Method of Manufactured Solutions Code Verification of Elastostatic Solid Mechanics Problems in a Commercial Finite Element Solver
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Much progress has been made in advancing and standardizing verification, validation, and uncertainty quantification practices for computational modeling in recent decades. However, examples of rigorous code verification for solid mechanics problems in the literature remain scarce, particularly for commercial software and for the non-trivial large-deformation analyses and nonlinear materials typically needed to simulate medical devices. Here, we apply the method of manufactured solutions (MMS) to verify a commercial finite element code for elastostatic solid mechanics analyses using linear-elastic, hyperelastic (neo-Hookean), and quasi-hyperelastic (Hencky) constitutive models. Analytical source terms are generated using either Python/SymPy or Mathematica and are implemented in ABAQUS/Standard without modification to the solver source code. Source terms for the three constitutive models are found to vary nearly six orders of magnitude in the number of mathematical operations they contain. Refinement studies reveal second-order displacement convergence in response to mesh refinement for all constitutive models and first-order displacement convergence in response to increment refinement for the finite-strain problems. We also investigate the sensitivity of MMS convergence order to minor coding errors using an exploratory case. Code used to generate the MMS source terms and the input files for the simulations are provided as supplemental material.
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