ABSTRACT
A longitudinally unbounded strip with two free surfaces reaches its initial state by stretching the solid parallel to its length. Three different configurations are considered (Figure 1). In the natural configuration, free of stress and strain, the material point P is retrieved by the vector a, with components a1 and a2. Physical quantities in this configuration are referred to by the superscript “0”. The initial configuration is stressed and strained, and the vector X, with components X1 and X2, defines the position of P as follows:
In (1) ui is the displacement vector from the natural to the initial state. The physical quantities of the latter are referred to by the superscript “i”. We assume that this initial state is attained by a static homogeneous transformation ui =Aa. The final configuration is due to a dynamic disturbance superimposed on the initial state.The vector x, with components x1 and x2, defines the position of P as follows:
In (2) u(t) represents the displacement from the initial to the final state, the physical quantities of which are referred to by the superscript “f ”. We may write:
The tensor of finite strains is:
In (4) the derivatives are calculated with respect to the position a in the natural configuration.
