This article is concerned with some essential aspects of representative ideas and viewpoints as well as developments in formulations
of rate-independent elastoplasticity beyond the small deformation range. Kinematical and physical foundations underlying the
basic variables, and the essential constitutive structures implied by the work postulate are examined and discussed,
pro and
con, from an integrated viewpoint based on certain coherent threads running through various formulations. Their constitutive
and computational implications are elucidated and contrasted by analysing the main structural features based on their basic
variables. Emphasis is placed on new issues and new understanding, and on physically pertinent variables and formulations.
In particular, attention is focused on the essential complexity of elastoplastic fields. It is suggested that residual stress
fields attendant upon the removal of external loadings or actions should be indispensable prerequisites for ensuring the geometrical
compatibility property of an elastoplastic body as material continuum. A further artificial process of destressing an elastoplastic
body would inevitably lead to the loss of its geometrical compatibility and thus to the loss of the kinematical grounds for
the usual compatible continuous bodies, such as the loss of the notion of line elements, etc. This might suggest that the
elastoplastic deformation should be an inherently inseparable physical entity in the usual sense of compatibility.
It is explained that a physically pertinent formulation for the incremental essence of flow-like characteristics of elastoplastic
behaviour should be an objective Eulerian formulation based upon the Kirchhoff stress (weighted Cauchy stress) and the natural
deformation rate (stretching). According to the latest development, it is possible to establish a straightforward Eulerian
rate theory without involving additional ``elastic'' or ``plastic'' deformation-like variables. With so many possibilities
in formulating objective Eulerian rate constitutive relations, in particular, for the choices of objective rates among an
unlimited number of plausible candidates, it is demonstrated how a unique, self-consistent, general constitutive structure
may be derived from two physical consistency criteria by synthesizing and developing a number of essential ideas contributed
in previous efforts. With this general self-consistent structure based on Kirchhoff stress and the stretching, it is rigorously
found from the work postulate that the normality rule for plastic flow and the convexity property of the yield surface in
classical elastoplasticity for the small deformation range may be extended to be general facts even for the case covering
the whole deformation range, thus leading to a self-consistent Eulerian rate theory of finite elastoplasticity with the appealingly
simple essential structure as in the classical case.