Displaying similar documents to “Existence and uniqueness of solutions for a three-dimensional thermoelastic system”

Existence and uniqueness for the three-dimensional thermoelasticity system in shape memory problems

Irena Pawłow, Antoni Żochowski (2003)

Banach Center Publications

Similarity:

A thermodynamically consistent model of shape memory alloys in three dimensions is studied. The thermoelasticity system, based on the strain tensor, its gradient and the absolute temperature, generalizes the well-known one-dimensional Falk model. Under simplifying structural assumptions we prove global in time existence and uniqueness of the solution.

Well-posedness of a thermo-mechanical model for shape memory alloys under tension

Pavel Krejčí, Ulisse Stefanelli (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

Similarity:

We present a model of the full thermo-mechanical evolution of a shape memory body undergoing a uniaxial tensile stress. The well-posedness of the related quasi-static thermo-inelastic problem is addressed by means of hysteresis operators techniques. As a by-product, details on a time-discretization of the problem are provided.

Mathematical study of an evolution problem describing the thermomechanical process in shape memory alloys

Pierluigi Colli (1991)

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

Similarity:

In this paper we prove existence, uniqueness, and continuous dependence for a one-dimensional time-dependent problem related to a thermo-mechanical model of structural phase transitions in solids. This model assumes the free energy depending on temperature, macroscopic deformation and also on the proportions of the phases. Here we neglect regularizing terms in the momentum balance equation and in the constitutive laws for the phase proportions.

A phase-field model for compliance shape optimization in nonlinear elasticity

Patrick Penzler, Martin Rumpf, Benedikt Wirth (2012)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

Shape optimization of mechanical devices is investigated in the context of large, geometrically strongly nonlinear deformations and nonlinear hyperelastic constitutive laws. A weighted sum of the structure compliance, its weight, and its surface area are minimized. The resulting nonlinear elastic optimization problem differs significantly from classical shape optimization in linearized elasticity. Indeed, there exist different definitions for the compliance: the change in potential energy...