Ordered rate constitutive theories in Lagrangian description for thermoviscoelastic solids with memory

摘要: This paper presents ordered rate constitutive theories in Lagrangian description for compressible as well incompressible homogeneous, isotropic thermoviscoelastic solid matter with memory which the material derivative of order m deviatoric stress tensor and heat vector are functions temperature, temperature gradient, time derivatives conjugate strain up to any desired n, m−1 tensor. The solids described by these called due fact that dependent on orders n tensors. highest tensors define solid. derived here show applicable have fading memory. As is known, second law thermodynamics must form basis deriving all deforming (to ensure thermodynamic equilibrium during evolution), since other conservation balance laws independent constitution matter. entropy inequality expressed terms Helmholtz free energy density \({\Phi}\) does not provide a mechanism derive theory when its argument rates addition others. With decomposition into tensors, deterministic from inequality. However, tensor, requires set inequalities be satisfied but theory. In present work, we utilize generators invariants based axioms principles continuum mechanics. keep mind satisfy resulting thermodynamics. q derived: (i) strictly using conditions inequality; (ii) admissible consistent simplifying assumptions employed yield much simplified theories. It shown presented describe Mechanisms dissipation demonstrated discussed, derivation modulus presented. forms general result models may resemble currently used same. work viewed extension current models; rather, it framework physics derivations within mechanics purpose illustrate possible simplest here.