Displaying similar documents to “Existence and uniqueness for the three-dimensional thermoelasticity system in shape memory problems”

Existence and uniqueness of solutions for a three-dimensional thermoelastic system

Irena Pawłow, Antoni Żochowski

Similarity:

A thermodynamically consistent model of shape memory alloys in three dimensions is studied. The thermoelastic system, based on the strain tensor, its gradient and the absolute temperature, is a generalization of the well-known one-dimensional Falk model. The key assumptions concerning the form of constitutive relations are discussed. The detailed and selfcontained proof of the global-in-time existence and uniqueness of solutions is presented.

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.

Asymptotic Analysis of the Shape and Composition of Alloy Islands in Epitaxial Solid Films

M. Blanariu, B. J. Spencer (2008)

Mathematical Modelling of Natural Phenomena

Similarity:

We consider the formation of solid drops (“islands”) occurring in the growth of strained solid films. Beginning from a detailed model for the growth of an alloy film that incorporates the coupling between composition, elastic stress and the morphology of the free boundary, we develop an asymptotic description of the shape and compositional nonuniformity of small alloy islands grown at small deposition rates. A key feature of the analysis is a “thin domain” scaling in the island which...

Shape Correspondence Analysis for Biomolecules Based on Volumetric Eigenfunctions

Tao Liao, Hao-Chih Lee, Ge Yang, Yongjie Jessica Zhang (2015)

Molecular Based Mathematical Biology

Similarity:

The functionality of biomolecules depends on their flexible structures, which can be characterized by their surface shapes. Tracking the deformation and comparing biomolecular shapes are essential in understanding their mechanisms. In this paper, a new spectral shape correspondence analysis method is introduced for biomolecules based on volumetric eigenfunctions. The eigenfunctions are computed from the joint graph of two given shapes, avoiding the sign flipping and confusion in the...

Triangular mesh analysis with application on hip bone

Pajerová, Nikola, Linkeová, Ivana

Similarity:

Shape analyses and similarity measuring is a very often solved problem in computer graphics. The shape distribution approach based on shape functions is frequently used for this determination. The experience from a comparison of ball-bar standard triangular meshes was used to match hip bones triangular meshes. The aim is to find relation between similarity measures obtained by shape distributions approach.

Function spaces and shape theories

Jerzy Dydak, Sławomir Nowak (2002)

Fundamenta Mathematicae

Similarity:

The purpose of this paper is to provide a geometric explanation of strong shape theory and to give a fairly simple way of introducing the strong shape category formally. Generally speaking, it is useful to introduce a shape theory as a localization at some class of “equivalences”. We follow this principle and we extend the standard shape category Sh(HoTop) to Sh(pro-HoTop) by localizing pro-HoTop at shape equivalences. Similarly, we extend the strong shape category of Edwards-Hastings...

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...