On the modeling of thermo-mechanical phase transformations in solids
type: Item
instance of: scholarly article
title: On the modeling of thermo-mechanical phase transformations in solids
zbMATH Open document ID: 0782.73012
DOI: 10.1007/BF00042249
author: Qing Jiang
published in: Journal of Elasticity
publication date: 1994-01-02T00:00:00Z
review text: The paper models coupled thermo-mechanical effects in the macroscopic response of solids that arise from the occurrence of phase transformations. A Helmholtz free energy potential is constructed to describe the response of the thermoelastic material. An annular cylinder is deformed to a state of radially symmetric, finite anti-plane shear in the presence of differing inner and outer surface temperatures. After constructing all radially symmetric weak solutions involving at most a single surface of discontinuity of strain or temperature gradient, we determine the implications for quasi-static motions of the second law of thermodynamics. In particular, the results concerning creep as predicted by the present model are in qualitative agreement with the results of the motivating experiment.
Mathematics Subject Classification ID: 74A15
Mathematics Subject Classification ID: 80A22
Mathematics Subject Classification ID: 74B99
zbMATH DE Number: 475071
zbMATH Keywords: phase transformations
zbMATH Keywords: Helmholtz free energy potential
zbMATH Keywords: annular cylinder
zbMATH Keywords: radially symmetric weak solutions
zbMATH Keywords: quasi-static motions
zbMATH Keywords: second law of thermodynamics
zbMATH Keywords: creep
MaRDI profile type: Publication
cites work: Equilibrium of bars
cites work: On the dissipation associated with equilibrium shocks in finite elasticity
cites work: Discontinuous deformation gradients in plane finite elastostatics of incompressible materials
cites work: Finite deformation by mechanical twinning
cites work: Two-phase deformations of elastic solids
cites work: Displacive phase transformations in solids
cites work: On the emergence and propagation of a phase boundary in an elastic bar with a suddenly applied end load
cites work: Non-elliptic elastic materials and the modeling of dissipative mechanical behavior: An example
cites work: Non-elliptic elastic materials and the modelling of elastic-plastic behavior for finite deformation
cites work: Phase changes induced by deformation in isothermal elastic crystals
cites work: Ellipticity and deformations with discontinuous gradients in finite elastostatics
cites work: On the driving traction acting on a surface of strain discontinuity in a continuum
cites work: Q3951722
cites work: On the dissipative response due to discontinuous strains in bars of unstable elastic material
cites work: On finite anti-plane shear for imcompressible elastic materials
cites work: A note on anti-plane shear for compressible materials in finite elastostatics
cites work: On the Scale of the Nonlinear Effect in a Crack Problem
cites work: A class of compressible elastic materials capable of sustaining finite anti-plane shear
description: scientific article; zbMATH DE number 475071