Finite-strain thermoelasticity based on multiplicative decomposition of deformation gradient

The constitutive formulation of the finite-strain thermoelasticity is revisited within the thermodynamic framework and the multiplicative decomposition of the deformation gradient into its elastic and thermal parts. An appealing structure of the Helmholtz free energy is proposed. The corresponding stress response and the entropy expressions are derived. The results are specified in the case of quadratic dependence of the elastic strain energy on the finite elastic strain. The specific and latent heats are discussed, and the comparison with the results of the classical thermoelasticity are given. .

[1]  W. Nowacki.  COUPLE STRESSES IN THE THEORY OF THERMOELASTICITY III , 1968 .

[2]  Nicolas Triantafyllidis,et al.  Derivation of higher order gradient continuum theories in 2,3-D non-linear elasticity from periodic lattice models , 1994 .

[3]  R. Stojanovitch.  On the stress relation in non-linear thermoelasticity , 1969 .

[4]  K. S. Havner,et al.  Finite Plastic Deformation of Crystalline Solids , 1992 .

[5]  C. Kittel.  Introduction to solid state physics , 1954 .

[6]  En-Jui Lee.  Elastic-Plastic Deformation at Finite Strains , 1969 .

[7]  G. Johnson,et al.  Decomposition of the Deformation Gradient in Thermoelasticity , 1998 .

[8]  Ilya Prigogine,et al.  Introduction to Thermodynamics of Irreversible Processes , 1967 .

[9]  D. Whiffen.  Thermodynamics , 1973, Nature.

[10]  R. Ogden.  Non-Linear Elastic Deformations , 1984 .

[11]  C. Truesdell,et al.  The Nonlinear Field Theories in Mechanics , 1968 .

[12]  N. Fleck,et al.  Strain gradient plasticity , 1997 .

[13]  Elias C. Aifantis,et al.  The physics of plastic deformation , 1987 .

[14]  V. Lubarda.  Finite compression of solids: second order thermoelastic analysis , 1986 .

[15]  Gerhard A. Holzapfel,et al.  Nonlinear Solid Mechanics: A Continuum Approach for Engineering Science , 2000 .

[16]  Carl Eckart,et al.  The Thermodynamics of Irreversible Processes. IV. The Theory of Elasticity and Anelasticity , 1948 .

[17]  E. Kröner,et al.  Allgemeine Kontinuumstheorie der Versetzungen und Eigenspannungen , 1959 .