A NUMERICAL-SOLUTION SCHEME FOR SOFTENING PROBLEMS INVOLVING TOTAL STRAIN CONTROL

Nonlinear structural problems in which material softening is present constitute a severe challenge to solution algorithms. Most of the existing computational codes are based on using an incremental procedure with iterations and suitable constraints. Among the constraints are load control, direct or indirect displacement control, and arc-length control involving a combination of load and displacement parameters. For many problems in which softening and localization occur, these algorithms fail at some point in the post-peak regime. In an attempt to remedy this problem, an alternative constraint condition is proposed whereby a combination of the total strain components is prescribed at the most critical point in the body. The critical point is defined to be that point where a suitable measure of strain is a maximum. Numerical solutions for both plane strain and plane stress problems are given to illustrate the ability of the procedure to capture post-peak responses of structures governed by materially nonlinear behavior. © 1990.