We introduce an immersed meshfree formulation for modeling heterogeneous materials with flexible non-body-fitted discretizations, approximations, and quadrature rules. The interfacial compatibility condition is imposed by a volumetric constraint, which avoids a tedious contour integral for complex material geometry. The proposed immersed approach is formulated under a variational multiscale based formulation, termed the variational multiscale immersed method (VMIM). Under this framework, the solution approximation on either the foreground or the background can be decoupled into coarse-scale and fine-scale in the variational equations, where the fine-scale approximation represents a correction to the residual of the coarse-scale equations. The resulting fine-scale solution leads to a residual-based stabilization in the VMIM discrete equations. The employment of reproducing kernel (RK) approximation for the coarse- and fine-scale variables allows arbitrary order of continuity in the approximation, which is particularly advantageous for modeling heterogeneous materials. The effectiveness of VMIM is demonstrated with several numerical examples, showing accuracy, stability, and discretization efficiency of the proposed method.
This is an addendum to the Sierra/SolidMechanics 4.58 User's Guide that documents additional capabilities available only in alternate versions of the Sierra/SolidMechanics (Sierra/SM) code. These alternate versions are enhanced to provide capabilities that are regulated under the U.S. Department of State's International Traffic in Arms Regulations (ITAR) export control rules. The ITAR regulated codes are only distributed to entities that comply with the ITAR export control requirements. The ITAR enhancements to Sierra/SM include material models with an energy-dependent pressure response (appropriate for very large deformations and strain rates) and capabilities for blast modeling. This document is an addendum only; the standard Sierra/SolidMechanics 4.58 User's Guide should be referenced for most general descriptions of code capability and use.
This user’s guide documents capabilities in Sierra/SolidMechanics which remain “in-development” and thus are not tested and hardened to the standards of capabilities listed in Sierra/SM 4.58 User’s Guide. Capabilities documented herein are available in Sierra/SM for experimental use only until their official release. These capabilities include, but are not limited to, novel discretization approaches such as peridynamics and the reproducing kernel particle method (RKPM), numerical fracture and failure modeling aids such as the extended finite element method (XFEM) and /-integral, explicit time step control techniques, dynamic mesh rebalancing, as well as a variety of new material models and finite element formulations
This is an addendum to the Sierra/SolidMechanics 4.56 User's Guide that documents additional capabilities available only in alternate versions of the Sierra/SolidMechanics (Sierra/SM) code. These alternate versions are enhanced to provide capabilities that are regulated under the U.S. Department of State's International Traffic in Arms Regulations (ITAR) export control rules. The ITAR regulated codes are only distributed to entities that comply with the ITAR export control requirements. The ITAR enhancements to Sierra/SM include material models with an energy-dependent pressure response (appropriate for very large deformations and strain rates) and capabilities for blast modeling. This document is an addendum only; the standard Sierra/SolidMechanics 4.56 User's Guide should be referenced for most general descriptions of code capability and use.
This user's guide documents capabilities in Sierra/SolidMechanics which remain "in-development" and thus are not tested and hardened to the standards of capabilities listed in Sierra/SM 4.56 User's Guide. Capabilities documented herein are available in Sierra/SM for experimental use only until their official release. These capabilities include, but are not limited to, novel discretization approaches such as peridynamics and the reproducing kernel particle method (RKPM), numerical fracture and failure modeling aids such as the extended finite element method (XFEM) and J-integral, explicit time step control techniques, dynamic mesh rebalancing, as well as a variety of new material models and finite element formulations.
Presented in this document are the theoretical aspects of capabilities contained in the Sierra/SM code. This manuscript serves as an ideal starting point for understanding the theoretical foundations of the code. For a comprehensive study of these capabilities, the reader is encouraged to explore the many references to scientific articles and textbooks contained in this manual. It is important to point out that some capabilities are still in development and may not be presented in this document. Further updates to this manuscript will be made as these capabilities come closer to production level.
Sierra/SolidMechanics (Sierra/SM) is a Lagrangian, three-dimensional finite element analysis code for solids and structures subjected to extensive contact and large deformations, encompassing explicit and implicit dynamic as well as quasistatic loading regimes. This document supplements the primary Sierra/SM 4.56 User’s Guide, describing capabilities specific to Goodyear analysis use cases, including additional implicit solver options, material models, finite element formulations, and contact settings.
We propose new projection methods for treating near-incompressibility in small and large deformation elasticity and plasticity within the framework of particle and meshfree methods. Using the B¯ and F¯ techniques as our point of departure, we develop projection methods for the conforming reproducing kernel method and the immersed-particle or material point-like methods. The methods are based on the projection of the dilatational part of the appropriate measure of deformation onto lower-dimensional approximation spaces, according to the traditional B¯ and F¯ approaches, but tailored to meshfree and particle methods. The presented numerical examples exhibit reduced stress oscillations and are free of volumetric locking and hourglassing phenomena.
The Waste Isolation Pilot Plant (WIPP) is a geologic repository for defense-related nuclear waste. If left undisturbed, the virtually impermeable rock salt surrounding the repository will isolate the nuclear waste from the biosphere. If humans accidentally intrude into the repository in the future, then the likelihood of a radionuclide release to the biosphere will depend significantly on the porosity and permeability of the repository itself. Room ceilings and walls at the WIPP tend to collapse over time, causing rubble piles to form on floors of empty rooms. The surrounding rock formation will gradually compact these rubble piles until they eventually become solid salt, but the length of time for a rubble pile to reach a certain porosity and permeability is unknown. This report details the first efforts to build models to predict the porosity and permeability evolution of an empty room as it closes. Conventional geomechanical numerical methods would struggle to model empty room collapse and rubble pile consolidation, so three different meshless methods, the Immersed Isogeometric Analysis Meshfree, Reproducing Kernel Particle Method (RKPM), and the Conformal Reproducing Kernel method, were assessed. First, the meshless methods and the finite element method each simulated gradual room closure, without ceiling or wall collapse. All three methods produced equivalent room closure predictions with comparable computational speed. Second, the Immersed Isogeometric Analysis Meshfree method and RKPM simulated two-dimensional empty room collapse and rubble pile consolidation. Both methods successfully simulated large viscoplastic deformations, fracture, and rubble pile rearrangement to produce qualitatively realistic results. In addition to geomechanical simulations, the flow channels in damaged salt and crushed salt were measured using micro-computed tomography, and input into a computational fluid dynamics simulation to predict the salt's permeability. Although room for improvement exists, the current simulation approaches appear promising.
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.
Window functions provide a base for the construction of approximation functions in many meshfree methods. They control the smoothness and extent of the approximation functions and are commonly defined using Euclidean distances which helps eliminate the need for a meshed discretization, simplifying model development for some classes of problems. However, for problems with complicated geometries such as nonconvex or multi-body domains, poor solution accuracy and convergence can occur unless the extents of the window functions, and thus approximation functions, are carefully controlled, often a time consuming or intractable task. In this paper, we present a method to provide more control in window function design, allowing efficient and systematic handling of complex geometries. “Conforming” window functions are constructed using Bernstein–Bézier splines defined on local triangulations with constraints imposed to control smoothness. Graph distances are used in conjunction with Euclidean metrics to provide adequate information for shaping the window functions. The conforming window functions are demonstrated using the Reproducing Kernel Particle Method showing improved accuracy and convergence rates for problems with challenging geometries. Conforming window functions are also demonstrated as a means to simplify the imposition of essential boundary conditions.
The Reproducing Kernel Particle Method (RKPM), a meshfree method, has been implemented in Sandia's Sierra/SolidMechanics in a collaboration between Sandia and the University of California San Diego's Center for Extreme Events Research (UCSD/CEER). Meshfree methods, like RKPM, have an advantage over mesh-based methods, like the Finite Element Method (FEM), in applications where achieving or maintaining a quality mesh becomes burdensome or impractical. For example, using FEM for problems with very large deformations will result in poor element Jacobians which causes problems with the parametric mapping. RKPM constructs the approximation functions in the physical domain, circumventing the parametric mapping issue. Also, reconstructing the approximation functions at very large deformations is straight-forward. RKPM has an advantage over traditional meshfree methods such as Smoothed-Particle Hydrodynamics (SPH) due to its ability to reproduce linear or higher-order functions exactly. This removes the tensile instabilities that are present in SPH and allows preservation of angular momentum. The point of this memo is to explore the capabilities and limitations of the current implementation by testing it on three different applications: 1) a quasi-static ductile shearing problem 2) a dynamic concrete panel perforation problem and 3) a set of dynamic metal panel perforation problems. In summary, areas where RKPM appears to be a promising alternative to current methods have been identified. Also, outstanding inefficiencies and issues (bugs) with code are noted, ways to improve the capabilities using material from literature are mentioned and areas deserving of new research are highlighted.