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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.
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.
NSR&D FY17 Report: CartaBlanca Capability Enhancements
Over the last several years, particle technology in the CartaBlanca code has been matured and has been successfully applied to a wide variety of physical problems. It has been shown that the particle methods, especially Los Alamos's dual domain material point method, is capable of computing many problems involves complex physics, chemistries accompanied by large material deformations, where the traditional finite element or Eulerian method encounter significant difficulties. In FY17, the CartaBlanca code has been enhanced with physical models and numerical algorithms. We started out to compute penetration and HE safety problems. Most of the year we focused on the TEPLA model improvement testing against the sweeping wave experiment by Gray et al., because it was found that pore growth and material failure are essentially important for our tasks and needed to be understood for modeling the penetration and the can experiments efficiently. We extended the TEPLA mode from the point view of ensemble phase average to include the effects of nite deformation. It is shown that the assumed pore growth model in TEPLA is actually an exact result from the theory. Alone this line, we then generalized the model to include finite deformations to consider nonlinear dynamics of large deformation. The interaction between the HE product gas and the solid metal is based on the multi-velocity formation. Our preliminary numerical results suggest good agreement between the experiment and the numerical results, pending further verification. To improve the parallel processing capabilities of the CartaBlanca code, we are actively working with the Next Generation Code (NGC) project to rewrite selected packages using C++. This work is expected to continue in the following years. This effort also makes the particle technology developed with CartaBlanca project available to other part of the laboratory. Working with the NGC project and rewriting some parts of the code also given us an opportunity to improve our numerical implementations of the method and to take advantage of recently advances in the numerical methods, such as multiscale algorithms.
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
A 3D Computational Head Model Under Dynamic Head Rotation and Head Extension Validated Using Live Human Brain Data, Including the Falx and the Tentorium
We employ an advanced 3D computational model of the head with high anatomical fidelity, together with measured tissue properties, to assess the consequences of dynamic loading to the head in two distinct modes: head rotation and head extension. We use a subject-specific computational head model, using the material point method, built from T1 magnetic resonance images, and considering the anisotropic properties of the white matter which can predict strains in the brain under large rotational accelerations. The material model now includes the shear anisotropy of the white matter. We validate the model under head rotation and head extension motions using live human data, and advance a prior version of the model to include biofidelic falx and tentorium. Furthermore we then examine the consequences of incorporating the falx and tentorium in terms of the predictions from the computational head model.
Peridynamics as a rigorous coarse-graining of atomistics for multiscale materials design.
This report summarizes activities undertaken during FY08-FY10 for the LDRD Peridynamics as a Rigorous Coarse-Graining of Atomistics for Multiscale Materials Design. The goal of our project was to develop a coarse-graining of finite temperature molecular dynamics (MD) that successfully transitions from statistical mechanics to continuum mechanics. The goal of our project is to develop a coarse-graining of finite temperature molecular dynamics (MD) that successfully transitions from statistical mechanics to continuum mechanics. Our coarse-graining overcomes the intrinsic limitation of coupling atomistics with classical continuum mechanics via the FEM (finite element method), SPH (smoothed particle hydrodynamics), or MPM (material point method); namely, that classical continuum mechanics assumes a local force interaction that is incompatible with the nonlocal force model of atomistic methods. Therefore FEM, SPH, and MPM inherit this limitation. This seemingly innocuous dichotomy has far reaching consequences; for example, classical continuum mechanics cannot resolve the short wavelength behavior associated with atomistics. Other consequences include spurious forces, invalid phonon dispersion relationships, and irreconcilable descriptions/treatments of temperature. We propose a statistically based coarse-graining of atomistics via peridynamics and so develop a first of a kind mesoscopic capability to enable consistent, thermodynamically sound, atomistic-to-continuum (AtC) multiscale material simulation. Peridynamics (PD) is a microcontinuum theory that assumes nonlocal forces for describing long-range material interaction. The force interactions occurring at finite distances are naturally accounted for in PD. Moreover, PDs nonlocal force model is entirely consistent with those used by atomistics methods, in stark contrast to classical continuum mechanics. Hence, PD can be employed for mesoscopic phenomena that are beyond the realms of classical continuum mechanics and atomistic simulations, e.g., molecular dynamics and density functional theory (DFT). The latter two atomistic techniques are handicapped by the onerous length and time scales associated with simulating mesoscopic materials. Simulating such mesoscopic materials is likely to require, and greatly benefit from multiscale simulations coupling DFT, MD, PD, and explicit transient dynamic finite element methods FEM (e.g., Presto). The proposed work fills the gap needed to enable multiscale materials simulations.
Simulations of Failure via Three-Dimensional Cracking in Fuel Cladding for Advanced Nuclear Fuels
Enhancing performance of fuel cladding and duct alloys is a key means of increasing fuel burnup. This project will address the failure of fuel cladding via three-dimensional cracking models. Researchers will develop a simulation code for the failure of the fuel cladding and validate the code through experiments. The objective is to develop an algorithm to determine the failure of fuel cladding in the form of three-dimensional cracking due to prolonged exposure under varying conditions of pressure, temperature, chemical environment, and irradiation. This project encompasses the following tasks: 1. Simulate 3D crack initiation and growth under instantaneous and/or fatigue loads using a new variant of the material point method (MPM); 2. Simulate debonding of the materials in the crack path using cohesive elements, considering normal and shear traction separation laws; 3. Determine the crack propagation path, considering damage of the materials incorporated in the cohesive elements to allow the energy release rate to be minimized; 4. Simulate the three-dimensional fatigue crack growth as a function of loading histories; 5. Verify the simulation code by comparing results to theoretical and numerical studies available in the literature; 6. Conduct experiments to observe the crack path and surface profile in unused fuel cladding and validate against simulation results; and 7. Expand the adaptive mesh refinement infrastructure parallel processing environment to allow adaptive mesh refinement at the 3D crack fronts and adaptive mesh merging in the wake of cracks. Fuel cladding is made of materials such as stainless steels and ferritic steels with added alloying elements, which increase stability and durability under irradiation. As fuel cladding is subjected to water, chemicals, fission gas, pressure, high temperatures, and irradiation while in service, understanding performance is essential. In the fast fuel used in advanced burner reactors, simulations of the nuclear fuels are critical to understand the burnup, and thus the fuel efficiency.
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.
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.
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.
Simulating stochastic and additively manufactured foams at large strains and high strain rates (Progress Summary)
Understanding the mechanical response of polymer foams is essential in developing system material models and in designing replacements for legacy pads and cushions. Simulations can help elucidate structure-property relationships and compare local stress distributions to understand aging behavior and improve designs. In many applications, these materials experience significant loadings and computations need the capability to reproduce those conditions. We are applying are previously developed material point method (MPM) simulation capability to understand the aging properties of loaded direct ink write resins. Significant particle loading of a stiffer material in siloxane networks exhibit different compression set behavior than unloaded specimens. We are applying our computational mechanics capabilities to understand this difference at the continuum level. Figure 1 highlights preliminary results, depicting renderings of an unloaded DIW filament alongside one containing a 20% volume loading of spherical particles. Also, the stress distribution of a neat filament at 20% compression is shown. We are planning to study this behavior for a range of loading fractions, particle sizes, and material stiffness ratios. We will explore the sensitivity of the stress response to these variables which could inform aging models of these materials.
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.
Simulating stochastic and additively manufactured foams at large strains and high strain rates
Understanding the mechanical response of polymer foams is essential in developing system material models and in designing replacements for legacy pads and cushions. Simulations can help elucidate structure-property relationships and compare local stress distributions to understand aging behavior and improve designs. In many applications, these materials experience significant loadings and computations need the capability to reproduce those conditions. We are applying are previously developed material point method (MPM) simulation capability to understand the aging properties of loaded direct ink write (DIW) resins.
ExaMPM
ExaMPM is a mini-application for the Material Point Method (MPM) for studying the application of MPM to future exascale computing systems. MPM is a general method for computational mechanics and fluids and is used in a wide variety of science and engineering disciplines to study problems with large deformations, phase change, fracture, and other phenomena. ExaMPM provides a reference implementation of MPM as described in the 1994 work of Sulsky et.al. (Sulsky, Deborah, Zhen Chen, and Howard L. Schreyer. "A particle method for history-dependent materials." Computer methods in applied mechanics and engineering 118.1-2 (1994): 179-196.). The software can solve basic MPM problems in solid mechanics using the original algorithm of Sulsky with explicit time integration, basic geometries, and free-slip and no-slip boundary conditions as described in the reference. ExaMPM is intended to be used as a starting point to design new parallel algorithms for the next generation of DOE supercomputers.
ExaMPM
ExaMPM is a mini-application for the Material Point Method (MPM) for studying the application of MPM to future exascale computing systems. MPM is a general method for computational mechanics and fluids and is used in a wide variety of science and engineering disciplines to study problems with large deformations, phase change, fracture, and other phenomena. ExaMPM provides a reference implementation of MPM as described in the 1994 work of Sulsky et.al. (Sulsky, Deborah, Zhen Chen, and Howard L. Schreyer. "A particle method for history-dependent materials." Computer methods in applied mechanics and engineering 118.1-2 (1994): 179-196.). The software can solve basic MPM problems in solid mechanics using the original algorithm of Sulsky with explicit time integration, basic geometries, and free-slip and no-slip boundary conditions as described in the reference. ExaMPM is intended to be used as a starting point to design new parallel algorithms for the next generation of DOE supercomputers.
Tomography and Simulation of Microstructure Evolution of a Closed-Cell Polymer Foam in Compression
Closed-cell foams in compression exhibit complex deformation characteristics that remain incompletely understood. In this paper the microstructural evolution of closed-cell polymethacrylimide foam was simulated in compression undergoing elastic, compaction, and densification stages. The three-dimensional microstructure of the foam is determined using Micro-Computed Tomography ({micro}-CT), and is converted to material points for simulations using the material point method (MPM). The properties of the cell-walls are determined from nanoindentation on the wall of the foam. MPM simulations captured the three stages of deformations in foam compression. Features of the microstructures from simulations are compared qualitatively with the in-situ observations of the foam under compression using {micro}-CT. The stress-strain curve simulated from MPM compares reasonably with the experimental results. Based on the results from {micro}-CT and MPM simulations, it was found that elastic buckling of cell-walls occurs even in the elastic regime of compression. Within the elastic region, less than 35% of the cell-wall material carries the majority of the compressive load. In the experiment, a shear band was observed as a result of collapse of cells in a weak zone. From this collapsed weak zone a compaction (collapse) wave was seen traveling which eventually lead to the collapse of the entire foam cell-structure. Overall, this methodology will allow prediction of material properties for microstructures driving the optimization of processing and performance in foam materials.
An adaptive granular representative volume element model with an evolutionary periodic boundary for hierarchical multiscale analysis
The hierarchical multiscale analysis normally utilizes a microscopic representative volume element (RVE) model to capture path/history-dependent macroscopic responses instead of using phenomenological constitutive models. However, for problems involving large deformation, the current RVE model used in geomechanics may lose representative properties due to the progressive distortion of the RVE box, unless a proper reinitialization is applied. This work develops an adaptive RVE model in conjunction with an evolutionary periodic boundary (EPB) algorithm for hierarchical multiscale analysis of granular materials undergoing large deformation based on a recent RVE model proposed for coupling molecular dynamics and the material point method. The proposed adaptive RVE model avoids the reinitialization of the RVE box that even undergoes extremely large shear deformation; meanwhile, it accounts for the deformation history of the RVE model and treats the interaction between boundary particles and other image particles in a more efficient way. Numerical examples with extremely large deformation are used to illustrate the adaptive granular RVE model enhanced by the proposed EPB algorithm. Furthermore, some key features of this new methodology are further discussed for clarification.