Ordered Rate Constitutive Theories: Development of Rate Constitutive Equations for Solids, Liquids, and Gases

摘要

In this research, the rate constitutive theories for ordered thermoviscous fluids, ordered thermoelastic solids and ordered thermoviscoelastic polymeric fluids in contra- and co-variant bases are developed. Such theories are necessitated when the mathematical models of the deforming matter are derived using the Eulerian description. In each case, the dependent variables in the rate constitutive theory and their argument tensors describing the physics of the deforming matter are identified. The dependent variables in the constitutive theory are expressed as a linear combination of the combined generators of the argument tensors. The coefficients in the linear combinations are functions of the combined invariants of the argument tensors, temperature, and density (for compressible matter; in the current configuration). The coefficients in the linear combination are determined by considering their Taylor's series expansions about the reference configuration and limiting the expansion to linear terms in the combined invariants and temperature.