Publications / SAND Report

An Agile Design-to-Simulation Workflow Using a New Conforming Moving Least Squares Method

Koester, Jacob K.; Tupek, Michael R.; Mitchell, Scott A.

This report summarizes the accomplishments and challenges of a two year LDRD effort focused on improving design-to-simulation agility. The central bottleneck in most solid mechanics simulations is the process of taking CAD geometry and creating a discretization of suitable quality, i.e., the "meshine effort. This report revisits meshfree methods and documents some key advancements that allow their use on problems with complex geometries, low quality meshes, nearly incompressible materials or that involve fracture. The resulting capability was demonstrated to be an effective part of an agile simulation process by enabling rapid discretization techniques without increasing the time to obtain a solution of a given accuracy. The first enhancement addressed boundary-related challenges associated with meshfree methods. When using point clouds and Euclidean metrics to construct approximation spaces, the boundary information is lost, which results in low accuracy solutions for non-convex geometries and mate rial interfaces. This also complicates the application of essential boundary conditions. The solution involved the development of conforming window functions which use graph and boundary information to directly incorporate boundaries into the approximation space. The next enhancement was a procedure for producing a quality approximation with a low quality mesh. Unlike, the finite element method, meshfree approximation spaces do not require a mesh. However, meshes can be useful in providing domain boundary information and performing domain integration. A process was developed which aggregates low quality elements to create polyhedra of agreeable quality for domain integration. Stable time increments for transient dynamic simulations were observed to be up to 1000x larger than finite element simulations and solution quality and robustness were vastly superior. Obtaining a solution which is free of nonphysical displacement or pressure oscillations is a challenge for many methods when simulating nearly incompressible materials. Existing nodally integrated meshfree methods suffer from this limitation as well. New techniques were developed that combine B / F methods and the strain smoothing technique used in nodal integration to provide agreeable solutions for problems with nearly incompressible materials. The last major contribution enabled efficient simulations of material fracture with mass conservation. An inter-particle connectivity degradation approach was developed using ideas from peridynamics and cohesive zone modeling to disassociate nodes when fracture conditions are met. The method can, in principal, be applied to any material model with a specified failure criterion. For a mode-I ductile crack propagation problem, the method demonstrates mesh-size independent behavior without the particle instabilities near the fracture surface that are common to other particle methods. Addressing the aforementioned challenges of meshfree methods opens the approach to a broader class of problems and enables an agile simulation development process for problems of interest to Sandia.