A velocity approach to finite element calculation of elastoplastic and viscoplastic deformation processes

The constitutive equations for the deformation of elastoplastic, viscoplastic or compressible materials are presented for the small strain approximation and for the large strain theory of Hill. A velocity approach is proposed for time discretization, which leads to a second order approximation for small strain, and an incrementally objective second order approximation for large deformation processes. Two other quasi second order formulations are discussed. The finite element space discretization is outlined and the solution procedure is described.

[1]  J. Nagtegaal,et al.  Some computational aspects of elastic-plastic large strain analysis , 1981 .

[2]  David Bushnell,et al.  A STRATEGY FOR THE SOLUTION OF PROBLEMS INVOLVING LARGE DEFLECTIONS, PLASTICITY AND CREEP , 1977 .

[3]  C. H. Lee,et al.  New Solutions to Rigid-Plastic Deformation Problems Using a Matrix Method , 1973 .

[4]  L. M. Taylor,et al.  Some computational aspects of large deformation, rate-dependent plasticity problems , 1983 .

[5]  D. M. Tracey,et al.  Computational fracture mechanics , 1973 .

[6]  T. Hsu,et al.  An integrated load increment method for finite elasto–plastic stress analysis , 1980 .

[7]  G. Strang,et al.  The solution of nonlinear finite element equations , 1979 .

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

[9]  Satya N. Atluri,et al.  Objectivity of incremental constitutive relations over finite time steps in computational finite deformation analyses , 1983 .

[10]  P. Pinsky,et al.  Numerical integration of rate constitutive equations in finite deformation analysis , 1983 .

[11]  J. Chenot,et al.  An implicit incrementally objective formulation for the solution of elastoplastic problems at finite strain by the F.E.M. , 1986 .

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

[13]  Peter Hartley,et al.  A new linearized expression for strain increment in finite-element analyses of deformations involving finite rotation , 1986 .

[14]  J. C. Marques,et al.  Implicit-explicit time integration in quasistatic elastoviscoplasticity using finite and infinite elements , 1984 .

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

[16]  Rodney Hill,et al.  Some basic principles in the mechanics of solids without a natural time , 1959 .

[17]  O. C. Zienkiewicz,et al.  Elasto‐plastic solutions of engineering problems ‘initial stress’, finite element approach , 1969 .

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

[19]  Y. Yamada,et al.  Plastic stress-strain matrix and its application for the solution of elastic-plastic problems by the finite element method , 1968 .

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

[21]  Graham H. Powell,et al.  Evaluation of solution schemes for nonlinear structures , 1978 .

[22]  Nguyen Quoc Son.  On the elastic plastic initial‐boundary value problem and its numerical integration , 1977 .

[23]  T. Hughes,et al.  Finite rotation effects in numerical integration of rate constitutive equations arising in large‐deformation analysis , 1980 .

[24]  Ian P. King,et al.  Elastic-plastic analysis of two-dimensional stress systems by the finite element method , 1967 .

[25]  Jean-Loup Chenot,et al.  Finite element formulations for non‐steady‐state large viscoplastic deformation , 1985 .