Material response: Measures of stress and strain

Abstract

Amongst the many pillars upon which the FEM solutions stand is the pillar of material response. This defines the physical behaviour of the material type under investigation in the FEM problem. It is under this pillar that one distinguishes between rubbery, elastic, nonlinear, fracture and interface failure mechanisms. It is a key component of the FEM problem and must be correctly defined if one is to obtain reliable solutions. A common theme for this pillar of the FEM process is what is described as predictive modelling, which is the use of computational methods to determine the material behaviour of a given material. In this chapter, we have presented the principles of the material response module of an FEM scheme. The focus here is exploiting the principles of continuum mechanics in defining the response of a material body. Specifically, this chapter introduces the kinematics of finite deformation of a material body; measures of strains and stresses; and concludes with the practical formulations of stresses needed by engineers during the design process. Such practical stress formulations include: principal stresses, von Mises stresses, etc. This chapter lays down the theory needed to understand the material model implementations in the finite element solver.