An improved return-mapping scheme for nonsmooth yield surfaces: PART I - the Haigh-Westergaard coordinates

The paper is devoted to the numerical solution of elastoplastic constitutive initial value problems. An improved form of the implicit return-mapping scheme for nonsmooth yield surfaces is proposed that systematically builds on a subdifferential formulation of the flow rule. The main advantage of this approach is that the treatment of singular points, such as apices or edges at which the flow direction is multivalued involves only a uniquely defined set of non-linear equations, similarly to smooth yield surfaces. This paper (PART I) is focused on isotropic models containing: $a)$ yield surfaces with one or two apices (singular points) laying on the hydrostatic axis; $b)$ plastic pseudo-potentials that are independent of the Lode angle; $c)$ nonlinear isotropic hardening (optionally). It is shown that for some models the improved integration scheme also enables to a priori decide about a type of the return and investigate existence, uniqueness and semismoothness of discretized constitutive operators in implicit form. Further, the semismooth Newton method is introduced to solve incremental boundary-value problems. The paper also contains numerical examples related to slope stability with available Matlab implementation.Comment: 25 pages, 10 figure

On the formulation of closest-point projection algorithms in elastoplasticity. Part I: The variational structure.

Report UCB/SEMM 2000-01 - Dept. of Civil Engineering - University of California at Berkeley, USAWe present in this paper the characterization of the variational structure behind the discrete equa- tions defining the closest-point projection approximation in elastoplasticity. Rate-independent and viscoplastic formulations are considered in the infinitesimal and the finite deformation range, the later in the context of isotropic finite strain multiplicative plasticity. Primal variational prin- ciples in terms of the stresses and stress-like hardening variables are presented first, followed by the formulation of dual principles incorporating explicitly the plastic multiplier. Augmented La- grangian extensions are also presented allowing a complete regularization of the problem in the constrained rate-independent limit. The variational structure identified in this paper leads to the proper framework for the development of new improved numerical algorithms for the integration of the local constitutive equations of plasticity as it is undertaken in Part II of this work.Preprin

Formulation of hybrid Trefftz finite element method for elastoplasticity

AbstractThe present investigation provides a hybrid Trefftz finite element approach for analysing elastoplastic problems. A dual variational functional is constructed and used to derive hybrid Trefftz finite element formulation for elastoplasticity of bulky solids. The formulation is applicable to either strain hardening or elastic-perfectly plastic materials. A solution algorithm based on initial stress formulation is introduced into the new element model. The performance of the proposed element model is assessed by three examples and comparison is made with results obtained by other approaches. The hybrid Trefftz finite element approach is demonstrated to be particularly suited for nonlinear analysis of two-dimensional elastoplastic problems