THE CONCEPT OF PHYSICAL METRIC IN THERMODYNAMICS

In this paper we introduce a new geometric object, the physical metric , g, for the measurement of distance between material particles in the reference configuration. We then treat g as an internal variable and thereby obtain hereditary constitutive equations for dissipative solid s under conditions of large deformation. We demonstrate that g is in f act a measure of non-affine deformation and introduce the concept of t he hypercontinuum which allows the existence of multiple velocities in a material neighborhood, thereby leading to a deformation field with multiple metrics.