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  • Isogeometric continuity constraints for multi-patch shells governed by fourth-order deformation and phase field models
    arXiv.cs.CE Pub Date : 2020-01-16
    Karsten Paul; Christopher Zimmermann; Thang X. Duong; Roger A. Sauer

    This work presents numerical techniques to enforce continuity constraints on multi-patch surfaces for three distinct problem classes. The first involves structural analysis of thin shells that are described by general Kirchhoff-Love kinematics. Their governing equation is a vector-valued, fourth-order, nonlinear, partial differential equation (PDE) that requires at least $C^1$-continuity within a displacement-based finite element formulation. The second class are surface phase separations modeled by a phase field. Their governing equation is the Cahn-Hilliard equation - a scalar, fourth-order, nonlinear PDE - that can be coupled to the thin shell PDE. The third class are brittle fracture processes modeled by a phase field approach. In this work, these are described by a scalar, fourth-order, nonlinear PDE that is similar to the Cahn-Hilliard equation and is also coupled to the thin shell PDE. Using a direct finite element discretization, the two phase field equations also require at least a $C^1$-continuous formulation. Isogeometric surface discretizations - often composed of multiple patches - thus require constraints that enforce the $C^1$-continuity of displacement and phase field. For this, two numerical strategies are presented: A Lagrange multiplier formulation and a penalty regularization. They are both implemented within the curvilinear shell and phase field formulations of Duong et al. (2017), Zimmermann et al. (2019) and Paul et al. (2019) and illustrated by several numerical examples. These consider deforming shells, phase separations on evolving surfaces, and dynamic brittle fracture.

  • Assessing the Performance of Leja and Clenshaw-Curtis Collocation for Computational Electromagnetics with Random Input Data
    arXiv.cs.CE Pub Date : 2017-12-19
    Dimitrios Loukrezis; Ulrich Römer; Herbert De Gersem

    We consider the problem of quantifying uncertainty regarding the output of an electromagnetic field problem in the presence of a large number of uncertain input parameters. In order to reduce the growth in complexity with the number of dimensions, we employ a dimension-adaptive stochastic collocation method based on nested univariate nodes. We examine the accuracy and performance of collocation schemes based on Clenshaw-Curtis and Leja rules, for the cases of uniform and bounded, non-uniform random inputs, respectively. Based on numerical experiments with an academic electromagnetic field model, we compare the two rules in both the univariate and multivariate case and for both quadrature and interpolation purposes. Results for a real-world electromagnetic field application featuring high-dimensional input uncertainty are also presented.

  • Non-Intrusive Parametric Model Order Reduction With Error Correction Modeling for Changing Well Locations Using a Machine Learning Framework
    arXiv.cs.CE Pub Date : 2020-01-12
    Hardikkumar Zalavadia; Eduardo Gildin

    The objective of this paper is to develop a global non-intrusive Parametric Model Order Reduction (PMOR) methodology for the problem of changing well locations in an oil field, that can eventually be used for well placement optimization to gain significant computational savings. In this work, we propose a proper orthogonal decomposition (POD) based PMOR strategy that is non-intrusive to the simulator source code and hence extends its applicability to any commercial simulator. The non-intrusiveness of the proposed technique stems from formulating a novel Machine Learning (ML) based framework used with POD. The features of ML model are designed such that they take into consideration the temporal evolution of the state solutions and thereby avoiding simulator access for time dependency of the solutions. We represent well location changes as a parameter by introducing geometry-based features and flow diagnostics inspired physics-based features. An error correction model based on reduced model solutions is formulated later to correct for discrepancies in the state solutions at well gridblocks. It was observed that the global PMOR could predict the overall trend in pressure and saturation solutions at the well blocks but some bias was observed that resulted in discrepancies in prediction of quantities of interest (QoI). Thus, the error correction model that considers the physics based reduced model solutions as features, proved to reduce the error in QoI significantly. This workflow is applied to a heterogeneous channelized reservoir that showed good solution accuracies and speed-ups of 50x-100x were observed for different cases considered. The method is formulated such that all the simulation time steps are independent and hence can make use of parallel resources very efficiently and also avoid stability issues that can result from error accumulation over timesteps.

  • GPU acceleration of \emph{CaNS} for massively-parallel direct numerical simulations of canonical fluid flows
    arXiv.cs.CE Pub Date : 2020-01-15
    Pedro Costa; Everett Phillips; Luca Brandt; Massimiliano Fatica

    This work presents the GPU acceleration of the open-source code \emph{CaNS} for very fast massively-parallel simulations of canonical fluid flows. The distinct feature of the many-CPU Navier-Stokes solver in \emph{CaNS} is its fast \new{direct} solver for the second-order finite-difference Poisson equation, based on the method of eigenfunction expansions. The solver implements all the boundary conditions valid for this type of problems in a unified framework. Here, we extend the solver for GPU-accelerated clusters using CUDA Fortran. The porting \new{makes extensive use of CUF kernels and} has been greatly simplified by the unified memory feature of CUDA Fortran, which handles the data migration between host (CPU) and device (GPU) without defining new arrays in the source code. The overall implementation has been validated against benchmark data for turbulent channel flow and its performance assessed on a NVIDIA DGX-2 system (16 Tesla V100 32Gb, connected with NVLink via NVSwitch). The wall-clock time per time step of the GPU-accelerated implementation is impressively small when compared to its CPU implementation on state-of-the-art many-CPU clusters, as long as the domain partitioning is sufficiently small that the data resides mostly on the GPUs. The implementation has been made freely available and open-source under the terms of an MIT license.

  • A Physics-Constrained Data-Driven Approach Based on Locally Convex Reconstruction for Noisy Database
    arXiv.cs.CE Pub Date : 2019-07-26
    Qizhi He; Jiun-Shyan Chen

    Physics-constrained data-driven computing is an emerging hybrid approach that integrates universal physical laws with data-driven models of experimental data for scientific computing. A new data-driven simulation approach coupled with a locally convex reconstruction, termed the local convexity data-driven (LCDD) computing, is proposed to enhance accuracy and robustness against noise and outliers in data sets in the data-driven computing. In this approach, for a given state obtained by the physical simulation, the corresponding optimum experimental solution is sought by projecting the state onto the associated local convex manifold reconstructed based on the nearest experimental data. This learning process of local data structure is less sensitive to noisy data and consequently yields better accuracy. A penalty relaxation is also introduced to recast the local learning solver in the context of non-negative least squares that can be solved effectively. The reproducing kernel approximation with stabilized nodal integration is employed for the solution of the physical manifold to allow reduced stress-strain data at the discrete points for enhanced effectiveness in the LCDD learning solver. Due to the inherent manifold learning properties, LCDD performs well for high-dimensional data sets that are relatively sparse in real-world engineering applications. Numerical tests demonstrated that LCDD enhances nearly one order of accuracy compared to the standard distance-minimization data-driven scheme when dealing with noisy database, and a linear exactness is achieved when local stress-strain relation is linear.

  • Massively parallel finite difference elasticity using a block-structured adaptive mesh refinement with a geometric multigrid solver
    arXiv.cs.CE Pub Date : 2020-01-10
    Brandon Runnels; Vinamra Agrawal; Weiqun Zhang; Ann Almgren

    The finite element method (FEM) is, by far, the dominant method for performing elasticity calculations. The advantages are primarily (1) its ability to handle meshes of complex geometry using isoparametric elements, and (2) the weak formulation which eschews the need for computation of second derivatives. Despite its widespread use, FEM performance is sub-optimal when working with adaptively refined meshes, due to the excess overhead involved in reconstructing stiffness matrices. Furthermore, FEM is no longer advantageous when working with representative volume elements (RVEs) that use regular grids. Blockstructured AMR (BSAMR) is a method for adaptive mesh refinement that exhibits good scaling and is well-suited for many problems in materials science. Here, it is shown that the equations of elasticity can be efficiently solved using BSAMR using the finite difference method. The boundary operator method is used to treat different types of boundary conditions, and the "reflux-free" method is introduced to efficiently and easily treat the coarse-fine boundaries that arise in BSAMR. Examples are presented that demonstrate the use of this method in a variety of cases relevant to materials science, including Eshelby inclusions, material discontinuities, and phase field fracture. It is shown that the implementation scales very well to tens of millions of grid points and exhibits good AMR efficiency

  • Identification of the partial differential equations governing microstructure evolution in materials: Inference over incomplete, sparse and spatially non-overlapping data
    arXiv.cs.CE Pub Date : 2020-01-11
    Z. Wang; X. Huan; K. Garikipati

    Pattern formation is a widely observed phenomenon in diverse fields including materials physics, developmental biology and ecology among many others. The physics underlying the patterns is specific to the mechanisms, and is encoded by partial differential equations (PDEs). With the aim of discovering hidden physics, we have previously presented a variational approach to identifying such systems of PDEs in the face of noisy data at varying fidelities (Computer Methods in Applied Mechanics and Engineering, 353:201-216, 2019). Here, we extend our methods to address the challenges presented by image data on microstructures in materials physics. PDEs are formally posed as initial and boundary value problems over combinations of time intervals and spatial domains whose evolution is either fixed or can be tracked. However, the vast majority of microscopy techniques for evolving microstructure in a given material system deliver micrographs of pattern evolution wherein the domain at one instant does not spatially overlap with that at another time. The temporal resolution can rarely capture the fastest time scales that dominate the early dynamics, and noise abounds. Finally data for evolution of the same phenomenon in a material system may well be obtained from different physical samples. Against this backdrop of spatially non-overlapping, sparse and multi-source data, we exploit the variational framework to make judicious choices of moments of fields and identify PDE operators from the dynamics. This step is preceded by an imposition of consistency to parsimoniously infer a minimal set of the spatial operators at steady state. The framework is demonstrated on synthetic data that reflects the characteristics of the experimental material microscopy images.

  • Continuum modelling of stress diffusion interactions in an elastoplastic medium in the presence of geometric discontinuity
    arXiv.cs.CE Pub Date : 2020-01-11
    Rupesh Kumar Mahendran; Hirshikesh; Ratna Kumar Annabattula; Sundararajan Natarajan

    Chemo-mechanical coupled systems have been a subject of interest for many decades now. Previous attempts to solve such models have mainly focused on elastic materials without taking into account the plastic deformation beyond yield, thus causing inaccuracies in failure calculations. This paper aims to study the effect of stress-diffusion interactions in an elastoplastic material using a coupled chemo-mechanical system. The induced stress is dependent on the local concentration in a one way coupled system, and vice versa in a two way coupled system. The time-dependent transient coupled system is solved using a finite element formulation in an open-source finite element solver FEniCS. This paper attempts to computationally study the interaction of deformation and diffusion and its effect on the localization of plastic strain. We investigate the role of geometric discontinuities in scenarios involving diffusing species, namely, a plate with a notch/hole/void and particle with a void/hole/core. We also study the effect of stress concentrations and plastic yielding on the diffusion-deformation. The developed code can be from https://github.com/mrupeshkumar/Elastoplastic-stress-diffusion-coupling

  • Accurate iteration-free mixed-stabilised formulation for laminar incompressible Navier-Stokes: Applications to fluid-structure interaction
    arXiv.cs.CE Pub Date : 2020-01-14
    Chennakesava Kadapa; Wulf G Dettmer; Djordje Peric

    Stabilised mixed velocity-pressure formulations are one of the widely-used finite element schemes for computing the numerical solutions of laminar incompressible Navier-Stokes. In these formulations, the Newton-Raphson scheme is employed to solve the nonlinearity in the convection term. One fundamental issue with this approach is the computational cost incurred in the Newton-Raphson iterations at every load/time step. In this paper, we present an iteration-free mixed-stabilised finite element formulation for incompressible Navier-Stokes that preserves second-order temporal accuracy for both velocity and pressure fields. We prove the second-order temporal accuracy using an example with a manufactured solution. We then illustrate the accuracy and the computational benefits of the proposed scheme by studying the benchmark example of flow past a fixed circular cylinder and then using two benchmark examples in fluid-flexible structure interaction.

  • Modelling Orebody Structures: Block Merging Algorithms and Block Model Spatial Restructuring Strategies Given Mesh Surfaces of Geological Boundaries
    arXiv.cs.CE Pub Date : 2020-01-13
    Raymond Leung

    This paper describes a framework for capturing geological structures in a 3D block model and improving its spatial fidelity, including the correction of stratigraphic boundaries, given new mesh surfaces. Using surfaces that represent geological boundaries, the objectives are to identify areas where refinement is needed, increase spatial resolution to minimise surface approximation error, reduce redundancy to increase the compactness of the model, and identify the geological domain on a block-by-block basis. These objectives are fulfilled by four system components which perform block-surface overlap detection, spatial structure decomposition, sub-blocks consolidation and block tagging, respectively. The main contributions are a coordinate-ascent merging algorithm and a flexible architecture for updating the spatial structure of a block model when given multiple surfaces, which emphasises the ability to selectively retain or modify previously assigned block labels. The techniques employed include block-surface intersection analysis based on the separable axis theorem and ray-tracing for establishing the location of blocks relative to surfaces. To demonstrate the robustness and applicability of the block merging technique to a wider class of problem, the core approach is extended to reduce fragmentation in a block model where surfaces are not directly involved. The results show the proposed method produces merged blocks with less extreme aspect ratios and is highly amenable to parallel processing. The overall framework is applicable to orebody modelling given mineralisation or stratigraphic boundaries, and 3D segmentation more generally, where there is a need to delineate spatial regions using mesh surfaces within a block model.

  • Reliable and interoperable computational molecular engineering: 2. Semantic interoperability based on the European Materials and Modelling Ontology
    arXiv.cs.CE Pub Date : 2020-01-13
    Martin Thomas Horsch; Silvia Chiacchiera; Youness Bami; Georg J. Schmitz; Gabriele Mogni; Gerhard Goldbeck; Emanuele Ghedini

    The European Materials and Modelling Ontology (EMMO) is a top-level ontology designed by the European Materials Modelling Council to facilitate semantic interoperability between platforms, models, and tools in computational molecular engineering, integrated computational materials engineering, and related applications of materials modelling and characterization. Additionally, domain ontologies exist based on data technology developments from specific platforms. The present work discusses the ongoing work on establishing a European Virtual Marketplace Framework, into which diverse platforms can be integrated. It addresses common challenges that arise when marketplace-level domain ontologies are combined with a top-level ontology like the EMMO by ontology alignment.

  • Multi-Objective Optimisation of Damper Placement for Improved Seismic Response in Dynamically Similar Adjacent Buildings
    arXiv.cs.CE Pub Date : 2019-12-29
    Mahesh B. Patil; Ramakrishna U.; Mohan S. C

    Multi-objective optimisation of damper placement in dynamically symmetric adjacent buildings is considered with identical viscoelastic dampers used for vibration control. First, exhaustive search is used to describe the solution space in terms of various quantities of interest such as maximum top floor displacement, maximum floor acceleration, base shear, and interstorey drift. With the help of examples, it is pointed out that the Pareto fronts in these problems contain a very small number of solutions. The effectiveness of two commonly used multi-objective evolutionary algorithms, viz., NSGA-II and MOPSO, is evaluated for a specific example.

  • A stable SPH with adaptive B-spline kernel
    arXiv.cs.CE Pub Date : 2020-01-04
    Saptarshi Kumar Lahiri; Kanishka Bhattacharya; Amit Shaw; L S Ramachandra

    Tensile instability, often observed in smoothed particle hydrodynamics (SPH), is a numerical artifact that manifests itself by unphysical clustering or separation of particles. The instability originates in estimating the derivatives of the smoothing functions which, when interact with material constitution may result in negative stiffness in the discretized system. In the present study, a stable formulation of SPH is developed where the kernel function is continuously adapted at every material point depending on its state of stress. Bspline basis function with a variable intermediate knot is used as the kernel function. The shape of the kernel function is then modified by changing the intermediate knot position such that the condition associated with instability does not arise. While implementing the algorithm the simplicity and computational efficiency of SPH are not compromised. One-dimensional dispersion analysis is performed to understand the effect adaptive kernel on the stability. Finally, the efficacy of the algorithm is demonstrated through some benchmark elastic dynamics problems.

  • A machine learning based plasticity model using proper orthogonal decomposition
    arXiv.cs.CE Pub Date : 2020-01-07
    Dengpeng Huang; Jan Niklas Fuhg; Christian Weißenfels; Peter Wriggers

    Data-driven material models have many advantages over classical numerical approaches, such as the direct utilization of experimental data and the possibility to improve performance of predictions when additional data is available. One approach to develop a data-driven material model is to use machine learning tools. These can be trained offline to fit an observed material behaviour and then be applied in online applications. However, learning and predicting history dependent material models, such as plasticity, is still challenging. In this work, a machine learning based material modelling framework is proposed for both elasticity and plasticity. The machine learning based hyperelasticity model is developed with the Feed forward Neural Network (FNN) directly whereas the machine learning based plasticity model is developed by using of a novel method called Proper Orthogonal Decomposition Feed forward Neural Network (PODFNN). In order to account for the loading history, the accumulated absolute strain is proposed to be the history variable of the plasticity model. Additionally, the strain-stress sequence data for plasticity is collected from different loading-unloading paths based on the concept of sequence for plasticity. By means of the POD, the multi-dimensional stress sequence is decoupled leading to independent one dimensional coefficient sequences. In this case, the neural network with multiple output is replaced by multiple independent neural networks each possessing a one-dimensional output, which leads to less training time and better training performance. To apply the machine learning based material model in finite element analysis, the tangent matrix is derived by the automatic symbolic differentiation tool AceGen. The effectiveness and generalization of the presented models are investigated by a series of numerical examples using both 2D and 3D finite element analysis.

  • Explainable Deep Convolutional Candlestick Learner
    arXiv.cs.CE Pub Date : 2020-01-08
    Jun-Hao Chen; Samuel Yen-Chi Chen; Yun-Cheng Tsai; Chih-Shiang Shur

    Candlesticks are graphical representations of price movements for a given period. The traders can discovery the trend of the asset by looking at the candlestick patterns. Although deep convolutional neural networks have achieved great success for recognizing the candlestick patterns, their reasoning hides inside a black box. The traders cannot make sure what the model has learned. In this contribution, we provide a framework which is to explain the reasoning of the learned model determining the specific candlestick patterns of time series. Based on the local search adversarial attacks, we show that the learned model perceives the pattern of the candlesticks in a way similar to the human trader.

  • A Generalized Probabilistic Learning Approach for Multi-Fidelity Uncertainty Propagation in Complex Physical Simulations
    arXiv.cs.CE Pub Date : 2020-01-09
    Jonas Nitzler; Jonas Biehler; Niklas Fehn; Phaedon-Stelios Koutsourelakis; Wolfgang A. Wall

    Two of the most significant challenges in uncertainty propagation pertain to the high computational cost for the simulation of complex physical models and the high dimension of the random inputs. In applications of practical interest both of these problems are encountered and standard methods for uncertainty quantification either fail or are not feasible. To overcome the current limitations, we propose a probabilistic multi-fidelity framework that can exploit lower-fidelity model versions of the original problem in a small data regime. The approach circumvents the curse of dimensionality by learning dependencies between the outputs of high-fidelity models and lower-fidelity models instead of explicitly accounting for the high-dimensional inputs. We complement the information provided by a low-fidelity model with a low-dimensional set of informative features of the stochastic input, which are discovered by employing a combination of supervised and unsupervised dimensionality reduction techniques. The goal of our analysis is an efficient and accurate estimation of the full probabilistic response for a high-fidelity model. Despite the incomplete and noisy information that low-fidelity predictors provide, we demonstrate that accurate and certifiable estimates for the quantities of interest can be obtained in the small data regime, i.e., with significantly fewer high-fidelity model runs than state-of-the-art methods for uncertainty propagation. We illustrate our approach by applying it to challenging numerical examples such as Navier-Stokes flow simulations and monolithic fluid-structure interaction problems.

  • A Class of Analytic Solutions for Verification and Convergence Analysis of Linear and Nonlinear Fluid-Structure Interaction Algorithms
    arXiv.cs.CE Pub Date : 2019-06-07
    Andreas Hessenthaler; Maximilian Balmus; Oliver Röhrle; David Nordsletten

    Fluid-structure interaction (FSI) problems are pervasive in the computational engineering community. The need to address challenging FSI problems has led to the development of a broad range of numerical methods addressing a variety of application-specific demands. While a range of numerical and experimental benchmarks are present in the literature, few solutions are available that enable both verification and spatiotemporal convergence analysis. In this paper, we introduce a class of analytic solutions to FSI problems involving shear in channels and pipes. Comprised of 16 separate analytic solutions, our approach is permuted to enable progressive verification and analysis of FSI methods and implementations, in two and three dimensions, for static and transient scenarios as well as for linear and hyperelastic solid materials. Results are shown for a range of analytic models exhibiting progressively complex behavior. The utility of these solutions for analysis of convergence behavior is further demonstrated using a previously published monolithic FSI technique. The resulting class of analytic solutions addresses a core challenge in the development of novel FSI algorithms and implementations, providing a progressive testbed for verification and detailed convergence analysis.

  • ILS-MPM: an implicit level-set-based material point method for frictional particulate contact mechanics of deformable particles
    arXiv.cs.CE Pub Date : 2020-01-08
    Chuanqi Liu; Waiching Sun

    Finite element simulations of frictional multi-body contact problems via conformal meshes can be challenging and computationally demanding. To render geometrical features, unstructured meshes must be used and this unavoidably increases the degrees of freedom and therefore makes the construction of slave/master pairs more demanding. In this work, we introduce an implicit material point method designed to bypass the meshing of bodies by employing level set functions to represent boundaries at structured grids. This implicit function representation provides an elegant mean to link an unbiased intermediate reference surface with the true boundaries by closest point projection as shown in leichner et al. (2019). We then enforce the contact constraints by a penalty method where the Coulomb friction law is implemented as an elastoplastic constitutive model such that a return mapping algorithm can be used to provide constitutive updates for both the stick and slip states. To evolve the geometry of the contacts properly, the Hamilton-Jacobi equation is solved incrementally such that the level set and material points are both updated accord to the deformation field. To improve the accuracy and regularity of the numerical integration of the material point method, a moving least square method is used to project numerical values of the material points back to the standard locations for Gaussian-Legendre quadrature. Several benchmarks are used to verify the proposed model. Comparisons with discrete element simulations are made to analyze the importance of stress fields on predicting the macroscopic responses of granular assemblies.

  • D3BA: A Tool for Optimizing Business Processes Using Non-Deterministic Planning
    arXiv.cs.CE Pub Date : 2020-01-08
    Tathagata Chakraborti; Yasaman Khazaeni

    This paper builds upon recent work in the declarative design of dialogue agents and proposes an exciting new tool -- D3BA -- Declarative Design for Digital Business Automation, built to optimize business processes using the power of AI planning. The tool provides a powerful framework to build, optimize, and maintain complex business processes and optimize them by composing with services that automate one or more subtasks. We illustrate salient features of this composition technique, compare with other philosophies of composition, and highlight exciting opportunities for research in this emerging field of business process automation.

  • Preliminary Studies on the Usefulness of Nonlinear Boundary Element Method for Real-Time Simulation of Biological Organs
    arXiv.cs.CE Pub Date : 2020-01-06
    Kirana Kumara P

    There is some literature on the application of linear boundary element method (BEM) for real-time simulation of biological organs. However, literature is scant when it comes to the application of nonlinear BEM, although there is a possibility that the use of nonlinear BEM would result in better simulations. Hence the present paper explores the possibility of using nonlinear BEM for real-time simulation of biological organs. This paper begins with a general discussion about using the nonlinear BEM for real-time simulation of biological organs. Literature on nonlinear BEM is reviewed and the literature that deal with nonlinear formulations and coding are noted down next. In the later sections, some results obtained from nonlinear analyses are compared with the corresponding results from linear analyses. The last section concludes with remarks that indicate that it might be possible to obtain better simulations in the future by using nonlinear BEM.

  • Highly Efficient Feasible Direction Method (HEFDiM) for Structural Topology Optimization
    arXiv.cs.CE Pub Date : 2020-01-07
    Zhi Zeng; Fulei Ma

    Feasible Direction Method (FDM) is a concise yet rigorous mathematical method for structural topology optimization, which can be easily applied to different types of problems with less modification. In addition, the FDM always converges to a near optimum rapidly. However, the problem of inefficiency stays unsolved. In this work, we advance the state-of-the-art by proposing a highly efficient feasible direction method (HEFDiM), which substantially improves the efficiency of the FDM with negligible loss of accuracy. The proposed method can benefit us in at least four aspects: 1) Analytical gradient projection; 2) Fewer heuristics and clear physical meaning; 3) Negligible memory and time-cost for updating; 4) Directly applied to different problems without extra efforts. In particular, we address problems including 1) Efficient determination of effective constraints for gradient projection; 2) Acceleration of null-space projection calculation; 3) Avoidance of time costing 1-D searching; 4) Elimination of split-stepping and zig-zag problems. Benchmark problems, including the MBB, the force inverter mechanism, and the 3D cantilever beam are used to validate the effectiveness of the method. Specifically, the results show that the updating speed of the HEFDiM is approximately 10 times higher (even faster for larger-scale optimization problems) with lower objective value than that of the classical efficient 88-line MATLAB code (Andreassen et, al. 2011). The HEFDiM is implemented in MATLAB which is open-sourced for educational usage.

  • A phase field model for cohesive fracture in micropolar continua
    arXiv.cs.CE Pub Date : 2020-01-04
    Hyoung Suk Suh; WaiChing Sun; Devin O'Connor

    While crack nucleation and propagation in the brittle or quasi-brittle regime can be predicted via variational or material-force-based phase field fracture models, these models often assume that the underlying elastic response of the material is non-polar and yet a length scale parameter must be introduced to enable the sharp cracks represented by a regularized implicit function. However, many materials with internal microstructures that contain surface tension, micro-cracks, micro-fracture, inclusion, cavity or those of particulate nature often exhibit size-dependent behaviors in both the path-independent and path-dependent regimes. This paper is intended to introduce a unified treatment that captures the size effect of the materials in both elastic and damaged states. By introducing a cohesive micropolar phase field fracture theory, along with the computational model and validation exercises, we explore the interacting size-dependent elastic deformation and fracture mechanisms exhibits in materials of complex microstructures. To achieve this goal, we introduce the distinctive degradation functions of the force-stress-strain and couple-stress-micro-rotation energy-conjugated pairs for a given regularization profile such that the macroscopic size-dependent responses of the micropolar continua is insensitive to the length scale parameter of the regularized interface. Then, we apply the variational principle to derive governing equations from the micropolar stored energy and dissipative functionals. Numerical examples are introduced to demonstrate the proper way to identify material parameters and the capacity of the new formulation to simulate complex crack patterns in the quasi-static regime.

  • The Radial Point Interpolation Mixed Collocation (RPIMC) Method for the Solution of Transient Diffusion Problems
    arXiv.cs.CE Pub Date : 2020-01-04
    Konstantinos A. Mountris; Esther Pueyo

    The Radial Point Interpolation Mixed Collocation (RPIMC) method is proposed in this paper for transient analysis of diffusion problems. RPIMC is an efficient purely meshless method where the solution of the field variable is obtained through collocation. The field function and its gradient are both interpolated (mixed collocation approach) leading to reduced $C$-continuity requirement compared to strong-form collocation schemes. The method's accuracy is evaluated in heat conduction benchmark problems. The RPIMC convergence is compared against the Meshless Local Petrov-Galerkin Mixed Collocation (MLPG-MC) method and the Finite Element Method (FEM). Due to the delta Kronecker property of RPIMC, improved accuracy can be achieved as compared to MLPG-MC. RPIMC is proven to be a promising meshless alternative to FEM for transient diffusion problems.

  • Machine learning materials physics: Multi-resolution neural networks learn the free energy and nonlinear elastic response of evolving microstructures
    arXiv.cs.CE Pub Date : 2019-12-31
    Xiaoxuan Zhang; Krishna Garikipati

    Many important multi-component crystalline solids undergo mechanochemical spinodal decomposition: a phase transformation in which the compositional redistribution is coupled with structural changes of the crystal, resulting in dynamic and intricate microstructures. The ability to rapidly compute the macroscopic behavior based on these detailed microstructures is of paramount importance for accelerating material discovery and design. However, the evaluation of macroscopic, nonlinear elastic properties purely based on direct numerical simulations (DNS) is computationally very expensive, and hence impractical for material design when a large number of microstructures need to be tested. A further complexity of a hierarchical nature arises if the elastic free energy and its variation with strain is a small scale fluctuation on the dominant trajectory of the total free energy driven by microstructural dynamics. To address these challenges, we present a data-driven approach, which combines advanced neural network (NN) models with DNS to predict the mechanical free energy and homogenized stress fields on microstructures in a family of two-dimensional multi-component crystalline solids. The microstructres are numerically generated by solving a coupled, Cahn-Hilliard and nonlinear strain gradient elasticity problem. The hierarchical structure of the free energy's evolution induces a multi-resolution character to the machine learning paradigm: We construct knowledge-based neural networks (KBNNs) with either pre-trained fully connected deep neural networks (DNNs) or pre-trained convolutional neural networks (CNNs) that describe the dominant feature of the data to fully represent the hierarchichally evolving free energy. We demonstrate multi-resolution learning of the materials physics of nonlinear elastic response for both fixed and evolving microstructures.

  • RBF-FD analysis of 2D time-domain acoustic wave propagation in heterogeneous Earth's subsurface
    arXiv.cs.CE Pub Date : 2020-01-02
    Jure Močnik - Berljavac; Pankaj K Mishra; Jure Slak; Gregor Kosec

    Radial Basis Function-generated Finite Differences (RBF-FD) is a popular variant of local strong-form meshless methods that do not require a predefined connection between the nodes, making it easier to adapt node-distribution to the problem under consideration. This paper investigates a RBF-FD solution of time-domain acoustic wave propagation in the context of seismic modeling in the Earth's subsurface. Through a number of numerical tests, ranging from homogeneous to highly-heterogeneous velocity models, we demonstrate that the present approach can be further generalized to solve large-scale seismic modeling and full waveform inversion problems in arbitrarily complex models --- enabling more robust interpretations to geophysical observations.

  • Development, Demonstration, and Validation of Data-driven Compact Diode Models for Circuit Simulation and Analysis
    arXiv.cs.CE Pub Date : 2020-01-06
    K. Aadithya; P. Kuberry; B. Paskaleva; P. Bochev; K. Leeson; A. Mar; T. Mei; E. Keiter

    Compact semiconductor device models are essential for efficiently designing and analyzing large circuits. However, traditional compact model development requires a large amount of manual effort and can span many years. Moreover, inclusion of new physics (eg, radiation effects) into an existing compact model is not trivial and may require redevelopment from scratch. Machine Learning (ML) techniques have the potential to automate and significantly speed up the development of compact models. In addition, ML provides a range of modeling options that can be used to develop hierarchies of compact models tailored to specific circuit design stages. In this paper, we explore three such options: (1) table-based interpolation, (2)Generalized Moving Least-Squares, and (3) feed-forward Deep Neural Networks, to develop compact models for a p-n junction diode. We evaluate the performance of these "data-driven" compact models by (1) comparing their voltage-current characteristics against laboratory data, and (2) building a bridge rectifier circuit using these devices, predicting the circuit's behavior using SPICE-like circuit simulations, and then comparing these predictions against laboratory measurements of the same circuit.

  • Convolutional Neural Network-based Topology Optimization (CNN-TO) By Estimating Sensitivity of Compliance from Material Distribution
    arXiv.cs.CE Pub Date : 2019-12-23
    Yusuke Takahashi; Yoshiro Suzuki; Akira Todoroki

    This paper proposes a new topology optimization method that applies a convolutional neural network (CNN), which is one deep learning technique for topology optimization problems. Using this method, we acquire a structure with a little higher performance that could not be obtained by the previous topology optimization method. In particular, in this paper, we solve a topology optimization problem aimed at maximizing stiffness with a mass constraint, which is a common type of topology optimization. In this paper, we first formulate the conventional topology optimization by the solid isotropic material with penalization method. Next, we formulate the topology optimization using CNN. Finally, we show the effectiveness of the proposed topology optimization method by solving a verification example, namely a topology optimization problem aimed at maximizing stiffness. In this research, as a result of solving the verification example for a small design area of 16x32 element, we obtain the solution different from the previous topology optimization method. This result suggests that stiffness information of structure can be extracted and analyzed for structural design by analyzing the density distribution using CNN like an image. This suggests that CNN technology can be utilized in the structural design and topology optimization.

  • Numerical investigation into fracture resistance of bone following adaptation
    arXiv.cs.CE Pub Date : 2020-01-02
    Karol Lewandowski; Łukasz Kaczmarczyk; Ignatios Athanasiadis; John F. Marshall; Chris J. Pearce

    Bone adapts in response to its mechanical environment. This evolution of bone density is one of the most important mechanisms for developing fracture resistance. A finite element framework for simulating bone adaptation, commonly called bone remodelling, is presented. This is followed by a novel method to both quantify fracture resistance and to simulate fracture propagation. The authors' previous work on the application of configurational mechanics for modelling fracture is extended to include the influence of heterogeneous bone density distribution. The main advantage of this approach is that configurational forces, and fracture energy release rate, are expressed exclusively in terms of nodal quantities. This approach avoids the need for post-processing and enables a fully implicit formulation for modelling the evolving crack front. In this paper density fields are generated from both (a) bone adaptation analysis and (b) subject-specific geometry and material properties obtained from CT scans. It is shown that, in order to correctly evaluate the configurational forces at the crack front, it is necessary to have a spatially smooth density field with higher regularity than if the field is directly approximated on the finite element mesh. Therefore, discrete density data is approximated as a smooth density field using a Moving Weighted Least Squares method. Performance of the framework is demonstrated using numerical simulations for bone adaptation and subsequent crack propagation, including consideration of an equine 3rd metacarpal bone. The degree of bone adaption is shown to influence both fracture resistance and the resulting crack path.

  • Optimization of Solidification in Die Casting using Numerical Simulations and Machine Learning
    arXiv.cs.CE Pub Date : 2019-01-08
    Shantanu Shahane; Narayana Aluru; Placid Ferreira; Shiv G Kapoor; Surya Pratap Vanka

    In this paper, we demonstrate the combination of machine learning and three dimensional numerical simulations for multi-objective optimization of low pressure die casting. The cooling of molten metal inside the mold is achieved typically by passing water through the cooling lines in the die. Depending on the cooling line location, coolant flow rate and die geometry, nonuniform temperatures are imposed on the molten metal at the mold wall. This boundary condition along with the initial molten metal temperature affect the product quality quantified in terms of micro-structure parameters and yield strength. A finite volume based numerical solver is used to determine the temperature-time history and correlate the inputs to outputs. The objective of this research is to develop and demonstrate a procedure to obtain the initial and wall temperatures so as to optimize the product quality. The non-dominated sorting genetic algorithm (NSGA-II) is used for multi-objective optimization in this work. The number of function evaluations required for NSGA-II can be of the order of millions and hence, the finite volume solver cannot be used directly for optimization. Therefore, a multilayer perceptron feed-forward neural network is first trained using the results from the numerical solution of the fluid flow and energy equations and is subsequently used as a surrogate model. As an assessment, simplified versions of the actual problem are designed to first verify results of the genetic algorithm. An innovative local sensitivity based approach is then used to rank the final Pareto optimal solutions and select a single best design.

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上海纽约大学William Glover