Manufactured Solutions for Solid Mechanics Code Verification -- Hyperelastic Material Case

Abstract

Increased emphasis on computational simulation for NW qualification merits a corresponding increased diligence in verifying our codes. A manufactured solution process (implemented in Mathematica) for finite deformation, hyperelastic problems is presented that has been used to verify Sierra/SM for this class of problems. The process "manufactures a problem" given either a displacement field or motion map. Four test problems are examined; two provide sanity checks on symbolically calculated results, and two provide code verification results. While simple solutions from linear elasticity can be used to "seed" a manufactured solution, one from beam theory is shown to yield a n unexpectedly complex boundary value problem. The last problem combines two approaches that can significantly simplify the solution of some hypoelasticity problems, which require integration over time; a semi-manufactured approach is proposed and examined that yields the same observed rates of convergence as the classical approach at significantly reduced analytical effort.