Plasticity computations using the Mohr—Coulomb yield criterion

The paper describes the derivation and application of a range of numerical algorithms for implementing the Mohr—Coulomb yield criterion in a non‐linear finite element computer program. Emphasis is placed on the difficulties associated with the corners of the yield surface. In contrast to the more conventional forward‐Euler procedures, a backward‐Euler integration technique is adopted. A range of methods, including a ‘consistent approach’ are used to derive the tangent modular matrix. Numerical experiments are presented which involve solution algorithms including the modified and full Newton—Raphson procedures, ‘line‐searches’ and the arc‐length method. It is shown that the introduction of efficient integration and tangency algorithms can lead to very substantial improvements in the convergence characteristics.

[1]  Jose Couto Marques,et al.  Stress computation in elastoplasticity , 1984 .

[2]  J. Nagtegaal.  On the implementation of inelastic constitutive equations with special reference to large deformation problems , 1982 .

[3]  M. A. Crisfield,et al.  Accelerating and damping the modified Newton-Raphson method , 1984 .

[4]  C. Nyssen.  AN EFFICIENT AND ACCURATE ITERATIVE METHOD, ALLOWING LARGE INCREMENTAL STEPS, TO SOLVE ELASTO-PLASTIC PROBLEMS , 1981 .

[5]  Scott W. Sloan,et al.  Removal of singularities in tresca and mohr–coulomb yield functions , 1986 .

[6]  Michael Ortiz,et al.  An analysis of a new class of integration algorithms for elastoplastic constitutive relations , 1986 .

[7]  D. C. Drucker,et al.  Soil mechanics and plastic analysis or limit design , 1952 .

[8]  M. Crisfield.  A FAST INCREMENTAL/ITERATIVE SOLUTION PROCEDURE THAT HANDLES "SNAP-THROUGH" , 1981 .

[9]  M. Crisfield,et al.  Nonlinear Analysis of Concrete and Masonry Structures , 1986 .

[10]  G. Gudehus,et al.  Elastoplastische Stoffgleichungen für trockenen Sand , 1973 .

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

[12]  W. T. Koiter.  Stress-strain relations, uniqueness and variational theorems for elastic-plastic materials with a singular yield surface , 1953 .

[13]  O. C. Zienkiewicz,et al.  Elasto‐plastic stress analysis. A generalization for various contitutive relations including strain softening , 1972 .

[14]  E. P. Popov,et al.  Accuracy and stability of integration algorithms for elastoplastic constitutive relations , 1985 .

[15]  R. D. Krieg,et al.  Accuracies of Numerical Solution Methods for the Elastic-Perfectly Plastic Model , 1977 .

[16]  M. Abouaf,et al.  An implicit and incremental formulation for the solution of elastoplastic problems by the finite element method , 1986 .

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

[18]  R. de Borst,et al.  Non-linear analysis of frictional materials , 1986 .