Implementation of the Material Point Method on a Spherical Voronoi Mesh for MPAS-SI-MPM
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Peterson, Kara J.↗
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Enhanced Sea Ice Mechanics with the Material-Point Method
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Peterson, Kara J.↗
Enhanced Sea Ice Mechanics with the Material Point Method
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Peterson, Kara J. [Sandia National Laboratories (S↗
Enhanced Sea-Ice Mechanics with the Material Point Method
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Peterson, Kara J. [Sandia National Laboratories (S↗
Results of the Micromorphic Upscaling Workflow for the PSAAP III Year 3 Report
Predicting the mechanical response and failure of heterogeneous materials has proven difficult. Multiscale numerical methods based in higher order continuum theories attempt to bridge the gap between microscale and macroscale structural behavior. Micromorphic continuum theories have shown promise. The Tardigrade software package is an implementation of Eringen’s micromorphic continuum theory with capabilities to support multiscale material modeling workflows. These include homogenization through the Micromorphic Filter, calibration of micromorphic material models, and macroscale simulation in Tardigrade-MOOSE. This work discusses micromorphic upscaling efforts of the University of Colorado Boulder PSAAP III multidisciplinary simulation center (MSC). Verification studies are presented that compare the accuracy of the upscaling workflow with analytical solutions for a trivial stress state and homogeneous material using direct numerical simulations (DNS) conducted in the Ratel finite element method (FEM) and GEOS material point method (MPM) codes. These verification studies consider upscaling using the Micromorphic Filter for a “single filter domain”. Finally, DNS of a heterogeneous composite material is upscaled using a “multiple filter domain” method.
36 MATERIALS SCIENCE↗
Numerical investigation of thermomechanical response of multiscale porous Ultra-High Temperature Ceramics
Recent advances in Ultra-High Temperature Ceramics (UHTC) manufacturing have permitted the development of multiscale porous UHTC microstructures. Within the target application of hypersonic vehicles, dense UHTCs are suitable for thermal protection on leading edges, whereas porous UHTCs may find a role in providing thermally insulated interfaces for temperature-sensitive interior components. Designing vehicles incorporating porous UHTCs requires a characterization of their thermomechanical properties across the full range of expected operating temperatures spanning –20 °C–2500 °C. This research represents a preliminary study in performing this characterization. Several numerical experiments are performed using a coupled thermomechanical implementation of the Material Point Method to determine the temperature dependence of effective material properties both with and without damage. Furthermore, complex time-dependent boundary conditions derived from known hypersonic flight profiles are simulated in order to probe the various couplings between deformation, damage and heat transfer. It is shown that the model reveals the importance of micro-buckling in determining effective material stiffness and thermal conductivity.
36 MATERIALS SCIENCE↗
Meshfree Methods
Meshfree methods have undergone substantial development and have received much attention in the last two decades. This new family of numerical methods is designed to inherit the main advantages of the finite element method such as compact supports of shape functions and good approximation properties while, at the same time, overcome the main disadvantages of the finite element method caused by the mesh dependence. The meshfree methods share a common feature that no mesh is needed and shape functions are constructed from sets of points, thus eliminating the need for time consuming mesh generation. The most significant advantage of meshfree methods is the flexibility in customizing approximation functions for desired regularity and for capturing essential physics and features of the particular problems of interest. Adaptivity formulation and multiple-scale solution strategies also can be implemented with relative ease. It has become clear that the meshfree methods provide considerable advantages over the conventional finite element methods in solving problems involving moving discontinuities, evolving material interfaces, multiple-scale phenomena, large material distortion and structural deformation, and fracture and damage processes. This Chapter gives an overview of many classes of meshfree methods, with more detailed discussions on Smoothed Particle Hydrodynamics (SPH), the Reproducing Kernel Particle Method (RKPM), Peridynamics (PD), the Material Point Method (MPM), as well as their applications in various challenging engineering problems.2
Chen, Jiun-Shyan↗
Enhanced MPM framework with multipatch isogeometric analysis for geotechnical applications
Achieving stable stress solutions at large strains using the Material Point Method (MPM) is challenging due to the accumulation of errors associated with geometry discretization, cell-crossing noise, and volumetric locking. Several simplified attempts exist in the literature to mitigate these errors, including higher-order frameworks. However, the stability of the MPM solution in such frameworks has been limited to simple geometries and the single-phase formulation (i.e., neglecting pore fluid). Although never explored, multipatch isogeometric analysis offers desirable qualities to simulate complex geometries while mitigating errors in the MPM. The degree of required high-order spatial integration has also never been investigated to infer a minimum limit for the stability of the stress solution in MPM. This paper presents a general-purpose numerical framework for simulating stable stresses in porous media, capturing both near incompressibility and multiphase interactions. First, the numerical framework is presented considering Non-Uniform Rational B-splines (NURBS) to perform isogeometric analysis (IGA) in MPM. Additionally, a volumetric strain smoothing algorithm is used to alleviate errors associated with volumetric locking. Second, the manifestation of cell-crossing errors is assessed via a series of problems with orders ranging from linear to cubic interpolation functions. Third, the use of NURBS is investigated and verified for problems with circular geometries. Finally, multipatch analysis is deployed to simulate plane strain and 3D penetration in soils, considering nearly incompressible elastoplastic (total stress) analysis and fully-coupled hydro-mechanical (effective stress) analysis. The stability of the solution is also analyzed for different constitutive models. From the results, it can be concluded that the framework using cubic interpolation functions with strain smoothing is the most convenient, presenting stable stress solutions for a broad range of multiphase geotechnical applications.
58 GEOSCIENCES↗
Exploring strain rate effects upon 3D materials using high speed in situ X-ray tomoscopy
Cellular materials are ubiquitous in our modern society. They may be stochastic gas-blown foams (e.g., polyurethane), foamed starches (e.g., cereals), or, in this case, 3D printed microlattices. Failure in these materials is often driven by surface or sub-surface defects, which may be nucleated at a surface roughness, an interior void, or inclusion interfaces that may not be typically observable. Obfuscating our understanding further, bulk materials are known to exhibit strain-rate-dependent mechanical response, making a subsurface understanding of damage even more critical. For the first time, an in situ uniaxial mechanical loading stage that simultaneously rotates specimens up to 18 Hz was fielded at a synchrotron for 3D tomographic imaging. This capability opens a plethora of materials science opportunities to explore strain rate effects in materials and examining deformation, fracture, and delamination’s (in composites) for a complete 3D picture (movie) of material response. We demonstrate the deformation of 3D printed polymer lattice structures, of three different material types, at 0.25, 1.1, and 2.2 s −1 strain rates. We successfully imaged the 3D deformation of these materials and can directly compare the same printed structure to the three material types at three strain rates, all in 3D. Material point method simulations were applied to one of the materials to better understand the role of voids on the 3D printed structure’s performance.
36 MATERIALS SCIENCE↗
Tardigrade-examples V0.1.0
Tardigrade-examples is a repository of computational workflows that exercise the Tardigrade software package. The Tardigrade software package is an implementation of Eringen’s micromorphic continuum theory with capabilities to support multiscale material modeling. These capabilities include homogenization through the Micromorphic Filter, calibration of micromorphic material models, and macroscale simulation in Tardigrade-MOOSE. This repository investigates continuum upscaling of various direct numerical simulations (DNS) conducted in Abaqus finite element (FE), Ratel FE, and GEOS material point method (MPM) software. Verification of the upscaling workflow is first investigated by considering DNS of trivial stress states for homogeneous materials, results of which indicate that classical continuum behavior is recovered as expected. DNS of heterogeneous materials are then considered.
Allard, Thomas↗
An Efficient B-Spline Lagrangian/Eulerian Method for Compressible Flow, Shock Waves, and Fracturing Solids
This study presents a new method for modeling the interaction between compressible flow, shock waves, and deformable structures, emphasizing destructive dynamics. Extending advances in time-splitting compressible flow and the Material Point Methods (MPM), we develop a hybrid Eulerian and Lagrangian/Eulerian scheme for monolithic flow-structure interactions. We adopt the second-order WENO scheme to advance the continuity equation. To stably resolve deforming boundaries with sub-cell particles, we propose a blending treatment of reflective and passable boundary conditions inspired by the theory of porous media. The strongly coupled velocity-pressure system is discretized with a new mixed-order finite element formulation employing B-spline shape functions. Shock wave propagation, temperature/density-induced buoyancy effects, and topology changes in solids are unitedly captured.
97 MATHEMATICS AND COMPUTING↗
Assessment of the hydromechanical higher-order MPM for the simulation of geotechnical problems
The Material Point Method (MPM) has been increasingly used to simulate large strain deformations. Linear interpolation functions are commonly used to perform the spatial integration. It is well-known that the discontinuities in the interpolation function derivatives induce shock-like artifacts known as ‘cell-crossing’ error. These errors compound with volumetric locking errors when used with hydromechanical formulations for porous media, where different velocity fields are used for each phase. The capabilities of higher-order MPM frameworks have not been explored for real-scale geotechnical problems. As such, this paper aims to assess, validate, and further discuss a higher-order B-spline MPM (BS-MPM) framework. First, the BS-MPM framework is verified against the large-strain oedometer consolidation problem. Second, the framework is validated against a real-scale slope failure experiment triggered by pore water pressure recharge. Landslide features that are captured using the higher-order framework are specifically highlighted, and results (e.g., pore water pressure and deformation) are validated with field measurements. A generally convergent numerical solution is observed when using cubic interpolation functions. Third, a footing penetration problem is simulated using the multi-patch BS-MPM. Trends are examined with respect to penetration velocity and variation in hydraulic conductivity. The BS-MPM framework ultimately presents a stabilized numerical solution that captures plausible hydromechanical interaction trends important in geotechnical engineering applications.
36 MATERIALS SCIENCE↗
Modeling detonation with CartaBlanca simulations
The accurate modeling of high explosive (HE) detonation and the con- sequent large solid deformation, failure, plastic flow, porosity growth, and shock wave propagation is important because simulations can capture spatial and temporal features that experimental diagnostics cannot capture. However, the simulation of the explosive event poses challenges to a computational scientist. These include the accurate modeling of ductile damage, crack formation, plastic deformation, as well as physical and nu- merical instabilities. The material response can be history-dependent and subject to large material deformation. Our research simulates the impact of a high explosive (Detasheet) onto a tantulum metal plate. We performed the simulations using CartaBlanca at different mesh resolutions. We decided the study would be impactful if we perform the simulations with the Material Point Method. Differences were observed at the different mesh resolutions in velocity and nodal stress magnitude, so increased mesh resolutions may be required. In addition, the Discontinuous Galerkin method would be needed to account for the large gas expansion.
97 MATHEMATICS AND COMPUTING↗
Material point generation from an STL file
In this short note we describe a method for generating material points from a file in the stere olithography (STL) format commonly used in computer aided design (CAD), 3-D printing, and computer aided manufacturing applications. In this file format the surface of an object is described by triangles in three-dimensional space. The coordinates of the triangle vertexes are provided in the file. In this note we assume that the object of interest is inside of the enclosing set of triangles. Similar methods can also be used to generate material points outside of the enclosing triangles.
42 ENGINEERING↗
Fuel Properties of Oxymethylene Ethers with Terminating Groups from Methyl to Butyl
Oxymethylene ethers (OMEs) have been studied as possible additives or replacements for diesel fuels. Typically, studies have considered only methyl-terminated OMEs. Recent structure-property relationship models suggest that extended-alkyl OMEs may provide improvements to many of the properties of methyl-terminated OMEs that make them less suitable as diesel fuel blendstocks. In this work, we describe the synthesis and characterization of 16 different OMEs with methyl, ethyl, propyl, butyl, isopropyl, and isobutyl terminating alkyl groups with varying oxymethylene chain length. Indicated Cetane Number, Lower Heating Value, Flash Point, Density, Viscosity, Vapor Pressure, and Oxidative Stability are tested via ASTM standard methods. Additionally, Water Solubility, Boiling Point, seal material compatibility, and sooting propensity (via the Yield Sooting Index) are measured for these fuels. For diesel compatibility, all tested OMEs except smaller methyl and ethyl OMEs, and the branched isopropyl OME, meet cetane number requirements. Further, extending the alkyl end group increases the heating value, but all OMEs, due to their oxygen content, have heating values less than diesel; despite this, all OMEs show significant reductions in soot production per unit heating value. Only the heaviest OMEs meet diesel viscosity requirements, and most are higher density than diesel. OMEs with larger alkyl groups show the highest stability under accelerated auto-oxidation conditions. Increases in alkyl group length cause order of magnitude reduction in water solubility, from hundreds of g/L for methyl terminated OMEs to hundreds of mg/L for butyl terminated OMEs. Limited seal material testing indicates that PEEK polymers are unaffected by OMEs; while extended alkyl groups may improve compatibility with FKM (Viton), other common elastomers (NBR, silicone) remain incompatible with all tested OMEs. Overall, it is found that methyl-terminated OMEs exhibit the most potential for soot reduction, but OMEs with larger propyl and butyl terminating alkyl groups show improved compatibility with existing diesel systems.
09 BIOMASS FUELS↗
Crack opening calculation in phase-field modeling of fluid-filled fracture: A robust and efficient strain-based method
The phase-field method has become popular for the numerical modeling of fluid-filled fractures, thanks to its ability to represent complex fracture geometry without algorithms. However, the algorithm-free representation of fracture geometry poses a significant challenge in calculating the crack opening (aperture) of phase-field fracture, which governs the fracture permeability and hence the overall hydromechanical behavior. Although several approaches have been devised to compute the crack opening of phase-field fracture, they require a sophisticated algorithm for post-processing the phase-field values or an additional parameter sensitive to the element size and alignment. Here, we develop a novel method for calculating the crack opening of fluid-filled phase-field fracture, which enables one to obtain the crack opening without additional algorithms or parameters. Here we transform the displacement-jump-based kinematics of a fracture into a continuous strain-based version, insert it into a force balance equation on the fracture, and apply the phase-field approximation. Through this procedure, we obtain a simple equation for the crack opening which can be calculated with quantities at individual material points. We verify the proposed method with analytical and numerical solutions obtained based on discrete representations of fractures, demonstrating its capability to calculate the crack opening regardless of the element size or alignment.
58 GEOSCIENCES↗
Fully self-consistent finite-temperature $GW$ in Gaussian Bloch orbitals for solids
In this work, we present algorithmic and implementation details for the fully self-consistent finite-temperature $GW$ method in Gaussian Bloch orbitals for solids. Our implementation is based on the finite-temperature Green's function formalism in which all equations are solved on the imaginary axis, without resorting to analytical continuation during the self-consistency. No quasiparticle approximation is employed and all matrix elements of the self-energy are explicitly evaluated. The method is tested by evaluating the band gaps of selected semiconductors and insulators. We show agreement with other, differently formulated, finite-temperature sc $GW$ implementations when finite-size corrections and basis-set errors are taken into account. By migrating computationally intensive calculations to graphics processing units, we obtain scalable results on large supercomputers with nearly optimal performance. Our work demonstrates the applicability of Gaussian orbital based sc $GW$ for ab initio correlated material simulations and provides a sound starting point for embedding methods built on top of $GW$.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
A Novel Rotating Flexure-Test Technique for Brittle Materials with Circular Geometries
The four-point bend test is one of the simplest and often the preferred flexural strength evaluation method for brittle materials. In this loading mode, fracture often initiates from a critical surface (or subsurface) flaw when subjected to a tensile stress state. However, if the critical flaw exists on the compression side of the test specimen, it may not activate to grow a crack and hence the resulting flexural strength will be higher than the true value. The goal of this study is to measure the true flexural strength of a solid or hollow cylindrical brittle specimen by ensuring that failure occurs at its weakest point by rotating along its longitudinal axis, thereby exposing and activating its critical surface flaw during a four-point bend test. A novel test fixture has been designed and fabricated, and the true flexural strengths of cylindrical brittle and quasi-brittle tubular specimens have been measured and compared to existing experimental data obtained through traditional four-point bend tests. In this work, experimental results showcase the orientation dependance on flexural strength for various materials. Additionally, similarities between experimental findings and those available in literature, including observations of fracture surfaces and relationships between surface roughness and material strength, are discussed.
36 MATERIALS SCIENCE↗