A continuum model of a thermoelastic solid capable of undergoing phase transitions

DOI10.1016/0022-5096(93)90048-KzbMath0825.73058MaRDI QIDQ1209001

Rohan C. Abeyaratne, James K. Knowles

Publication date: 16 May 1993

Published in: Journal of the Mechanics and Physics of Solids (Search for Journal in Brave)

Mathematics Subject Classification ID

Thermodynamics in solid mechanics (74A15) Stefan problems, phase changes, etc. (80A22) Theory of constitutive functions in solid mechanics (74A20)

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Cites Work

• Unnamed Item
• Unnamed Item
• On the driving traction acting on a surface of strain discontinuity in a continuum
• On the dissipative response due to discontinuous strains in bars of unstable elastic material
• Equilibrium of bars
• On the dissipation associated with equilibrium shocks in finite elasticity
• Kinetic relations and the propagation of phase boundaries in solids
• Implications of Viscosity and Strain-Gradient Effects for the Kinetics of Propagating Phase Boundaries in Solids
• On the propagation of maximally dissipative phase boundaries in solids