Kumar Sambasivan, Shiv; Shashkov, Mikhail J.; Burton, Donald E. A cell-centered Lagrangian finite volume approach for computing elasto-plastic response of solids in cylindrical axisymmetric geometries. (English) Zbl 1286.74113 J. Comput. Phys. 237, 251-288 (2013). Summary: A finite volume cell-centered Lagrangian formulation is presented for solving large deformation problems in cylindrical axisymmetric geometries. Since solid materials can sustain significant shear deformation, evolution equations for stress and strain fields are solved in addition to mass, momentum and energy conservation laws. The total strain-rate realized in the material is split into an elastic and plastic response. The elastic and plastic components in turn are modeled using hypo-elastic theory. In accordance with the hypo-elastic model, a predictor-corrector algorithm is employed for evolving the deviatoric component of the stress tensor. A trial elastic deviatoric stress state is obtained by integrating a rate equation, cast in the form of an objective (Jaumann) derivative, based on Hooke’s law. The dilatational response of the material is modeled using an equation of state of the Mie-Grüneisen form. The plastic deformation is accounted for via an iterative radial return algorithm constructed from the \(J_{2}\) von Mises yield condition. Several benchmark example problems with non-linear strain hardening and thermal softening yield models are presented. Extensive comparisons with representative Eulerian and Lagrangian hydrocodes in addition to analytical and experimental results are made to validate the current approach. Cited in 11 Documents MSC: 74S10 Finite volume methods applied to problems in solid mechanics 74C05 Small-strain, rate-independent theories of plasticity (including rigid-plastic and elasto-plastic materials) 74D10 Nonlinear constitutive equations for materials with memory Keywords:Lagrangian; finite volume; hypo-elastic; elasto-plastic; cell-centered; mimetic; axisymmetric geometries; material strength; solid mechanics; hydrodynamics Software:LS-DYNA; DYNA3D; CAVEAT; HE-E1GODF PDFBibTeX XMLCite \textit{S. Kumar Sambasivan} et al., J. Comput. Phys. 237, 251--288 (2013; Zbl 1286.74113) Full Text: DOI