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Consistent tangent matrices for density-dependent finite plasticity models Agusti Perez-Foguet, Antonio Rodriguez-Ferran and Antonio Huerta*·t Departament de Matematiaz Aplicada III, E. TS. de Ingenieros de Caminos, Canales y Puertas, Universitat Politecniaz de Catalunya, Jordi Girona 1, E-08034 Barcelona, Spain SUMMARY The consistent tangent matrix for density-dependent plastic models within the theory of isotropic multiplica tive hyperelastoplasticity is presented here. Plastic equations expressed as general functions of the Kirchhoff stresses and density are considered. They include the Cauchy-based plastic models as a particular case. The standard exponential return-mapping algorithm is applied, with the density playing the role of a fixed parameter during the nonlinear plastic corrector problem. The consistent tangent matrix has the same structure as in the usual density-independent plastic models. A simple additional term takes into account the influence of the density on the plastic corrector problem. Quadratic convergence results are shown for several representative examples involving geomaterial and powder constitutive models. KEY WORDS: finite strain multiplicative plasticity; Cauchy stresses; consistent tangent operators; geomaterial plastic models; powder compaction; arbitrary Lagrangian-Eulerian (ALE) formulation 1. INTRODUCTION Consistent tangent matrices [1,2] are an essential ingredient for the efficient solution via implicit methods of complex problems in non-linear computational mechanics. Consistent tangent matrices are needed to solve the elastoplastic boundary value problem with quadratic conver gence, via a full Newton-Raphson linearization. They are computed from the consistent tangent moduli at Gauss-point level. The expression of the consistent tangent moduli for a wide variety of material models can be found in the literature. Consistent tangent moduli for different small-strain elastoplastic models and time-integration rules can be found in References [1-5] among many others. * Correspondence to: Antonio Huerta, Departament de Matematica Aplicada III, E.T.S. de Ingenieros de Caminos, Canales y Puertos, Universitat Politecnica de Catalunya, Jordi Girona 1, E-08034 Barcelona, Spain t E-mail: antonio[email protected] Contract grant sponsor: Ministerio de Educaci6n y Cultura; contract/grant number: TAP98-0421 Contract grant sponsor: Comisi6n Interministerial de Ciencia y Technologia; contract/grant number: 2FD97-1206 Arbitrary Lagrangian-Eulerian Simulation of Powder Compaction Processes, Pérez-Foguet, A., RodríguezFerran, A. and Huerta, A., International Journal of Forming Processes, Vol. 4 Issues 3, 4, pp. 535-549, 2001