Kinematics and kinetics modeling of thermoelastic continua based on the multiplicative decomposition of the deformation gradient

Solids usually show complex material behavior. If deformation is finite, the description of the kinematics makes the mechanical model complicated. In fact, one of the basic questions in the formulation and analysis procedures of finite deformation thermoelasticity is: “How can the finite deformation thermoelasticity response be best accounted for in the kinematic formulation?” A rather attractive way to proceed is to use the approach of small strain analysis, and decompose the total strain into a mechanical part and a thermal part. In this paper, based on the multiplicative decomposition of the deformation gradient, the mechanical and thermal strains are defined in the power and exponential forms. Also, the decomposition of the total strain into the mechanical and thermal strains is investigated for extension of various constitutive models at small deformation to the finite deformation thermoelasticity. In order to model the mechanical behavior of thermoelastic continua in the stress-producing process of nonisothermal deformation, an isothermal effective stress-strain equation based on the proposed strains is considered. Regards to this constitutive equation and assuming a linear dependence of the specific heat on temperature, the state functions including the internal energy, free energy, entropy and stress tensor are derived in the case of finite deformation thermoelasticity. Based on this decomposition and the proposed strains, it can be seen that these state functions are an extension from small deformation to finite deformation thermoelasticity. In addition, the mechanical and thermal material parameters are determined using the mechanical tests done at constant and the free thermal expansion test data, respectively.