Implicit Damping Iterative Algorithm to Solve Elastoplastic Static and Dynamic Equations

Box 2

Increment iterative scheme (II).

For the th iteration:

We assume that , and , then execute the iterative loops by (24):

① Compute the total strain increments , stresses , yield function value , and the other coefficients.

② Compute by (13) and (18). If is very small (e.g. <1), let equal a high number (e.g. ), then obtain

  and by (24).

③ Determine the stress state: If , let .

④ Calculate the errors of and , and see if they satisfy the tolerance error requirement.

⑤ If not, repeat Steps  ①④, then conduct the th iteration, until achieving convergence.