Stress and strain‐driven algorithmic formulations for finite strain viscoplasticity for hybrid and standard finite elements

This work deals with the formulation and implementation of finite deformation viscoplasticity within the framework of stress-based hybrid finite element methods. Hybrid elements, which are based on a two-field variational formulation, are much less susceptible to locking than conventional displacement-based elements. The conventional return-mapping scheme cannot be used in the context of hybrid stress methods since the stress is known, and the strain and the internal plastic variables have to be recovered using this known stress field.We discuss the formulation and implementation of the consistent tangent tensor, and the return-mapping algorithm within the context of the hybrid method. We demonstrate the efficacy of the algorithm on a wide range of problems.

[1]  Peter Betsch,et al.  Numerical implementation of multiplicative elasto-plasticity into assumed strain elements with application to shells at large strains , 1999 .

[2]  C. Jog.  Derivatives of the Stretch, Rotation and Exponential Tensors in n-Dimensional Vector Spaces , 2006 .

[3]  M. Gellert,et al.  A mixed/hybrid FE formulation for solution of elasto-viscoplastic problems , 1992 .

[4]  J. Chaboche.  Constitutive equations for cyclic plasticity and cyclic viscoplasticity , 1989 .

[5]  J. C. Nadeau,et al.  Invariant Tensor-to-Matrix Mappings for Evaluation of Tensorial Expressions , 1998 .

[6]  K. Runesson,et al.  Computational modeling of inelastic large ratcheting strains , 2005 .

[7]  S. Atluri,et al.  On the existence and stability conditions for mixed-hybrid finite element solutions based on Reissner’s variational principle , 1985 .

[8]  A. Ibrahimbegovic,et al.  Viscoplasticity model at finite deformations with combined isotropic and kinematic hardening , 2000 .

[9]  L. Anand,et al.  Finite deformation constitutive equations and a time integrated procedure for isotropic hyperelastic—viscoplastic solids , 1990 .

[10]  S. Reese,et al.  On the theoretical and numerical modelling of Armstrong–Frederick kinematic hardening in the finite strain regime , 2004 .

[11]  Lallit Anand,et al.  The decomposition F = FeFp, material symmetry, and plastic irrotationality for solids that are isotropic-viscoplastic or amorphous , 2005 .

[12]  C. S. Jog,et al.  Non‐linear analysis of structures using high performance hybrid elements , 2006 .

[13]  M. Ortiz,et al.  A material‐independent method for extending stress update algorithms from small-strain plasticity to finite plasticity with multiplicative kinematics , 1992 .

[14]  Peter M. Pinsky,et al.  Operator split methods for the numerical solution of the elastoplastic dynamic problem , 1983 .

[15]  T. Pian,et al.  Rational approach for assumed stress finite elements , 1984 .

[16]  D. Steigmann,et al.  On the Evolution of Plasticity and Incompatibility , 2007 .

[17]  J. C. Simo,et al.  A framework for finite strain elastoplasticity based on maximum plastic dissipation and the multipli , 1988 .

[18]  J. C. Simo,et al.  A framework for finite strain elastoplasticity based on maximum plastic dissipation and the multiplicative decomposition. part II: computational aspects , 1988 .

[19]  Thomas J. R. Hughes,et al.  Unconditionally stable algorithms for quasi-static elasto/visco-plastic finite element analysis , 1978 .

[20]  G. Johnson,et al.  A discussion of stress rates in finite deformation problems , 1984 .

[21]  J. C. Simo,et al.  Algorithms for static and dynamic multiplicative plasticity that preserve the classical return mapping schemes of the infinitesimal theory , 1992 .

[22]  J. C. Simo,et al.  On a stress resultant geometrically exact shell model. Part V: Nonlinear plasticity: formulation and integration algorithms , 1992 .

[23]  G. Alfano,et al.  A general approach to the evaluation of consistent tangent operators for rate-independent elastoplasticity , 1998 .

[24]  J. C. Simo,et al.  Consistent tangent operators for rate-independent elastoplasticity☆ , 1985 .

[25]  L. Rosati,et al.  A return map algorithm for general isotropic elasto/visco‐plastic materials in principal space , 2004 .

[26]  W. N. Liu,et al.  A re-formulation of the exponential algorithm for finite strain plasticity in terms of cauchy stresses , 1999 .

[27]  Bob Svendsen,et al.  On the modelling of anisotropic elastic and inelastic material behaviour at large deformation , 2001 .

[28]  Klaus-Jürgen Bathe,et al.  A hyperelastic‐based large strain elasto‐plastic constitutive formulation with combined isotropic‐kinematic hardening using the logarithmic stress and strain measures , 1990 .

[29]  Adnan Ibrahimbegovic,et al.  Equivalent spatial and material descriptions of finite deformation elastoplasticity in principal axes , 1994 .

[30]  Robert L. Taylor,et al.  Complementary mixed finite element formulations for elastoplasticity , 1989 .

[31]  Theodore H. H. Pian,et al.  Relations between incompatible displacement model and hybrid stress model , 1986 .