Filters

2007 - 20096

More filters

20196
Reset filters

Settings

Author: Petrov, Adrien × End date: 2009 × Type: Text ×

Search Results

Now showing 1 - 6 of 6
  • Thumbnail Image
    Item
    On the stability of elastic-plastic systems with hardening
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2007) Martins, João A.C.; Monteiro Marques, Manuel D.P.; Petrov, Adrien
    This paper discusses the stability of quasi-static paths for a continuous elastic-plastic system with hardening in a one-dimensional (bar) domain. Mathematical formulations, as well as existence and uniqueness results for dynamic and quasi-static problems involving elastic-plastic systems with linear kinematic hardening are recalled in the paper. The concept of stability of quasi-static paths used here is essentially a continuity property of the system dynamic solutions relatively to the quasi-static ones, when (as in Lyapunov stability) the size of initial perturbations is decreased and the rate of application of the forces (which plays the role of the small parameter in singular perturbation problems) is also decreased to zero. The stability of the quasi-static paths of these elastic-plastic systems is the main result proved in the paper.
  • Thumbnail Image
    Item
    Thermally driven phase transformation in shape-memory alloys
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2007) Mielke, Alexander; Petrov, Adrien
    This paper analyzes a model for phase transformation in shape-memory alloys induced by temperature changes and by mechanical loading. We assume that the temperature is prescribed and formulate the problem within the framework of the energetic theory of rate-independent processes. Existence and uniqueness results are proved.
  • Thumbnail Image
    Item
    Mathematical results on existence for viscoelastodynamic problems with unilateral constraints
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2007) Petrov, Adrien; Schatzman, M.
    We study a damped wave equation and the evolution of a Kelvin-Voigt material, both problems have unilateral boundary conditions. Under appropriate regularity assumptions on the initial data, both problems possess a weak solution which is obtained as the limit of a sequence of penalized problems; the functional properties of all the traces are precisely identified through Fourier analysis, and this enables us to infer the existence of a strong solution.
  • Thumbnail Image
    Item
    Convergence of solutions of kinetic variational inequalities in the rate-independent quasi-static limit
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2008) Mielke, Alexander; Petrov, Adrien; Martins, João A.C.
    This paper discusses the convergence of kinetic variational inequalities to rate-independent quasi-static variational inequalities. Mathematical formulations as well as existence and uniqueness results for kinetic and rate-independent quasi-static problems are provided. Sharp a priori estimates for the kinetic problem are derived that imply that the kinetic solutions converge to the rate-independent ones, when the size of initial perturbations and the rate of application of the forces tends to 0. An application to three-dimensional elastic-plastic systems with hardening is given.
  • Thumbnail Image
    Item
    On existence and approximation for a 3D model of thermally-induced phase transformations in shape-memory alloys
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2008) Mielke, Alexander; Paoli, Laetitia; Petrov, Adrien
    This paper deals with a three-dimensional model for thermal stress-induced transformations in shape-memory materials. Microstructure, like twined martensites, is described mesoscopically by a vector of internal variables containing the volume fractions of each phase. We assume that the temperature variations are prescribed. The problem is formulated mathematically within the energetic framework of rate-independent processes. An existence result is proved and temporal regularity is obtained in case of uniform convexity. We study also space-time discretizations and establish convergence of these approximations.
  • Thumbnail Image
    Item
    Error estimates for space-time discretizations of a rate-independent variational inequality
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2009) Mielke, Alexander; Paoli, Laetitia; Petrov, Adrien; Stefanelli, Ulisse
    This paper deals with error estimates for space-time discretizations in the context of evolutionary variational inequalities of rate-independent type. After introducing a general abstract evolution problem, we address a fully-discrete approximation and provide a priori error estimates. The application of the abstract theory to a semilinear case is detailed. In particular, we provide explicit space-time convergence rates for the isothermal Souza-Auricchio model for shape-memory alloys.