Page 1 Next

## Displaying 1 – 20 of 40

Showing per page

### Almost classical solutions of static Stefan type problems involving crystalline curvature

Banach Center Publications

In this note we analyze equilibria of static Stefan type problems with crystalline/singular weighted mean curvature in the plane. Our main goal is to improve the meaning of variational solutions so that their properties allow us to call them almost classical solutions. The idea of our approach is based on a new definition of a composition of multivalued functions.

### An adaptive finite element method for solving a double well problem describing crystalline microstructure

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

### An adaptive finite element method for solving a double well problem describing crystalline microstructure

ESAIM: Mathematical Modelling and Numerical Analysis

The minimization of nonconvex functionals naturally arises in materials sciences where deformation gradients in certain alloys exhibit microstructures. For example, minimizing sequences of the nonconvex Ericksen-James energy can be associated with deformations in martensitic materials that are observed in experiments[2,3]. — From the numerical point of view, classical conforming and nonconforming finite element discretizations have been observed to give minimizers with their quality being highly dependent...

### Analysis of a one-dimensional variational model of the equilibrium shapel of a deformable crystal

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

### Analysis of a one-dimensional variational model of the equilibrium shapel of a deformable crystal

ESAIM: Mathematical Modelling and Numerical Analysis

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 functions : a genericity result with crystallographic implications

ESAIM: Control, Optimisation and Calculus of Variations

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

ESAIM: Control, Optimisation and Calculus of Variations

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...

### Approximation of a martensitic laminate with varying volume fractions

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

### Approximation of a Martensitic Laminate with Varying Volume Fractions

ESAIM: Mathematical Modelling and Numerical Analysis

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...

### Constrained elasticity

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Some foundational aspects of the constitutive theory of finite elasticity are considered in the case, regarded here as general, when internal kinematical constraints are imposed. The emphasis is on the algebraic-geometric structure induced by constraints. In particular, old and new examples of internal constraints are reviewed, and the material symmetry issue in the presence of constraints is discussed.

### Cross-effects in mechanics of solid continua.

Balkan Journal of Geometry and its Applications (BJGA)

### Curl bounds grad on SO(3)

ESAIM: Control, Optimisation and Calculus of Variations

Let ${F}^{\mathrm{p}}\in \mathrm{GL}\left(3\right)$ be the plastic deformation from the multiplicative decomposition in elasto-plasticity. We show that the geometric dislocation density tensor of Gurtin in the form $\mathrm{Curl}\left[{F}^{\mathrm{p}}\right]·{\left({F}^{\mathrm{p}}\right)}^{T}$ applied to rotations controls the gradient in the sense that pointwise $\forall R\in {C}^{1}\left({ℝ}^{3},\mathrm{SO}\left(3\right)\right):\parallel \mathrm{Curl}\left[R\right]·{R}^{T}{\parallel }_{{𝕄}^{3×3}}^{2}\ge \frac{1}{2}{\parallel \mathrm{D}R\parallel }_{{ℝ}^{27}}^{2}$. This result complements rigidity results [Friesecke, James and Müller, Comme Pure Appl. Math. 55 (2002) 1461–1506; John, Comme Pure Appl. Math. 14 (1961) 391–413; Reshetnyak, Siberian Math. J. 8 (1967) 631–653)] as well as an associated linearized theorem...

### Curl bounds Grad on SO(3)

ESAIM: Control, Optimisation and Calculus of Variations

Let ${F}^{\mathrm{p}}\in \mathrm{GL}\left(3\right)$ be the plastic deformation from the multiplicative decomposition in elasto-plasticity. We show that the geometric dislocation density tensor of Gurtin in the form $\mathrm{Curl}\left[{F}^{\mathrm{p}}\right]·{\left({F}^{\mathrm{p}}\right)}^{T}$ applied to rotations controls the gradient in the sense that pointwise $\forall R\in {C}^{1}\left({ℝ}^{3},\mathrm{SO}\left(3\right)\right):\parallel \mathrm{Curl}\left[R\right]·{R}^{T}{\parallel }_{{𝕄}^{3×3}}^{2}\ge \frac{1}{2}{\parallel \mathrm{D}R\parallel }_{{ℝ}^{27}}^{2}$. This result complements rigidity results [Friesecke, James and Müller, Comme Pure Appl. Math.55 (2002) 1461–1506; John, Comme Pure Appl. Math.14 (1961) 391–413; Reshetnyak, Siberian Math. J.8 (1967) 631–653)] as well as an associated linearized theorem saying...

### Designing textured polycrystals with specific isotropic material tensor: the ODF method.

Rendiconti del Seminario Matematico

### Direct approach to mean-curvature flow with topological changes

Kybernetika

This contribution deals with the numerical simulation of dislocation dynamics. Dislocations are described by means of the evolution of a family of closed or open smooth curves $\Gamma \left(t\right):S\to {ℝ}^{2}$, $t\geqq 0$. The curves are driven by the normal velocity $v$ which is the function of curvature $\kappa$ and the position. The evolution law reads as: $v=-\kappa +F$. The motion law is treated using direct approach numerically solved by two schemes, i. e., backward Euler semi-implicit and semi-discrete method of lines. Numerical stability is improved...

### Dislocation dynamics - analytical description of the interaction force between dipolar loops

Kybernetika

The interaction between dislocation dipolar loops plays an important role in the computation of the dislocation dynamics. The analytical form of the interaction force between two loops derived in the present paper from Kroupa’s formula of the stress field generated by a single dipolar loop allows for faster computation.

### Existence and uniqueness for a nonlinear parabolic/Hamilton-Jacobi coupled system describing the dynamics of dislocation densities

Annales de l'I.H.P. Analyse non linéaire

### Geometrically nonlinear shape-memory polycrystals made from a two-variant material

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

### Geometrically nonlinear shape-memory polycrystals made from a two-variant material

ESAIM: Mathematical Modelling and Numerical Analysis

Bhattacharya and Kohn have used small-strain (geometrically linear) elasticity to analyze the recoverable strains of shape-memory polycrystals. The adequacy of small-strain theory is open to question, however, since some shape-memory materials recover as much as 10 percent strain. This paper provides the first progress toward an analogous geometrically nonlinear theory. We consider a model problem, involving polycrystals made from a two-variant elastic material in two space dimensions. The linear theory...

Page 1 Next