Characteristics and Computational Procedure in Softening Plasticity

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Abstract
Characteristics of finite element solutions involving strain‐softening plasticity are discussed with reference to strain localization and stability for simple uniaxial problems. The stability of localized and nonlocalized solutions is evaluated with the aid of incremental potential energy expressions. An algorithm is devised for the incremental solution based on implicit integration, and it is demonstrated that a good predictor expression is absolutely essential in order to capture the most stable solution. It is shown that if the finite element space is increased in a regular manner, those solutions that were believed to be stable become unstable. A couple of alternative predictors are proposed along with an algorithm that is both reliable and efficient, when applied to simple test problems. The number of iterations that are required is small, and it is shown that the behavior of the scheme is quite insensitive to the size of the load steps. The algorithm can be generalized to multiaxial stress conditions. In order to enhance localization tendencies in the multiaxial case, it is noted that higher order approximations may be adapted within the elements, or the elements may be aligned with incipient discontinuities that are detected by bifurcation analysis, for example.

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