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Numerical calculations were performed for two examples of the response of elastic-plastic beams subjected to dynamic loads. These were a simply supported, axially restrained beam under suddenly applied uniform pressure, and an axially restrained, clamped beam with a central mass that is impacted by a projectile. Large elastic-plastic deflections were considered, and the method of finite differences was used. Two different constitutive equations were assumed: the elastic-perfectly plastic relation, and a special elastic-viscoplastic strain hardening model. Analysis of the results included examining the interaction between the bending moment and the axial force, the variation of the axial force, bending moment and deflection with time, and the propagation velocities of the various phenomena during motion. Experiments were carried out in which a rifle projectile hit a central mass which had been fastened to a clamped beam. Comparison between the theoretical and experimental dynamic deflections shows good agreement for relatively short response times. (Author)

A representation of anelastic material behavior, i.e. materials that exhibit energy losses and rate dependent moduli for geometrically reversible deformations, is proposed for multiaxial stress states and large deformations (finite strains). The constitutive equations are relations between the deformation rate and the stress components. An 'anelastic stress' is considered to be part of the total applied stress and to be responsible for the phenomena of energy losses, rate dependent moduli, and delayed elasticity (creep and recovery). In this incremental formulation, 'memory' and 'history' effects are incorporated into the current deformation state and the state variable, the elastic stress, which makes the method suitable for computer solution of structural problems involving arbitrary loading histories. The present analysis is limited to isothermal conditions but the procedure can be generalized to consider thermal effects., Also pub. as ISSN-0067-0340.

A set of constitutive equations has been formulated to represent elastic-viscoplastic strain hardening material behavior for large deformations and arbitrary loading histories. An essential feature of the formulation is that the total deformation rate is considered to be separable into elastic and inelastic components which are functions of state variables at all stages of loading and unloading. The theory, therefore, is independent of a yield criterion or loading and unloading conditions. The deformation rate components are determinable from the current state which permits an incremental formulation of problems. Strain hardening is considered in the equations by introducing plastic work as the representative state variable. The problem of uniaxial straining has been examined for a number of histories that included straining at various rates, rapid changes of strain rate, unloading and reloading, and stress relaxation. The calculations were based on material constants chosen to represent commercially pure titanium. The results are in good agreement with corresponding experiments on titanium specimens. (Author)

A large deformation elastic-viscoplastic theory is formulated which considers both elastic and inelastic deformations to be present at all stages of loading and unloading. The theory does not require the assumption of a yield criterion or the prior determination of whether the material is loading or unloading. The theory is based on relating the essential parameters to state variables; the particular constitutive relations are motivated by the equations of dislocation dynamics. A numerical scheme for calculating deformations is developed and applied to a thick walled spherical shell under internal pressure. Various numerical examples are presented. (Author)