Verification results for Sierra/SM using inexact reference solutions have often exhibited unsatisfactory convergence behavior. With an understanding of the convergence behavior for these types of tests, one can avoid falsely attributing pathologies of the test with incorrectness of the code. Simple theoretical results highlight that for an inexact reference solution two conditions must be met to observe asymptotic convergence. These conditions, and the resulting types of convergence behaviors, are further illustrated with graphical examples depicting the exact, inexact reference, and sequence of numerical solutions as vectors (in a function space). A stress concentration problem is adopted to contrast convergence behaviors when using inexact (classical linear elastic) and exact (manufactured) reference solutions. Convergence is not initially attained with the classical solution. Convergence with the manufactured solution indicates the convergence failure with the classical reference did not result from code error and provides insight on how for this problem asymptotic convergence could be attained with the classical reference solution by modifying the computational models.
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 fin ite deformation, hyperelastic problems is presented that h as 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 valu e problem . The last problem combines two approaches that can significantly simplify the solution of some hypoelasticity problems, which require integrat ion 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.
Solution verification is the process of verifying the solution of a finite element analysis by performing a series of analyses on meshes of increasing mesh densities, to determine if the solution is converging. Solution verification has historically been too expensive, relying upon refinement templates resulting in an 8X multiplier in the number of elements. For even simple convergence studies, the 8X and 64X meshes must be solved, quickly exhausting computational resources. In this paper, we introduce Mesh Scaling, a new global mesh refinement technique for building series of all-hexahedral meshes for solution verification, without the 8X multiplier. Mesh Scaling reverse engineers the block decomposition of existing all-hexahedral meshes followed by remeshing the block decomposition using the original mesh as the sizing function multiplied by any positive floating number (e.g. 0.5X, 2X, 4X, 6X, etc.), enabling larger series of meshes to be constructed with fewer elements, making solution verification tractable.
A method is described for applying a sequence of peridynamic models with different length scales concurrently to subregions of a body. The method allows the smallest length scale, and therefore greatest spatial resolution, to be focused on evolving defects such as cracks. The peridynamic horizon in each of the models is half of that of the next model in the sequence. The boundary conditions on each model are provided by the solution predicted by the model above it. Material property characterization for each model is derived by coarse-graining the more detailed resolution in the model below it. Implementation of the multiscale method in the PDMS code is described. Examples of crack growth modeling illustrate the ability of the method to reproduce the main features of crack growth seen in a model with uniformly small resolution. Comparison of the multiscale model results with XFEM and cohesive elements is also given for a crack growth problem.
Surface effects are critical to the accurate simulation of electromagnetics (EM) as current tends to concentrate near material surfaces. Sandia EM applications, which include exploding bridge wires for detonator design, electromagnetic launch of flyer plates for material testing and gun design, lightning blast-through for weapon safety, electromagnetic armor, and magnetic flux compression generators, all require accurate resolution of surface effects. These applications operate in a large deformation regime, where body-fitted meshes are impractical and multimaterial elements are the only feasible option. State-of-the-art methods use various mixture models to approximate the multi-physics of these elements. The empirical nature of these models can significantly compromise the accuracy of the simulation in this very important surface region. We propose to substantially improve the predictive capability of electromagnetic simulations by removing the need for empirical mixture models at material surfaces. We do this by developing an eXtended Finite Element Method (XFEM) and an associated Conformal Decomposition Finite Element Method (CDFEM) which satisfy the physically required compatibility conditions at material interfaces. We demonstrate the effectiveness of these methods for diffusion and diffusion-like problems on node, edge and face elements in 2D and 3D. We also present preliminary work on h -hierarchical elements and remap algorithms.