Algorithm for the solution of internal variable problems in plasticity
Computer Methods in Applied Mechanics and Engineering
A finite element–mathematical programming method for elastoplastic contact problems with friction
Finite Elements in Analysis and Design
Lectures on modern convex optimization: analysis, algorithms, and engineering applications
Lectures on modern convex optimization: analysis, algorithms, and engineering applications
Smoothing Functions for Second-Order-Cone Complementarity Problems
SIAM Journal on Optimization
SIAM Journal on Optimization
An unconstrained smooth minimization reformulation of the second-order cone complementarity problem
Mathematical Programming: Series A and B
Computational Optimization and Applications
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In this paper we present a new approach for solving elastoplastic problems as second order cone complementarity problems (SOCCPs). Specially, two classes of elastoplastic problems, i.e. the J 2 plasticity problems with combined linear kinematic and isotropic hardening laws and the Drucker-Prager plasticity problems with associative or non-associative flow rules, are taken as the examples to illustrate the main idea of our new approach. In the new approach, firstly, the classical elastoplastic constitutive equations are equivalently reformulated as second order cone complementarity conditions. Secondly, by employing the finite element method and treating the nodal displacements and the plasticity multiplier vectors of Gaussian integration points as the unknown variables, we obtain a standard SOCCP formulation for the elastoplasticity analysis, which enables the using of general SOCCP solvers developed in the field of mathematical programming be directly available in the field of computational plasticity. Finally, a semi-smooth Newton algorithm is suggested to solve the obtained SOCCPs. Numerical results of several classical plasticity benchmark problems confirm the effectiveness and robustness of the SOCCP approach.