The design of an efficient, accurate and economical technique to solve elasto-plastic problems with a great number of degrees of freedom still remains a challenging task. Most of the difficulties in the case of elastoplasticity stem from the irreversibility of the plastic strains and from the discontinuous change of the material properties. When incorporating the plasticity model into the finite element computation process, approximations occur not only due to the numerical assumptions but also due to the basic incremental character of the plasticity constitutive law. Therefore, we need to explore an efficient and accurate integration algorithm for the plastic constitutive law, that should be able to deal with relatively large load increments without alteration of the solution accuracy. Also, if necessary, the use of sub-increments may be employed to obtain an improved approximation to the plastic flow.
Since the stresses at discrete points are integrated independently, we will circumvent the matrix assembly to gather the nodal forces by calculating elementary contributions element-by-element. The only drawback of the explicit elasto-plastic solution is potential loss of stability during the time integration process due to the yielding behavior and the associated stress correction. This gives us the task of determining the largest time step for the stability of the explicit time integration scheme for elasto-plastic problems. On the other hand, the element-by-element approach is very suitable and attractive for parallel processing. We will fully exploit the parallelism involved in the computations at the element or nodal level.