A New Point-of-View at Plastic Materials of the Prandtl-Reuss Type

Lorentz group on Minkowski spacetime for construction of the two basic principles of plasticity

“…Notice that there is neither nor d in (1). While in ( 2) is merely a proportionality factor, the one in (3)…”

“…Next, the proportionality factor between the (deviatoric) stress components QG and the (plastic) strain increment components dq G had started becoming more and more appreciated. To illustrate the conceptual progress in this regard, let us write them in progressive order: (1) dq…”

“…"exp , has been de"ned with its evolution explored seriously (see, e.g., [1,2]). Fifth, X has been recognized as a new dimension in the augmented stress space of (X, X, 2 , XL, X) de"ned as…”

Integral-equation representations of flow elastoplasticity derived from rate-equation models

“…To this rate-equation point-of-view and model, the usual analysis approaches require numerical integrations of the incremental or rate equations over a discrete sequence of steps, keeping the plastic strain increment normal to the evolving yield surface at each step, meanwhile managing to attach the current stress state on the current yield surface, which is moving and deforming in stress space in a way corresponding back to the plastic strain increment in the plastic strain space. Because of the interwoven nature of the model ingredients, the difficulties involved and its great consumption of computational time, and the efficiency and accuracy of the global solutions of structural and mechanical problems being strongly influenced by the efficiency and accuracy of constitutive-equation solving schemes, it has drawn much attention over the past 25 years and has directed many efforts spent in this issue aiming at developing accurate and economic algorithms [1] - [4]. However, owing to the great difficulties rooted in the very nature of this highly nonlinear path-dependence problem, thorough solutions have still been pending.…”