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Return-mapping algorithms for associative isotropic hardening plasticity using conic optimization. (English) Zbl 1481.74082

Summary: We present a mathematical programming approach for elastoplastic constitutive initial value problems. Consideration of the associative plasticity and a linear isotropic hardening model allowed us to formulate the local discrete constitutive equations as conic programs. Specifically, we demonstrate that implicit return-mapping schemes for well-known yield criteria, such as the Rankine, von Mises, Tresca, Drucker-Prager, and Mohr-Coulomb criteria, can be expressed as second-order and semidefinite conic programs. Additionally, we propose a novel scheme for the numerical evaluation of the consistent elastoplastic tangent operator based on a first-order parameter derivative of the optimal solutions.

MSC:

74C05 Small-strain, rate-independent theories of plasticity (including rigid-plastic and elasto-plastic materials)
65K10 Numerical optimization and variational techniques
90C22 Semidefinite programming
90C90 Applications of mathematical programming
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