A sub-stepping approach for elasto-plasticity with rotational hardening

Within the framework of the finite element method, this paper presents new algorithms implementing implicit stress integration and consistent tangent matrix calculations for an elasto-plastic model with rotational hardening. The sub-stepping technique is used for both the numerical integration of the constitutive relations and determination of the consistent tangent matrix in order to overcome the convergence difficulty arising from the complexity of the elasto-plastic model with rotational hardening. The integration of the constitutive relations and the computation of the consistent tangent matrix are incorporated into a unique procedure. Numerical tests are carried out and discussed to demonstrate the global accuracy and stability of the presented algorithms.

[1]  Ronaldo I. Borja,et al.  Cam-Clay plasticity, Part II: implicit integration of constitutive equation based a nonlinear elastic stress predictor , 1991 .

[2]  N. Bićanić,et al.  Computational aspects of a softening plasticity model for plain concrete , 1996 .

[3]  Koichi Hashiguchi,et al.  Elastoplastic constitutive equation of soils with the subloading surface and the rotational hardening , 1998 .

[4]  Ronaldo I. Borja,et al.  Cam-Clay plasticity, part I: implicit integration of elastoplastic constitutive relations , 1990 .

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

[6]  T. Hughes.  Numerical Implementation of Constitutive Models: Rate-Independent Deviatoric Plasticity , 1984 .

[7]  Wolfgang Ehlers,et al.  A single-surface yield function for geomaterials , 1995 .

[8]  J. W. Wissmann,et al.  Efficient elastic-plastic finite element analysis with higher order stress-point algorithms , 1983 .

[9]  Stress-Strain Behaviour of Cohesionless Soils Experiments, Theory and Numerical Computations , 1998 .

[10]  D. Muir Wood,et al.  A new approach to anisotropic, bounding surface plasticity: general formulation and simulations of natural and reconstituted clay behaviour , 2001 .

[11]  Antonio Huerta,et al.  Consistent tangent matrices for substepping schemes , 2001 .

[12]  Scott W. Sloan,et al.  Substepping schemes for the numerical integration of elastoplastic stress–strain relations , 1987 .

[13]  R. F. Kulak,et al.  Accurate Numerical Solutions for Elastic-Plastic Models , 1979 .

[14]  I. F. Collins,et al.  A theoretical framework for constructing elastic/plastic constitutive models of triaxial tests , 2002 .

[15]  Scott W. Sloan,et al.  AN AUTOMATIC LOAD STEPPING ALGORITHM WITH ERROR CONTROL , 1996 .

[16]  S. Sloan,et al.  Refined explicit integration of elastoplastic models with automatic error control , 2001 .

[17]  Olaf Kolditz,et al.  Finite element analysis of poro-elastic consolidation in porous media: Standard and mixed approaches , 2006 .

[18]  David M. Potts,et al.  An evaluation of substepping and implicit stress point algorithms , 1994 .