There are several engineering applications in which the assumptions of homogenization and scale separation may be violated, in particular, for metallic structures constructed through additive manufacturing. Instead of resorting to direct numerical simulation of the macroscale system with an embedded fine scale, an alternative approach is to use an approximate macroscale constitutive model, but then estimate the model-form error using a posteriori error estimation techniques and subsequently adapt the macroscale model to reduce the error for a given boundary value problem and quantity of interest. Here, we investigate this approach to multiscale analysis in solids with unseparated scales using the example of an additively manufactured metallic structure consisting of a polycrystalline microstructure that is neither periodic nor statistically homogeneous. As a first step to the general nonlinear case, we focus here on linear elasticity in which each grain within the polycrystal is linear elastic but anisotropic.
An improved electrical contact resistance (ECR) model for elastic rough electrode contact is proposed, incorporating the effects of asperity interactions and temperature rise by frictional and joule heating. The analytical simulation results show that the ECR decreases steeply at the beginning of the contact between Al and Cu. However, it becomes stabilized after reaching a specific contact force. It is also found that the longer elapsed sliding contact time, the higher ECR due to the increase in electrical resistivity of electrode materials by the frictional temperature rise at the interface. The effects of surface roughness parameters on ECR are studied through the 32 full-factorial design-of-experiment analysis. Based on the two representative roughness parameters, i.e., root-mean-square (rms) roughness and asperity radius, their individual and coupled effects on the saturated ECR are examined. The saturated ECR increases with the rms roughness for a rough machined surface condition, but it is hardly affected by the asperity radius. On the other hand, the saturated ECR increases with both the rms roughness and the asperity radius under a smooth thin film surface condition.
The 2020 Nonlinear Mechanics and Dynamics (NOMAD) Research Institute was successfully held from June 15 to July 30, 2020. NOMAD brings together participants with diverse technical backgrounds to work in small teams to cultivate new ideas and approaches in engineering mechanics and dynamics research. NOMAD provides an opportunity for researchers – especially early career researchers - to develop lasting collaborations that go beyond what can be established from the limited interactions at their institutions or at annual conferences. A total of 11 students participated in the seven-week long program held virtually due to the COVID-19 health pandemic. The students collaborated on one of four research projects that were developed by various mentors from Sandia National Laboratories, the University of New Mexico, and other academic and research institutions. In addition to the research activities, the students attended weekly technical seminars, various virtual tours, and socialized at virtual gatherings. At the end of the summer, the students gave a final technical presentation on their research findings. Many of the research discoveries made at NOMAD 2020 are published as proceedings at technical conferences and have direct alignment with the critical mission work performed at Sandia.
This study employs nonlinear ultrasonic techniques to track microstructural changes in additively manufactured metals. The second harmonic generation technique based on the transmission of Rayleigh surface waves is used to measure the acoustic nonlinearity parameter, β. Stainless steel specimens are made through three procedures: traditional wrought manufacturing, laser-powder bed fusion, and laser engineered net shaping. The β parameter is measured through successive steps of an annealing heat treatment intended to decrease dislocation density. Dislocation density is known to be sensitive to manufacturing variables. In agreement with fundamental material models for the dislocation-acoustic nonlinearity relationship in the second harmonic generation, β drops in each specimen throughout the heat treatment before recrystallization. Geometrically necessary dislocations (GNDs) are measured from electron back-scatter diffraction as a quantitative indicator of dislocations; average GND density and β are found to have a statistical correlation coefficient of 0.852 showing the sensitivity of β to dislocations in additively manufactured metals. Moreover, β shows an excellent correlation with hardness, which is a measure of the macroscopic effect of dislocations.
We develop a generalized stress inversion technique (or the generalized inversion method) capable of recovering stresses in linear elastic bodies subjected to arbitrary cuts. Specifically, given a set of displacement measurements found experimentally from digital image correlation (DIC), we formulate a stress estimation inverse problem as a partial differential equation-constrained optimization problem. We use gradient-based optimization methods, and we accordingly derive the necessary gradient and Hessian information in a matrix-free form to allow for parallel, large-scale operations. By using a combination of finite elements, DIC, and a matrix-free optimization framework, the generalized inversion method can be used on any arbitrary geometry, provided that the DIC camera can view a sufficient part of the surface. We present numerical simulations and experiments, and we demonstrate that the generalized inversion method can be applied to estimate residual stress.
A stable and nodally integrated meshfree formulation for modeling shock waves in fluids is developed. The reproducing kernel approximation is employed to discretize the conservation equations for compressible flow, and a flux vector splitting approach is applied to allow proper numerical treatments for the advection and pressure parts, respectively, based on the characteristics of each flux term. To capture the essential shock physics in fluids, including the Rankine–Hugoniot jump conditions and the entropy condition, local Riemann enrichment is introduced under the stabilized conforming nodal integration (SCNI) framework. Meanwhile, numerical instabilities associated with the advection flux are eliminated by adopting a modified upwind scheme. To further enhance accuracy, a MUSCL-type method is introduced in conjunction with an oscillation limiter to avoid Gibbs phenomenon and ensure monotonic piecewise linear reconstruction in the smooth region. The present meshfree formulation is free from tunable artificial parameters and is capable of capturing shock and rarefaction waves without over/undershoots. Several numerical examples are analyzed to demonstrate the effectiveness of the proposed MUSCL-SCNI approach in meshfree modeling of complex shock phenomena, including shock diffraction, shock–vortex interaction, and high energy explosion processes.
Meshfree methods for solid mechanics have been in development since the early 1990’s. Initial motivations included alleviation of the burden of mesh creation and the desire to overcome the limitations of traditional mesh-based discretizations for extreme deformation applications. Here, the accuracy and robustness of both meshfree and mesh-based Lagrangian discretizations are compared using manufactured extreme deformation fields. For the meshfree discretizations, both moving least squares and maximum entropy are considered. Quantitative error and convergence results are presented for the best approximation in the H1 norm.
General polyhedral discretizations offer several advantages over classical approaches consisting of standard tetrahedra and hexahedra. These include increased flexibility and robustness in the meshing of geometrically complex domains and higher-quality solutions for both finite element and finite volume schemes. Currently, the use of general polyhedra is hampered by the lack of general-purpose polyhedral meshing algorithms and software. One approach for generating polyhedral meshes is the use of tetrahedral subdivisions and dual-cell aggregation. In this approach, each tetrahedron of an existing tetrahedral mesh is subdivided using one of several subdivision schemes. Polyhedral-dual cells may then be formed and formulated as finite elements with shape functions obtained through the use of generalized barycentric coordinates. We explore the use of dual-cell discretizations for applications in nonlinear solid mechanics using a displacement-based finite element formulation. Verification examples are presented that yield optimal rates of convergence. Accuracy of the methodology is demonstrated via several nonlinear examples that include large deformation and plasticity.
Additive Manufacturing (AM) offers the opportunity to transform design, manufacturing, and qualification with its unique capabilities. AM is a disruptive technology, allowing the capability to simultaneously create part and material while tightly controlling and monitoring the manufacturing process at the voxel level, with the inherent flexibility and agility in printing layer-by-layer. AM enables the possibility of measuring critical material and part parameters during manufacturing, thus changing the way we collect data, assess performance, and accept or qualify parts. It provides an opportunity to shift from the current iterative design-build-test qualification paradigm using traditional manufacturing processes to design-by-predictivity where requirements are addressed concurrently and rapidly. The new qualification paradigm driven by AM provides the opportunity to predict performance probabilistically, to optimally control the manufacturing process, and to implement accelerated cycles of learning. Exploiting these capabilities to realize a new uncertainty quantification-driven qualification that is rapid, flexible, and practical is the focus of this paper.
Residual stress is a common result of manufacturing processes, but it is one that is often overlooked in design and qualification activities. There are many reasons for this oversight, such as lack of observable indicators and difficulty in measurement. Traditional relaxation-based measurement methods use some type of material removal to cause surface displacements, which can then be used to solve for the residual stresses relieved by the removal. While widely used, these methods may offer only individual stress components or may be limited by part or cut geometry requirements. Diffraction-based methods, such as X-ray or neutron, offer non-destructive results but require access to a radiation source. With the goal of producing a more flexible solution, this LDRD developed a generalized residual stress inversion technique that can recover residual stresses released by all traction components on a cut surface, with much greater freedom in part geometry and cut location. The developed method has been successfully demonstrated on both synthetic and experimental data. The project also investigated dislocation density quantification using nonlinear ultrasound, residual stress measurement using Electronic Speckle Pattern Interferometry Hole Drilling, and validation of residual stress predictions in Additive Manufacturing process models.
Crystal plasticity-finite element method (CP-FEM) is now widely used to understand the mechanical response of polycrystalline materials. However, quantitative mesh convergence tests and verification of the necessary size of polycrystalline representative volume elements (RVE) are often overlooked in CP-FEM simulations. Mesh convergence studies in CP-FEM models are more challenging compared to conventional finite element analysis (FEA) as they are not only computationally expensive but also require explicit discretization of individual grains using many finite elements. Resolving each grains within a polycrystalline domain complicates mesh convergence study since mesh convergence is strongly affected by the initial crystal orientations of grains and local loading conditions. In this work, large-scale CP-FEM simulations of single crystals and polycrystals are conducted to study mesh sensitivity in CP-FEM models. Various factors that may affect the mesh convergence in CP-FEM simulations, such as initial textures, hardening models and boundary conditions are investigated. In addition, the total number of grains required to obtain adequate RVE is investigated. This work provides a list of guidelines for mesh convergence and RVE generation in CP-FEM modeling.
We describe an approach to predict failure in a complex, additively-manufactured stainless steel part as defined by the third Sandia Fracture Challenge. A viscoplastic internal state variable constitutive model was calibrated to fit experimental tension curves in order to capture plasticity, necking, and damage evolution leading to failure. Defects such as gas porosity and lack of fusion voids were represented by overlaying a synthetic porosity distribution onto the finite element mesh and computing the elementwise ratio between pore volume and element volume to initialize the damage internal state variables. These void volume fraction values were then used in a damage formulation accounting for growth of these existing voids, while new voids were allowed to nucleate based on a nucleation rule. Blind predictions of failure are compared to experimental results. The comparisons indicate that crack initiation and propagation were correctly predicted, and that an initial porosity field superimposed as higher initial damage may provide a path forward for capturing material strength uncertainty. The latter conclusion was supported by predicted crack face tortuosity beyond the usual mesh sensitivity and variability in predicted strain to failure; however, it bears further inquiry and a more conclusive result is pending compressive testing of challenge-built coupons to de-convolute materials behavior from the geometric influence of significant porosity.
New manufacturing technologies such as additive manufacturing require research and development to minimize the uncertainties in the produced parts. The research involves experimental measurements and large simulations, which result in huge quantities of data to store and analyze. We address this challenge by alleviating the data storage requirements using lossy data compression. We select wavelet bases as the mathematical tool for compression. Unlike images, additive manufacturing data is often represented on irregular geometries and unstructured meshes. Thus, we use Alpert tree-wavelets as bases for our data compression method. We first analyze different basis functions for the wavelets and find the one that results in maximal compression and miminal error in the reconstructed data. We then devise a new adaptive thresholding method that is data-agnostic and allows a priori estimation of the reconstruction error. Finally, we propose metrics to quantify the global and local errors in the reconstructed data. One of the error metrics addresses the preservation of physical constraints in reconstructed data fields, such as divergence-free stress field in structural simulations. While our compression and decompression method is general, we apply it to both experimental and computational data obtained from measurements and thermal/structural modeling of the sintering of a hollow cylinder from metal powders using a Laser Engineered Net Shape process. The results show that monomials achieve optimal compression performance when used as wavelet bases. The new thresholding method results in compression ratios that are two to seven times larger than the ones obtained with commonly used thresholds. Overall, adaptive Alpert tree-wavelets can achieve compression ratios between one and three orders of magnitude depending on the features in the data that are required to preserve. These results show that Alpert tree-wavelet compression is a viable and promising technique to reduce the size of large data structures found in both experiments and simulations.
This SAND report fulfills the final report requirement for the Born Qualified Grand Challenge LDRD. Born Qualified was funded from FY16-FY18 with a total budget of ~$13M over the 3 years of funding. Overall 70+ staff, Post Docs, and students supported this project over its lifetime. The driver for Born Qualified was using Additive Manufacturing (AM) to change the qualification paradigm for low volume, high value, high consequence, complex parts that are common in high-risk industries such as ND, defense, energy, aerospace, and medical. AM offers the opportunity to transform design, manufacturing, and qualification with its unique capabilities. AM is a disruptive technology, allowing the capability to simultaneously create part and material while tightly controlling and monitoring the manufacturing process at the voxel level, with the inherent flexibility and agility in printing layer-by-layer. AM enables the possibility of measuring critical material and part parameters during manufacturing, thus changing the way we collect data, assess performance, and accept or qualify parts. It provides an opportunity to shift from the current iterative design-build-test qualification paradigm using traditional manufacturing processes to design-by-predictivity where requirements are addressed concurrently and rapidly. The new qualification paradigm driven by AM provides the opportunity to predict performance probabilistically, to optimally control the manufacturing process, and to implement accelerated cycles of learning. Exploiting these capabilities to realize a new uncertainty quantification-driven qualification that is rapid, flexible, and practical is the focus of this effort.
In engineering practice, models are typically kept as simple as possible for ease of setup and use, computational efficiency, maintenance, and overall reduced complexity to achieve robustness. In solid mechanics, a simple and efficient constitutive model may be favored over one that is more predictive, but is difficult to parameterize, is computationally expensive, or is simply not available within a simulation tool. In order to quantify the modeling error due to the choice of a relatively simple and less predictive constitutive model, we adopt the use of a posteriori model-form error-estimation techniques. Based on local error indicators in the energy norm, an algorithm is developed for reducing the modeling error by spatially adapting the material parameters in the simpler constitutive model. The resulting material parameters are not material properties per se, but depend on the given boundary-value problem. As a first step to the more general nonlinear case, we focus here on linear elasticity in which the “complex” constitutive model is general anisotropic elasticity and the chosen simpler model is isotropic elasticity. The algorithm for adaptive error reduction is demonstrated using two examples: (1) A transversely-isotropic plate with hole subjected to tension, and (2) a transversely-isotropic tube with two side holes subjected to torsion.
This report summarizes the data analysis activities that were performed under the Born Qualified Grand Challenge Project from 2016 - 2018. It is meant to document the characterization of additively manufactured parts and processe s for this project as well as demonstrate and identify further analyses and data science that could be done relating material processes to microstructure to properties to performance.
Additive manufacturing (AM) processes for metals can yield as-built microstructures that vary significantly from their cast or wrought counterparts. These microstructural variations can in turn, have profound effects on the properties of a component. Here, a modeling methodology is presented to investigate microstructurally-influenced mechanical response in additively manufactured structures via direct numeral simulation. Three-dimensional, synthetic voxelized microstructures are generated by kinetic Monte Carlo (kMC) additive manufacturing process simulations performed at four scan speeds to create a thin-wall cylindrical geometry notionally constructed using a concentric-pathed directed energy deposition AM process. The kMC simulations utilize a steady-state molten pool geometry that is held constant throughout the study. Resultant microstructures are mapped onto a highly-refined conformal finite-element mesh of a part geometry. A grain-scale anisotropic crystal elasticity model is then used to represent the constitutive response of each grain. The response of the structure subjected to relatively simple load conditions is studied in order to provide understanding of both the influence of AM processing on microstructure as well as the microstructure's influence on the macroscale mechanical response.
A new model for determining band gaps for elastic wave propagation in a periodic composite beam structure is developed using a non-classical Bernoulli–Euler beam model that incorporates the microstructure, surface energy and rotational inertia effects. The Bloch theorem and transfer matrix method for periodic structures are employed in the formulation. The new model reduces to the classical elasticity-based model when both the microstructure and surface energy effects are not considered. The band gaps predicted by the new model depend on the microstructure and surface elasticity of each constituent material, the unit cell size, the rotational inertia, and the volume fraction. To quantitatively illustrate the effects of these factors, a parametric study is conducted. The numerical results reveal that the band gap predicted by the current non-classical model is always larger than that predicted by the classical model when the beam thickness is very small, but the difference is diminishing as the thickness becomes large. Also, it is found that the first frequency for producing the band gap and the band gap size decrease with the increase of the unit cell length according to both the current and classical models. In addition, it is observed that the effect of the rotational inertia is larger when the exciting frequency is higher and the unit cell length is smaller. Furthermore, it is seen that the volume fraction has a significant effect on the band gap size, and large band gaps can be obtained by tailoring the volume fraction and material parameters.
The texture of a polycrystalline material refers to the preferred orientation of the grains within the material. In metallic materials, texture can significantly affect the mechanical properties such as elastic moduli, yield stress, strain hardening, and fracture toughness. Recent advances in additive manufacturing of metallic materials offer the possibility in the not too distant future of controlling the spatial variation of texture. In this work, we investigate the advantages, in terms of mechanical performance, of allowing the texture to vary spatially. We use an adjoint-based gradient optimization algorithm within a finite element solver (COMSOL) to optimize several engineering quantities of interest in a simple structure (hole in a plate) and loading (uniaxial tension) condition. As a first step to general texture optimization, we consider the idealized case of a pure fiber texture in which the homogenized properties are transversely isotropic. In this special case, the only spatially varying design variables are the three Euler angles that prescribe the orientation of the homogenized material at each point within the structure. This work paves a new way to design metallic materials for tunable mechanical properties at the microstructure level.
Gas-gun experiments have probed the compression and release behavior of impact-loaded 304L stainless steel specimens that were machined from additively manufactured (AM) blocks as well as baseline ingot-derived bar stock. The AM technology permits direct fabrication of net-or near-net-shape metal parts. For the present investigation, velocity interferometer (VISAR) diagnostics provided time-resolved measurements of sample response for onedimensional (i.e., uniaxial strain) shock compression to peak stresses ranging from 0.2 to 7.0 GPa. The acquired waveprofile data have been analyzed to determine the comparative Hugoniot Elastic Limit (HEL), Hugoniot equation of state, spall strength, and high-pressure yield strength of the AM and conventional materials. The possible contributions of various factors, such as composition, porosity, microstructure (e.g., grain size and morphology), residual stress, and/or sample axis orientation relative to the additive manufacturing deposition trajectory, are considered to explain differences between the AM and baseline 304L dynamic material results.
The finite element method has revolutionized structural analysis since its inception over 50 years ago, by enabling the computer analysis of geometrically complex structures. The main requirement of the finite element method is that an appropriate partition, or mesh, of the structure be created first. The elements of the partition typically have standard shapes, such as the hexahedron, pentahedron, and tetrahedron. While this small library of standard element shapes is sufficient for many applications, there is a growing need for more general polyhedral shapes, ones that can have an arbitrary number of vertices, edges, and faces, and ones that can be non-convex. In this chapter, we discuss current and possible future applications of polyhedral finite elements in solid mechanics. These applications include rapid engineering analysis through novel meshing and discretization techniques, and fracture and fragmentation modeling. Several finite element formulations of general polyhedra have been developed. In this chapter we use a polyhedral formulation based on the use of harmonic shape functions. Harmonic shape functions are one example of several possible generalized barycentric coordinates, as discussed in Chapter 1.
Coupled reservoir and geomechanical simulations are significantly important to understand the long-term behavior of geologic carbon storage (GCS) systems. In this study, we performed coupled fluid flow and geomechanical modeling of CO2 storage using available field data to (1) validate our existing numerical model and (2) perform parameter estimation via inverse modeling to identify the impact of key geomechanical (Young's modulus and Biot's coefficient) and hydrogeological (permeability and anisotropy ratio) properties on surface uplift and the pore pressure buildup at In Salah in Algeria. Furthermore, two sets of surface uplift data featuring low and high uplifts above two injection wells and the maximum change in the pore pressure due to CO2 injection were used to constrain the inverse model.
An a posteriori error-estimation framework is introduced to quantify and reduce modeling errors resulting from approximating complex mesoscale material behavior with a simpler macroscale model. Such errors may be prevalent when modeling welds and additively manufactured structures, where spatial variations and material textures may be present in the microstructure. We consider a case where a <100> fiber texture develops in the longitudinal scanning direction of a weld. Transversely isotropic elastic properties are obtained through homogenization of a microstructural model with this texture and are considered the reference weld properties within the error-estimation framework. Conversely, isotropic elastic properties are considered approximate weld properties since they contain no representation of texture. Errors introduced by using isotropic material properties to represent a weld are assessed through a quantified error bound in the elastic regime. Lastly, an adaptive error reduction scheme is used to determine the optimal spatial variation of the isotropic weld properties to reduce the error bound.
Two fundamental approximations in macroscale solid-mechanics modeling are (1) the assumption of scale separation in homogenization theory and (2) the use of a macroscopic plasticity material model that represents, in a mean sense, the multitude of inelastic processes occurring at the microscale. With the goal of quantifying the errors induced by these approximations on engineering quantities of interest, we perform a set of direct numerical simulations (DNS) in which polycrystalline microstructures are embedded throughout a macroscale structure. The largest simulations model over 50,000 grains. The microstructure is idealized using a randomly close-packed Voronoi tessellation in which each polyhedral Voronoi cell represents a grain. An face centered cubic crystal-plasticity model is used to model the mechanical response of each grain. The overall grain structure is equiaxed, and each grain is randomly oriented with no overall texture. The detailed results from the DNS simulations are compared to results obtained from conventional macroscale simulations that use homogeneous isotropic plasticity models. The macroscale plasticity models are calibrated using a representative volume element of the idealized microstructure. Ultimately, we envision that DNS modeling will be used to gain new insights into the mechanics of material deformation and failure.
An a posteriori error-estimation framework is introduced to quantify and reduce modeling errors resulting from approximating complex mesoscale material behavior with a simpler macroscale model. Such errors may be prevalent when modeling welds and additively manufactured structures, where spatial variations and material textures may be present in the microstructure. We consider a case where a <100> fiber texture develops in the longitudinal scanning direction of a weld. Transversely isotropic elastic properties are obtained through homogenization of a microstructural model with this texture and are considered the reference weld properties within the error-estimation framework. Conversely, isotropic elastic properties are considered approximate weld properties since they contain no representation of texture. Errors introduced by using isotropic material properties to represent a weld are assessed through a quantified error bound in the elastic regime. An adaptive error reduction scheme is used to determine the optimal spatial variation of the isotropic weld properties to reduce the error bound.
Fracture and fragmentation are extremely nonlinear multiscale processes in which microscale damage mechanisms emerge at the macroscale as new fracture surfaces. Numerous numerical methods have been developed for simulating fracture initiation, propagation, and coalescence. Here, we present a computational approach for modeling pervasive fracture in quasi-brittle materials based on random close-packed Voronoi tessellations. Each Voronoi cell is formulated as a polyhedral finite element containing an arbitrary number of vertices and faces. Fracture surfaces are allowed to nucleate only at the intercell faces. Cohesive softening tractions are applied to new fracture surfaces in order to model the energy dissipated during fracture growth. The randomly seeded Voronoi cells provide a regularized discrete random network for representing fracture surfaces. The potential crack paths within the random network are viewed as instances of realizable crack paths within the continuum material. Mesh convergence of fracture simulations is viewed in a weak, or distributional, sense. The explicit facet representation of fractures within this approach is advantageous for modeling contact on new fracture surfaces and fluid flow within the evolving fracture network. Applications of interest include fracture and fragmentation in quasi-brittle materials and geomechanical applications such as hydraulic fracturing, engineered geothermal systems, compressed-air energy storage, and carbon sequestration.
Additive manufacturing (AM) technology has been developed to fabricate metal components that include complex prototype fabrication, small lot production, precision repair or feature addition, and tooling. However, the mechanical response of the AM materials is a concern to meet requirements for specific applications. Differences between AM materials as compared to wrought materials might be expected, due to possible differences in porosity (voids), grain size, and residual stress levels. When the AM materials are designed for impact applications, the dynamic mechanical properties in both compression and tension need to be fully characterized and understood for reliable designs. In this study, a 304L stainless steel was manufactured with AM technology. For comparison purposes, both the AM and wrought 304L stainless steels were dynamically characterized in compression Kolsky bar techniques. They dynamic compressive stress-strain curves were obtained and the strain rate effects were determined for both the AM and wrought 304L stainless steels. A comprehensive comparison of dynamic compressive response between the AM and wrought 304L stainless steels was performed. SAND2015-0993 C.
Predictive simulation capabilities for modeling fracture evolution provide further insight into quantities of interest in comparison to experimental testing. Based on the variational approach to fracture, the advent of phase-field modeling achieves the goal to robustly model fracture for brittle materials and captures complex crack topologies in three dimensions.
The reproducing kernel particle method (RKPM) is a meshfree method for computational solid mechanics that can be tailored for an arbitrary order of completeness and smoothness. The primary advantage of RKPM relative to standard finiteelement (FE) approaches is its capacity to model large deformations, material damage, and fracture. Additionally, the use of a meshfree approach offers great flexibility in the domain discretization process and reduces the complexity of mesh modifications such as adaptive refinement. We present an overview of the RKPM implementation in the Sierra/SolidMechanics analysis code, with a focus on verification, validation, and software engineering for massively parallel computation. Key details include the processing of meshfree discretizations within a FE code, RKPM solution approximation and domain integration, stress update and calculation of internal force, and contact modeling. The accuracy and performance of RKPM are evaluated using a set of benchmark problems. Solution verification, mesh convergence, and parallel scalability are demonstrated using a simulation of wave propagation along the length of a bar. Initial model validation is achieved through simulation of a Taylor bar impact test. The RKPM approach is shown to be a viable alternative to standard FE techniques that provides additional flexibility to the analyst community.
This report summarizes the work performed by the graduate student Jovanca Smith during a summer internship in the summer of 2012 with the aid of mentor Joe Bishop. The projects were a two-part endeavor that focused on the use of the numerical model called the Lattice Discrete Particle Model (LDPM). The LDPM is a discrete meso-scale model currently used at Northwestern University and the ERDC to model the heterogeneous quasi-brittle material, concrete. In the first part of the project, LDPM was compared to the Karagozian and Case Concrete Model (K&C) used in Presto, an explicit dynamics finite-element code, developed at Sandia National Laboratories. In order to make this comparison, a series of quasi-static numerical experiments were performed, namely unconfined uniaxial compression tests on four varied cube specimen sizes, three-point bending notched experiments on three proportional specimen sizes, and six triaxial compression tests on a cylindrical specimen. The second part of this project focused on the application of LDPM to simulate projectile perforation on an ultra high performance concrete called CORTUF. This application illustrates the strengths of LDPM over traditional continuum models.
This document summarizes research performed under the SNL LDRD entitled - Computational Mechanics for Geosystems Management to Support the Energy and Natural Resources Mission. The main accomplishment was development of a foundational SNL capability for computational thermal, chemical, fluid, and solid mechanics analysis of geosystems. The code was developed within the SNL Sierra software system. This report summarizes the capabilities of the simulation code and the supporting research and development conducted under this LDRD. The main goal of this project was the development of a foundational capability for coupled thermal, hydrological, mechanical, chemical (THMC) simulation of heterogeneous geosystems utilizing massively parallel processing. To solve these complex issues, this project integrated research in numerical mathematics and algorithms for chemically reactive multiphase systems with computer science research in adaptive coupled solution control and framework architecture. This report summarizes and demonstrates the capabilities that were developed together with the supporting research underlying the models. Key accomplishments are: (1) General capability for modeling nonisothermal, multiphase, multicomponent flow in heterogeneous porous geologic materials; (2) General capability to model multiphase reactive transport of species in heterogeneous porous media; (3) Constitutive models for describing real, general geomaterials under multiphase conditions utilizing laboratory data; (4) General capability to couple nonisothermal reactive flow with geomechanics (THMC); (5) Phase behavior thermodynamics for the CO2-H2O-NaCl system. General implementation enables modeling of other fluid mixtures. Adaptive look-up tables enable thermodynamic capability to other simulators; (6) Capability for statistical modeling of heterogeneity in geologic materials; and (7) Simulator utilizes unstructured grids on parallel processing computers.
Fracture or tearing of ductile metals is a pervasive engineering concern, yet accurate prediction of the critical conditions of fracture remains elusive. Sandia National Laboratories has been developing and implementing several new modeling methodologies to address problems in fracture, including both new physical models and new numerical schemes. The present study provides a double-blind quantitative assessment of several computational capabilities including tearing parameters embedded in a conventional finite element code, localization elements, extended finite elements (XFEM), and peridynamics. For this assessment, each of four teams reported blind predictions for three challenge problems spanning crack initiation and crack propagation. After predictions had been reported, the predictions were compared to experimentally observed behavior. The metal alloys for these three problems were aluminum alloy 2024-T3 and precipitation hardened stainless steel PH13-8Mo H950. The predictive accuracies of the various methods are demonstrated, and the potential sources of error are discussed.