Procedures to build trust in nonlinear elastoplastic integration algorithm: solution and code verification

In the last decades, with the development of a number of nonlinear elastic–plastic integration algorithms, the correctness or accuracy of the underlying solution becomes the main concern, in both academia and industry. Correctness or accuracy can be estimated (and improved) using verification. Verification is one of the main procedures to build trust in the numerical modeling of any phenomena. A full verification process comprises (a) solution verification (calculation verification) and (b) code verification. Presented in this paper are verification procedures for constitutive, elastic–plastic integration algorithms, as used in computational nonlinear solid mechanics. Both explicit and implicit integration algorithms for elastic–plastic constitutive equations are verified using existing and new developed verification technique. Verification techniques used include prescribed solution forcing and Richardson extrapolation. In addition, grid convergence index is applied to estimate the algorithmic uncertainty during the integration process. Verification of elastic–plastic integration algorithms is applied to a number of material models: from simple von Mises perfectly plastic to sophisticated hyperbolic Drucker–Prager with nonlinear Armstrong–Frederick rotational kinematic hardening. Besides, algorithmic uncertainty is estimated with both associative and non-associative material model. In addition, caveats and pitfalls to consider in the code/solution verification processes are deeply discussed.