An inverse problem for biharmonic equation.
Analysis of a one-dimensional variational model of the equilibrium shapel of a deformable crystal
Analysis of a one-dimensional variational model of the equilibrium shapel of a deformable crystal
The equilibrium configurations of a one-dimensional variational model that combines terms expressing the bulk energy of a deformable crystal and its surface energy are studied. After elimination of the displacement, the problem reduces to the minimization of a nonconvex and nonlocal functional of a single function, the thickness. Depending on a parameter which strengthens one of the terms comprising the energy at the expense of the other, it is shown that this functional may have a stable absolute...
Anisotropic and dissipative finite elasto-plastic composite.
Anisotropic functions : a genericity result with crystallographic implications
In the 1950’s and 1960’s surface physicists/metallurgists such as Herring and Mullins applied ingenious thermodynamic arguments to explain a number of experimentally observed surface phenomena in crystals. These insights permitted the successful engineering of a large number of alloys, where the major mathematical novelty was that the surface response to external stress was anisotropic. By examining step/terrace (vicinal) surface defects it was discovered through lengthy and tedious experiments...
Anisotropic functions: a genericity result with crystallographic implications
In the 1950's and 1960's surface physicists/metallurgists such as Herring and Mullins applied ingenious thermodynamic arguments to explain a number of experimentally observed surface phenomena in crystals. These insights permitted the successful engineering of a large number of alloys, where the major mathematical novelty was that the surface response to external stress was anisotropic. By examining step/terrace (vicinal) surface defects it was discovered through lengthy and tedious experiments...
Anisotropic geometric functionals and gradient flows
We survey some recent results on the gradient flow of an anisotropic surface energy, the integrand of which is one-homogeneous in the normal vector. We discuss the reasons for assuming convexity of the anisotropy, and we review some known results in the smooth, mixed and crystalline case. In particular, we recall the notion of calibrability and the related facet-breaking phenomenon. Minimal barriers as weak solutions to the gradient flow in case of nonsmooth anisotropies are proposed. Furthermore,...
Antiplane fracture analysis of a crack in a monlicnic composite.
Application of singular integral equations in the boundary value problems of electroelasticity.
Approximation numérique du cisaillement transverse dans les plaques minces en flexion.
Approximation of a martensitic laminate with varying volume fractions
Approximation of a Martensitic Laminate with Varying Volume Fractions
We give results for the approximation of a laminate with varying volume fractions for multi-well energy minimization problems modeling martensitic crystals that can undergo either an orthorhombic to monoclinic or a cubic to tetragonal transformation. We construct energy minimizing sequences of deformations which satisfy the corresponding boundary condition, and we establish a series of error bounds in terms of the elastic energy for the approximation of the limiting macroscopic deformation and...
Asymmetric deformation of anisotropic porous bodies.
Asymptotic behavior of eigenfunctions and eigenfrequencies of oscillation boundary value problems of the linear theory of elastic mixtures.
Axial shear modulus of a fiber-reinforced composite with random fiber cross-sections.