Constitutive laws

Abstract

Constitutive laws describe the relation among macroscopic quantities such as stress, strain, and strain rate. Although most of the constitutive laws for complex soft matter are empirically introduced, they are useful to quantitatively evaluate the deformation and flow states of soft matter. In this chapter, some classic constitutive laws such as viscoelasticity and viscoplasticity are first explained. Rebound and its restitution coefficient are explained using a simple viscoelastic oscillation. Then, models of transport phenomena such as diffusion and advection are briefly reviewed. After describing frictional constitutive laws, peculiar characteristics of granular matter are presented in terms of constitutive laws. The indefiniteness of the frictional property makes understanding static granular behaviors very difficult. Most of these discussions and characteristics are relevant to the analysis of granular-related soft impact phenomena.