62 research outputs found
A scalable domain decomposition method for FEM discretizations of nonlocal equations of integrable and fractional type
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
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Multiscale Modeling with Meshfree Methods
Multiscale modeling has become an important tool in material mechanics because material behavior can exhibit varied properties across different length scales. The use of multiscale modeling is essential for accurately capturing these characteristics and predicting material behavior. Mesh-free methods have also been gaining attention in recent years due to their innate ability to handle complex geometries and large deformations. These methods provide greater flexibility and efficiency in modeling complex material behavior, especially for problems involving discontinuities, such as fractures and cracks. Moreover, mesh-free methods can be easily extended to multiple lengths and time scales, making them particularly suitable for multiscale modeling.
The thesis focuses on two specific problems of multiscale modeling with mesh-free methods. The first problem is the atomistically informed constitutive model for the study of high-pressure induced densification of silica glass. Molecular Dynamics (MD) simulations are carried out to study the atomistic level responses of fused silica under different pressure and strain-rate levels, Based on the data obtained from the MD simulations, a novel continuum-based multiplicative hyper-elasto-plasticity model that accounts for the anomalous densification behavior is developed and then parameterized using polynomial regression and deep learning techniques. To incorporate dynamic damage evolution, a plasticity-damage variable that controls the shrinkage of the yield surface is introduced and integrated into the elasto-plasticity model. The resulting coupled elasto-plasticity-damage model is reformulated to a non-ordinary state-based peridynamics (NOSB-PD) model for the computational efficiency of impact simulations. The developed peridynamics (PD) model reproduces coarse-scale quantities of interest found in MD simulations and can simulate at a component level. Finally, the proposed atomistically-informed multiplicative hyper-elasto-plasticity-damage model has been validated against limited available experimental results for the simulation of hyper-velocity impact simulation of projectiles on silica glass targets.
The second problem addressed in the thesis involves the upscaling approach for multi-porosity media, analyzed using the so-called MultiSPH method, which is a sequential SPH (Smoothed Particle Hydrodynamics) solver across multiple scales. Multi-porosity media is commonly found in natural and industrial materials, and their behavior is not easily captured with traditional numerical methods. The upscaling approach presented in the thesis is demonstrated on a porous medium consisting of three scales, it involves using SPH methods to characterize the behavior of individual pores at the microscopic scale and then using a homogenization technique to upscale to the meso and macroscopic level. The accuracy of the MultiSPH approach is confirmed by comparing the results with analytical solutions for simple microstructures, as well as detailed single-scale SPH simulations and experimental data for more complex microstructures
Identifiability and data-adaptive RKHS Tikhonov regularization in nonparametric learning problems
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
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
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
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
Glasses are materials that lack a crystalline microstructure and longârange 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 structureâproperty 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 glassâlike 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, phaseâseparated glasses, and bioinspired glassâpolymer composites hold significant promise. Such materials are designed from the bottomâup, building on structureâproperty 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
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
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
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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