Surprises due to new elastoplastic equations of Prandtl-Reuss type

Abstract

New and perhaps unexpected progress in rate-independent elastoplastic modeling is reported with a unified approach toward simulating widely ranging non-elastic effects of various advanced engineering materials such as metals, shape memory alloys, granular materials, fiber-reinforced composites, as well as crystalline solids, etc. This progress originates from a simple idea of bypassing inherent limitations of usual elastoplastic formulations centered on the notion of yielding. With no reference to any yield criteria, the plastic strain-rate should be induced at all stress levels in a more realistic sense that it is small for stresses within a classical yield surface and becomes appreciable for stresses close to and on this surface. A new and unified flow rule for the plastic strain-rate is then proposed of the same smooth form for all cases of both the stress level and the stress rate. Without imposing the ad hoc simplified conditions introduced in usual Prandtl-Reuss equations, new elastoplastic equations are then established by incorporating such small deviations from realistic behaviors as neglected just by postulating these conditions. It turns out that the new equations are not only essentially simpler in both conceptual and structural formulations, but can automatically as inherent response features incorporate significant effects excluded from usual Prandtl-Reuss equations, such as the yielding and unloading behaviors with smooth transitions, the pseudo-elastic effect with hysteresis loops, the non-elastic recovery during unloading as well as failure effects under either monotone or cyclic loading conditions, etc. Since such effects not only go beyond the scope of usual elastoplastic equations but can be only partially simulated even if augmented constitutive equations are postulated toward further characterizing damaging and fracturing effects resulting from evolving micro-defects and macro-cracks, it may be probably surprising that now the new equations of essentially simpler structure not only can in a unified manner simulate all these effects but also can bypass numerical complexities in integrating various rate constitutive equations of complex structures. New results in treating long-standing issues in a few respects are presented, including (i) the yielding and the unloading behaviors with smooth transitions, (ii) the non-elastic recovery during unloading, (iii) the pseudo-elastic effect as extraordinary Bauschinger effect, (iv) failure effects under monotone and cyclic loading, (v) anisotropic multi-mode failure effects of unidirectional composites, (vi) new formulation of crystal elastoplasticity without involving non-uniqueness and singularity issues, (vii) non-normality effects for non-proportional multi-axial loading cases, and (viii) high efficiency algorithms for simulating multi-axial fatigue effects.