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The superelastic constitutive model implemented in the commercial finite element code ABAQUS is verified using the method of exact solutions (MES). An analytical solution for uniaxial strain is first developed under a set of simplifying assumptions including von Mises-like transformation surfaces, symmetric transformation behavior, and monotonic loading. Numerical simulations are then performed, and simulation predictions are compared to the exact analytical solutions. Results reveal the superelasticity model agrees with the analytical solution to within one ten-thousandth of a percent (0.0001%) or less for stress and strain quantities of interest when using displacement-driven boundary conditions. Full derivation of the analytical solution is provided in an Appendix, and simulation input files and post-processing scripts are provided as supplemental material., Comment: 23 pages, 4 figures

This paper introduces a sharp-interface approach to simulating fluid-structure interaction involving flexible bodies described by general nonlinear material models and across a broad range of mass density ratios. This new flexible-body immersed Lagrangian-Eulerian (ILE) approach incorporates the geometrical and domain solution flexibility of the immersed boundary (IB) method with an accuracy comparable to body-fitted approaches that sharply resolve flows and stresses up to the fluid-structure interface. Unlike many IB methods, our ILE formulation uses distinct momentum equations for the fluid and solid subregions with a Dirichlet-Neumann coupling strategy that connects fluid and solid subproblems through simple interface conditions. We use a penalty method involving two representations of the fluid-structure interface. These two representations are connected by approximate Lagrange multiplier forces that impose kinematic interface conditions. This approach also enables the use of multi-rate time stepping, which allows us to take different time step sizes for the fluid and structure subproblems. Our fluid solver relies on an immersed interface method for discrete surfaces to impose stress jump conditions along complex interfaces. The dynamics of the volumetric structural mesh are determined using a standard finite element approach to large-deformation nonlinear elasticity via a nearly incompressible solid mechanics formulation. This formulation also readily accommodates compressible structures for cases in which part of the solid boundary does not contact the incompressible fluid. Comparisons are made with computational and experimental benchmarks. We also demonstrate the capabilities of this methodology by applying it to model the transport and capture of a cylindrical blood clot in an inferior vena cava filter.

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., Comment: 31 pages, 7 figures