All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 3 Next

Displaying 41 – 60 of 360

Showing per page

Analytical results on a model for damaging in domains and interfaces

Elena Bonetti, Michel Frémond (2011)

ESAIM: Control, Optimisation and Calculus of Variations

This paper deals with a model describing damage processes in a (nonlinear) elastic body which is in contact with adhesion with a rigid support. On the basis of phase transitions theory, we detail the derivation of the model written in terms of a PDE system, combined with suitable initial and boundary conditions. Some internal constraints on the variables are introduced in the equations and on the boundary, to get physical consistency. We prove the existence of global in time solutions (to a suitable...

Analytical results on a model for damaging in domains and interfaces*

Elena Bonetti, Michel Frémond (2011)

ESAIM: Control, Optimisation and Calculus of Variations

This paper deals with a model describing damage processes in a (nonlinear) elastic body which is in contact with adhesion with a rigid support. On the basis of phase transitions theory, we detail the derivation of the model written in terms of a PDE system, combined with suitable initial and boundary conditions. Some internal constraints on the variables are introduced in the equations and on the boundary, to get physical consistency. We prove the existence of global in time solutions (to a suitable...

Approximation and numerical solution of contact problems with friction

Jaroslav Haslinger, Miroslav Tvrdý (1983)

Aplikace matematiky

The present paper deals with numerical solution of the contact problem with given friction. By a suitable choice of multipliers the whole problem is transformed to that of finding a saddle-point of the Lagrangian function ℒ on a certain convex set K × Λ . The approximation of this saddle-point is defined, the convergence is proved and the rate of convergence established. For the numerical realization Uzawa’s algorithm is used. Some examples are given in the conclusion.

Approximation of a Martensitic Laminate with Varying Volume Fractions

Bo Li, Mitchell Luskin (2010)

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...

Approximation of a nonlinear thermoelastic problem with a moving boundary via a fixed-domain method

Jindřich Nečas, Tomáš Roubíček (1990)

Aplikace matematiky

The thermoelastic stresses created in a solid phase domain in the course of solidification of a molten ingot are investigated. A nonlinear behaviour of the solid phase is admitted, too. This problem, obtained from a real situation by many simplifications, contains a moving boundary between the solid and the liquid phase domains. To make the usage of standard numerical packages possible, we propose here a fixed-domain approximation by means of including the liquid phase domain into the problem (in...

Collisions and fractures: a model in S ⁢ B ⁢ D

Elena Bonetti, Michel Frémond (2004)

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

We investigate collisions (assumed to be instantaneous) and fractures of three-dimensional solids. Equations of motion and constitutive laws provide a set of partial differential equations, whose corresponding variational problem may be solved in the space of special functions with bounded deformations ( S ⁢ B ⁢ D ), exploiting the direct method of calculus of variations.

Comparison of crack propagation criteria in linear elastic fracture mechanics

Mikeš, Karel (2015)

Programs and Algorithms of Numerical Mathematics

In linear fracture mechanics, it is common to use the local Irwin criterion or the equivalent global Griffith criterion for decision whether the crack is propagating or not. In both cases, a quantity called the stress intensity factor can be used. In this paper, four methods are compared to calculate the stress intensity factor numerically; namely by using the stress values, the shape of a crack, nodal reactions and the global energetic method. The most accurate global energetic method is used to...

Comportamiento asintótico de las ecuaciones de la termoelasticidad generalizada.

Alberto Falqués Serra (1982)

Stochastica

In this paper it is first shown that the linear evolution equations for a generalized thermoelastic solid generate a C0 semigroup. Next an analysis of the long time evolution behaviour yields the some results known for classical thermoelasticity: generically, the natural state is asymptotically stable.

Currently displaying 41 – 60 of 360