Bounds for finite deflections of impulsively loaded structures with time-dependent plastic behaviort

The paper shows that upper bounds on deflections of an impulsively loaded structure whose behavior in the plastic range is strain rate dependent may be obtained by an application of the theorem of minimum potential energy, with results valid for finite deflections and strains. The concepts of extremal path behavior in strain-time space, due to Ponter, are used in order to provide unique definitions of strain energy and complementary energy for the path dependent material. The theorems are illustrated by examples of fully constrained beams in which deflections of the order of the beam thickness lead to large forces of membrane type.