62 research outputs found

    A scalable domain decomposition method for FEM discretizations of nonlocal equations of integrable and fractional type

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    Nonlocal models allow for the description of phenomena which cannot be captured by classical partial differential equations. The availability of efficient solvers is one of the main concerns for the use of nonlocal models in real world engineering applications. We present a domain decomposition solver that is inspired by substructuring methods for classical local equations. In numerical experiments involving finite element discretizations of scalar and vectorial nonlocal equations of integrable and fractional type, we observe improvements in solution time of up to 14.6x compared to commonly used solver strategies

    Identifiability and data-adaptive RKHS Tikhonov regularization in nonparametric learning problems

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    We provide an identifiability analysis for the learning problems (1) nonparametric learning of kernels in operators and (2) unsupervised learning of observation functions in state space models (SSMs). We show that in either case the function space of identifiability (FSOI) from the quadratic loss functional is the closure of a system-intrinsic data-adaptive reproducing kernel Hilbert space (SIDA-RKHS). We introduce a new method, the Data-Adaptive RKHS Tikhonov Regularization method (DARTR). The regularized estimator is robust to noise and converges as data refines. The effectiveness of DARTR is demonstrated through the following problems (1) nonparametric learning of kernels in linear/nonlinear/nonlocal operators and (2) homogenization of wave propagation in meta-material. We introduce a nonparametric generalized moment method to estimate non-invertible observation functions in nonlinear SSMs. Numerical results shows that the first two moments and temporal correlations, along with upper and lower bounds, can identify functions ranging from piecewise polynomials to smooth functions. The limitations, such as non-identifiability due to symmetry and stationary, are also discussed

    A comparative review of peridynamics and phase-field models for engineering fracture mechanics

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    Computational modeling of the initiation and propagation of complex fracture is central to the discipline of engineering fracture mechanics. This review focuses on two promising approaches: phase-field (PF) and peridynamic (PD) models applied to this class of problems. The basic concepts consisting of constitutive models, failure criteria, discretization schemes, and numerical analysis are briefly summarized for both models. Validation against experimental data is essential for all computational methods to demonstrate predictive accuracy. To that end, the Sandia Fracture Challenge and similar experimental data sets where both models could be benchmarked against are showcased. Emphasis is made to converge on common metrics for the evaluation of these two fracture modeling approaches. Both PD and PF models are assessed in terms of their computational effort and predictive capabilities, with their relative advantages and challenges are summarized

    Computational Modelling of Concrete and Concrete Structures

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    Computational Modelling of Concrete and Concrete Structures contains the contributions to the EURO-C 2022 conference (Vienna, Austria, 23-26 May 2022). The papers review and discuss research advancements and assess the applicability and robustness of methods and models for the analysis and design of concrete, fibre-reinforced and prestressed concrete structures, as well as masonry structures. Recent developments include methods of machine learning, novel discretisation methods, probabilistic models, and consideration of a growing number of micro-structural aspects in multi-scale and multi-physics settings. In addition, trends towards the material scale with new fibres and 3D printable concretes, and life-cycle oriented models for ageing and durability of existing and new concrete infrastructure are clearly visible. Overall computational robustness of numerical predictions and mathematical rigour have further increased, accompanied by careful model validation based on respective experimental programmes. The book will serve as an important reference for both academics and professionals, stimulating new research directions in the field of computational modelling of concrete and its application to the analysis of concrete structures. EURO-C 2022 is the eighth edition of the EURO-C conference series after Innsbruck 1994, Bad Gastein 1998, St. Johann im Pongau 2003, Mayrhofen 2006, Schladming 2010, St. Anton am Arlberg 2014, and Bad Hofgastein 2018. The overarching focus of the conferences is on computational methods and numerical models for the analysis of concrete and concrete structures

    Phasenfeldmodellierung von Bruchbildungs-, Kristallisations- und AuflösungsvorgÀngen in hydrothermalen Umgebungen

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    This work focuses on the numerical investigation of fracture formation, crystallization, and crystal dissolution processes in subsurface hydrothermal environments on microscale. Phase-field models are presented and applied to these processes. The formation of mineral veins in limestones and in quartz-rich microstructures are modeled to investigate different factors which influence the evolving crystal structure. Moreover, crystal dissolution processes of different minerals are modeled

    Advancing the mechanical performance of glasses: Perspectives and challenges

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    Glasses are materials that lack a crystalline microstructure and long‐range atomic order. Instead, they feature heterogeneity and disorder on superstructural scales, which have profound consequences for their elastic response, material strength, fracture toughness, and the characteristics of dynamic fracture. These structure–property relations present a rich field of study in fundamental glass physics and are also becoming increasingly important in the design of modern materials with improved mechanical performance. A first step in this direction involves glass‐like materials that retain optical transparency and the haptics of classical glass products, while overcoming the limitations of brittleness. Among these, novel types of oxide glasses, hybrid glasses, phase‐separated glasses, and bioinspired glass–polymer composites hold significant promise. Such materials are designed from the bottom‐up, building on structure–property relations, modeling of stresses and strains at relevant length scales, and machine learning predictions. Their fabrication requires a more scientifically driven approach to materials design and processing, building on the physics of structural disorder and its consequences for structural rearrangements, defect initiation, and dynamic fracture in response to mechanical load. In this article, a perspective is provided on this highly interdisciplinary field of research in terms of its most recent challenges and opportunities.The mechanical performance of glassy materials presents a major challenge in modern glass science and technology. With a focus on visually transparent, inorganic and hybrid glasses, a perspective on the most recent developments in the field is provided herein, emphasizing the importance of translating fundamental insight from glass physics into future applications

    Bayesian Nonlocal Operator Regression (BNOR): A Data-Driven Learning Framework of Nonlocal Models with Uncertainty Quantification

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    We consider the problem of modeling heterogeneous materials where micro-scale dynamics and interactions affect global behavior. In the presence of heterogeneities in material microstructure it is often impractical, if not impossible, to provide quantitative characterization of material response. The goal of this work is to develop a Bayesian framework for uncertainty quantification (UQ) in material response prediction when using nonlocal models. Our approach combines the nonlocal operator regression (NOR) technique and Bayesian inference. Specifically, we use a Markov chain Monte Carlo (MCMC) method to sample the posterior probability distribution on parameters involved in the nonlocal constitutive law, and associated modeling discrepancies relative to higher fidelity computations. As an application, we consider the propagation of stress waves through a one-dimensional heterogeneous bar with randomly generated microstructure. Several numerical tests illustrate the construction, enabling UQ in nonlocal model predictions. Although nonlocal models have become popular means for homogenization, their statistical calibration with respect to high-fidelity models has not been presented before. This work is a first step towards statistical characterization of nonlocal model discrepancy in the context of homogenization

    OBMeshfree: An optimization-based meshfree solver for nonlocal diffusion and peridynamics models

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    We present OBMeshfree, an Optimization-Based Meshfree solver for compactly supported nonlocal integro-differential equations (IDEs) that can describe material heterogeneity and brittle fractures. OBMeshfree is developed based on a quadrature rule calculated via an equality constrained least square problem to reproduce exact integrals for polynomials. As such, a meshfree discretization method is obtained, whose solution possesses the asymptotically compatible convergence to the corresponding local solution. Moreover, when fracture occurs, this meshfree formulation automatically provides a sharp representation of the fracture surface by breaking bonds, avoiding the loss of mass. As numerical examples, we consider the problem of modeling both homogeneous and heterogeneous materials with nonlocal diffusion and peridynamics models. Convergences to the analytical nonlocal solution and to the local theory are demonstrated. Finally, we verify the applicability of the approach to realistic problems by reproducing high-velocity impact results from the Kalthoff-Winkler experiments. Discussions on possible immediate extensions of the code to other nonlocal diffusion and peridynamics problems are provided. OBMeshfree is freely available on GitHub.Comment: For associated code, see https://github.com/youhq34/meshfree_quadrature_nonloca

    A comparative review of peridynamics and phase-field models for engineering fracture mechanics

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    Computational modeling of the initiation and propagation of complex fracture is central to the discipline of engineering fracture mechanics. This review focuses on two promising approaches: phase-field (PF) and peridynamic (PD) models applied to this class of problems. The basic concepts consisting of constitutive models, failure criteria, discretization schemes, and numerical analysis are briefly summarized for both models. Validation against experimental data is essential for all computational methods to demonstrate predictive accuracy. To that end, the Sandia Fracture Challenge and similar experimental data sets where both models could be benchmarked against are showcased. Emphasis is made to converge on common metrics for the evaluation of these two fracture modeling approaches. Both PD and PF models are assessed in terms of their computational effort and predictive capabilities, with their relative advantages and challenges are summarized. © 2022, The Author(s)
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