ABSTRACT
This chapter explores work and energy concepts that form the basis of the nonlinear finite element analysis methods. It discusses the basic requirements of objectivity and frame indifference for valid stress and strain rates. The chapter presents the divergence theorem. The divergence theorem is one of several well-known integral theorems. The rate of work done by the body force acting on a differential element of volume dV¯ is vTb¯ dV¯. The chapter also examines the relation between Cauchy stress and second Piola–Kirchhoff (2PK) stress. The principle of virtual work (PVW) is the fundamental basis for powerful and versatile approximate numerical analysis procedures. It also provides a unified approach for formulating finite element models for all types of solid and structural components, and is equally applicable to nonlinear and linear analysis. For incremental-iterative numerical solution methods based on either a total Lagrangian or updated Lagrangian formulation, internal virtual work is calculated in the reference configuration.
