lie derivatives is proposed. The Lie covariant approach does not require an inner product and the Cauchy deformation tensor to start, but, at first order in a Galilean…
The paper addresses stability and finite element analysis of the stationary two-phase Stokes problem with a piecewise constant viscosity coefficient experiencing a jump across the interface between two fluid phases. We first prove a priori…
On the basis of the general nonlinear theory of a hyperelastic material with initial stress, initially without consideration of the origin of the initial stress, we determine explicit expressions for the stress-dependent tensor of…
It is classical that, when the small deformation is assumed, the incremental analysis problem of an elastoplastic structure with a piecewise-linear yield condition and a linear strain hardening model can be formulated as a convex quadratic…
The adiabatic elastic modulus is often useful in the high frequency response of materials. Unfortunately, it can be much more difficult to directly measure the adiabatic elastic modulus of material than the isothermal elastic modulus. We…