ABSTRACT
In finite-element analysis for finite deformation, it is necessary to carefully distinguish between the current (or “deformed”) configuration (i.e., at the current time or load step) and a reference configuration, which is usually considered strain-free. Here, both configurations are referred to the same orthogonal coordinate system characterized by the base vectors e1, e2, e3 (see Figure 1.1 in Chapter 1). Consider a body with volume V and surface S in the current configuration. The particle P occupies a position represented by the position vector x, and experiences (empirical) temperature T. In the corresponding undeformed configuration, the position of P is described by X, and the temperature has the value T0 independent of X. It is now assumed that x is a function of X and t and that T is also a function of X and t. The relations are written as x(X, t) and T(X, t), and it is assumed that x and T are continuously differentiable in X and t through whatever order needed in the subsequent development.
