Duality results and regularization schemes for Prandtl--Reuss perfect plasticity

We consider the time-discretized problem of the quasi-static evolution problem in perfect plasticity posed in a non-reflexive Banach space and we derive an equivalent version in a reflexive Banach space. A primal-dual stabilization scheme is shown to be consistent with the initial problem. As a consequence, not only stresses, but also displacement and strains are shown to converge to a solution of the original problem in a suitable topology. This scheme gives rise to a well-defined Fenchel dual problem which is a modification of the usual stress problem in perfect plasticity. The dual problem has a simpler structure and turns out to be well-suited for numerical purposes. For the corresponding subproblems an efficient algorithmic approach in the infinite-dimensional setting based on the semismooth Newton method is proposed

Finite element modeling of thermo-hydromechanically (THM) coupled problems in frozen ground engineering: state-of-the-art

Fully coupled Thermo-Hydro-Mechanical (THM) modeling has been widely studied in various areas of geomechanics, owing to the multiphase nature of geomaterials. Several researches have dealt with THM coupled modeling of geomaterials in high temperature regimes, but a limited work is available for geomaterials in low temperature regimes. A review and summary of existing work in the literature on THM coupled modeling of frozen soils is presented here. THM coupled modeling in general and its applications are pointed out. The basic governing equations of a coupled THM model in general form, namely mass, momentum and energy balance equations, are discussed. A review of fully coupled models is made and the numerical aspects of THM modeling are briefly discussed. A mechanical constitutive model makes up an important component of a fully coupled THM model and a brief review of existing constitutive models for frozen soils is presented. The models reviewed range from elastoplastic models to viscoplastic or creep and damage coupled models. Some models that consider different approaches from the plasticity framework are briefly reviewed. The state-of-the-art is summarized by pointing out the main aspects of THM coupled modeling and directions for future work

An enhanced Lemaitre model formulation for materials processing damage computation

The original publication is available at www.springerlink.comInternational audienceThe Lemaitre damage model is now widely used to deal with coupled damage analyses for various mechanical applications. In this article, different extensions of the model are presented and discussed to deal with complex multiaxial configurations--such as multi-stages bulk forming processes. A specific treatment is done to account for compressive damage growth, and a stress triaxiality cut-off value is considered to avoid any damage evolution below a critical negative triaxiality. The damage potential is also modified to deal with highly ductile materials, and the plastic strain is split into a negative part and a positive part to differentiate damage growth for compressive states of stress and for tensile states of stress. Finally, an anisotropic damage approach based on the comparison between grain flow orientation and principal loading directions is defined. A combination of these extensions is achieved within a single Lemaitre formulation. Application on different examples show the robustness and accuracy of the model defined in this paper

Gemischte Least-Squares-FEM für Elastoplastizität

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Nonlinear solid mechanics analysis using the parallel selective element-free Galerkin method

A variety of meshless methods have been developed in the last fifteen years with an intention to solve practical engineering problems, but are limited to small academic problems due to associated high computational cost as compared to the standard finite element methods (FEM). The main objective of this thesis is the development of an efficient and accurate algorithm based on meshless methods for the solution of problems involving both material and geometrical nonlinearities, which are of practical importance in many engineering applications, including geomechanics, metal forming and biomechanics. One of the most commonly used meshless methods, the element-free Galerkin method (EFGM) is used in this research, in which maximum entropy shape functions (max-ent) are used instead of the standard moving least squares shape functions, which provides direct imposition of the essential boundary conditions. Initially, theoretical background and corresponding computer implementations of the EFGM are described for linear and nonlinear problems. The Prandtl-Reuss constitutive model is used to model elasto-plasticity, both updated and total Lagrangian formulations are used to model finite deformation and consistent or algorithmic tangent is used to allow the quadratic rate of asymptotic convergence of the global Newton-Raphson algorithm. An adaptive strategy is developed for the EFGM for two- and three-dimensional nonlinear problems based on the Chung & Belytschko error estimation procedure, which was originally proposed for linear elastic problems. A new FE-EFGM coupling procedure based on max-ent shape functions is proposed for linear and geometrically nonlinear problems, in which there is no need of interface elements between the FE and EFG regions or any other special treatment, as required in the most previous research. The proposed coupling procedure is extended to become adaptive FE-EFGM coupling for two- and three-dimensional linear and nonlinear problems, in which the Zienkiewicz & Zhu error estimation procedure with the superconvergent patch recovery method for strains and stresses recovery are used in the FE region of the problem domain, while the Chung & Belytschko error estimation procedure is used in the EFG region of the problem domain. Parallel computer algorithms based on distributed memory parallel computer architecture are also developed for different numerical techniques proposed in this thesis. In the parallel program, the message passing interface library is used for inter-processor communication and open-source software packages, METIS and MUMPS are used for the automatic domain decomposition and solution of the final system of linear equations respectively. Separate numerical examples are presented for each algorithm to demonstrate its correct implementation and performance, and results are compared with the corresponding analytical or reference results