{
"code": 200,
"data": [
{
"_id": "5e68c5f591e0116bed041477",
"abstract": "Geologic fractures such as joints and faults are central to many problems in energy geotechnics. Notable examples include hydraulic fracturing, injection-induced earthquakes, and geologic carbon storage. Nevertheless, our current capabilities for simulating the development and evolution of geologic fractures in these problems are still insufficient in terms of efficiency and accuracy. Recently, phase-field modeling has emerged as an efficient numerical method for fracture simulation which does not require any algorithm for tracking the geometry of fracture. However, existing phase-field models of fracture neglected two distinct characteristics of geologic fractures, namely, the pressure-dependence and frictional contact. To overcome these limitations, new phase-field models have been developed and described in this paper. The new phase-field models are demonstrably capable of simulating pressure-dependent, frictional fractures propagating in arbitrary directions, which is a notoriously challenging task.",
"authors": [
{
"_id": "61b2dda36750f8276edd3a4e",
"name": "Jinhyun Choo",
"org": "Korea Adv Inst Sci & Technol, Dept Civil & Environm Engn, Daejeon, South Korea"
}
],
"doi": "10.1016/j.cma.2020.113265",
"keywords": [
"fracture",
"phase-field model",
"numerical analysis",
"computational mechanics",
"geomaterials"
],
"title": "A Phase-Field Model of Frictional Shear Fracture in Geologic Materials",
"venue": {
"raw": "FRONTIERS IN BUILT ENVIRONMENT"
},
"volume": "10",
"year": 2024
},
{
"_id": "6221834e5aee126c0f23c2a5",
"abstract": "In this paper, we introduce a shallow (one-hidden-layer) physics-informed neural network for solving partial differential equations on static and evolving surfaces. For the static surface case, with the aid of level set function, the surface normal and mean curvature used in the surface differential expressions can be computed easily. So instead of imposing the normal extension constraints used in literature, we write the surface differential operators in the form of traditional Cartesian differential operators and use them in the loss function directly. We perform a series of performance study for the present methodology by solving Laplace-Beltrami equation and surface diffusion equation on complex static surfaces. With just a moderate number of neurons used in the hidden layer, we are able to attain satisfactory prediction results. Then we extend the present methodology to solve the advection-diffusion equation on an evolving surface with given velocity. To track the surface, we additionally introduce a prescribed hidden layer to enforce the topological structure of the surface and use the network to learn the homeomorphism between the surface and the prescribed topology. The proposed network structure is designed to track the surface and solve the equation simultaneously. Again, the numerical results show comparable accuracy as the static cases. As an application, we simulate the surfactant transport on the droplet surface under shear flow and obtain some physically plausible results.",
"authors": [
{
"_id": "53f39148dabfae4b34a56846",
"name": "Wei-Fan Hu",
"org": "Natl Cent Univ, Dept Math, Taoyuan 32001, Taiwan"
},
{
"_id": "6525ed3d55b3f8ac46f8ce95",
"name": "Yi-Jun Shih",
"org": "Natl Yang Ming Chiao Tung Univ, Dept Appl Math, Hsinchu 30010, Taiwan"
},
{
"_id": "5631de9845ce1e5968c3f3d0",
"name": "Te-Sheng Lin",
"org": "Natl Yang Ming Chiao Tung Univ, Dept Appl Math, Hsinchu 30010, Taiwan"
},
{
"_id": "53f47e76dabfaec09f299f92",
"name": "Ming-Chih Lai",
"org": "Natl Yang Ming Chiao Tung Univ, Dept Appl Math, Hsinchu 30010, Taiwan"
}
],
"doi": "10.1016/j.cma.2023.116486",
"issn": "0045-7825",
"keywords": [
"Physics-informed neural networks",
"Surface partial differential equations",
"Laplace-Beltrami operator",
"Shallow neural network",
"Evolving surfaces"
],
"title": "A Shallow Physics-Informed Neural Network for Solving Partial Differential Equations on Surfaces",
"venue": {
"raw": "COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING"
},
"volume": "418",
"year": 2024
},
{
"_id": "623155ac5aee126c0f2ba59f",
"abstract": "While the popularity of physics-informed neural networks (PINNs) is steadily rising, to this date PINNs have not been successful in simulating dynamical systems whose solution exhibits multi-scale, chaotic or turbulent behavior. In this work we attribute this shortcoming to the inability of existing PINNs formulations to respect the spatio-temporal causal structure that is inherent to the evolution of physical systems. We argue that this is a fundamental limitation and a key source of error that can ultimately steer PINN models to converge towards erroneous solutions. We address this pathology by proposing a simple re-formulation of PINNs loss functions that can explicitly account for physical causality during model training. We demonstrate that this simple modification alone is enough to introduce significant accuracy improvements, as well as a practical quantitative mechanism for assessing the convergence of a PINNs model. We provide state-of-the-art numerical results across a series of benchmarks for which existing PINNs formulations fail, including the chaotic Lorenz system, the Kuramoto-Sivashinsky equation in the chaotic regime, and the Navier-Stokes equations in the turbulent regime. To the best of our knowledge, this is the first time that PINNs have been successful in simulating such systems, introducing new opportunities for their applicability to problems of industrial complexity.",
"authors": [
{
"_id": "645320c8ca4e0609eedd482c",
"name": "Sifan Wang",
"org": "Univ Penn, Grad Grp Appl Math & Computat Sci, Philadelphia, PA 19104 USA"
},
{
"_id": "65ed902f0b6735f4855eba41",
"name": "Shyam Sankaran",
"org": "Univ Penn, Dept Mech Engn & Appl Mech, Philadelphia, PA 19104 USA"
},
{
"_id": "6145a32d9e795e1aeca7521d",
"name": "Paris Perdikaris",
"org": "Univ Penn, Dept Mech Engn & Appl Mech, Philadelphia, PA 19104 USA"
}
],
"doi": "10.1016/j.cma.2024.116813",
"issn": "0045-7825",
"keywords": [
"Deep learning",
"Partial differential equations",
"Computational physics",
"Chaotic systems"
],
"title": "Respecting Causality is All You Need for Training Physics-Informed Neural Networks",
"venue": {
"raw": "COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING"
},
"volume": "421",
"year": 2024
},
{
"_id": "629ec1f85aee126c0fb6f6f3",
"abstract": "Mesh degeneration is a bottleneck for fluid-structure interaction (FSI) simulations and for shapeoptimization via the method of mappings. In both cases, an appropriate mesh motion techniqueis required. The choice is typically based on heuristics, e.g., the solution operators of partialdifferential equations (PDE), such as the Laplace or biharmonic equation. Especially the latter,which shows good numerical performance for large displacements, is expensive. Moreover,from a continuous perspective, choosing the mesh motion technique is to a certain extentarbitrary and has no influence on the physically relevant quantities. Therefore, we considerapproaches inspired by machine learning. We present a hybrid PDE-NN approach, where theneural network (NN) serves as parameterization of a coefficient in a second order nonlinearPDE. We ensure existence of solutions for the nonlinear PDE by the choice of the neuralnetwork architecture. Moreover, we present an approach where a neural network corrects theharmonic extension such that the boundary displacement is not changed. In order to avoidtechnical difficulties in coupling finite element and machine learning software, we work witha splitting of the monolithic FSI system into three smaller subsystems. This allows to solve themesh motion equation in a separate step. We assess the quality of the learned mesh motiontechnique by applying it to a FSI benchmark problem. In addition, we discuss generalizabilityand computational cost of the learned mesh motion operators",
"authors": [
{
"_id": "64c672ac75f2d36822f045ad",
"name": "Johannes Haubner",
"org": "Karl Franzens Univ Graz, Inst Germanist, Univ Pl 3, A-8010 Graz, Austria"
},
{
"name": "Ottar Hellan",
"org": "Simula Res Lab, Kristian Augusts Gate 23, N-0164 Oslo, Norway"
},
{
"_id": "64352fa0f2699869fc1e1acd",
"name": "Marius Zeinhofer",
"org": "Simula Res Lab, Kristian Augusts Gate 23, N-0164 Oslo, Norway"
},
{
"_id": "62e477a4d9f204418d685b48",
"name": "Miroslav Kuchta",
"org": "Simula Res Lab, Kristian Augusts Gate 23, N-0164 Oslo, Norway"
}
],
"doi": "10.1016/j.cma.2024.116890",
"issn": "0045-7825",
"keywords": [
"Fluid-structure interaction",
"Neural networks",
"Partial differential equations",
"Hybrid PDE-NN",
"Mesh moving techniques",
"Data-driven approaches"
],
"title": "Learning Mesh Motion Techniques with Application to Fluid-Structure Interaction",
"venue": {
"raw": "COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING"
},
"volume": "424",
"year": 2024
},
{
"_id": "6321467290e50fcafdb9bac6",
"abstract": "We present and analyze a methodology for numerical homogenization of spatial networks models, e.g. heat conduction and linear deformation in large networks of slender objects, such as paper fibers. The aim is to construct a coarse model of the problem that maintains high accuracy also on the micro-scale. By solving decoupled problems on local subgraphs we construct a low dimensional subspace of the solution space with good approximation properties. The coarse model of the network is expressed by a Galerkin formulation and can be used to perform simulations with different source and boundary data, at a low computational cost. We prove optimal convergence to the micro-scale solution of the proposed method under mild assumptions on the homogeneity, connectivity, and locality of the network on the coarse scale. The theoretical findings are numerically confirmed for both scalar-valued (heat conduction) and vector-valued (linear deformation) models.",
"authors": [
{
"_id": "53f432abdabfaeecd6939333",
"name": "F. Edelvik",
"org": "Fraunhofer Chalmers Ctr, Computat Engn & Design, Chalmers Sci Pk, S-41288 Gothenburg, Sweden"
},
{
"_id": "64b7dc9284100e3215e9afa9",
"name": "M. Gortz",
"org": "Fraunhofer Chalmers Ctr, Computat Engn & Design, Chalmers Sci Pk, S-41288 Gothenburg, Sweden"
},
{
"_id": "641140cd1d2dbd0c2a38abb9",
"name": "F. Hellman",
"org": "Chalmers Univ Technol, Dept Math Sci, S-41296 Gothenburg, Sweden"
},
{
"_id": "640471d7eef5911ab846ec46",
"name": "G. Kettil",
"org": "Fraunhofer Chalmers Ctr, Computat Engn & Design, Chalmers Sci Pk, S-41288 Gothenburg, Sweden"
},
{
"_id": "53f47788dabfaefedbbb24e7",
"name": "A. Malqvist",
"org": "Chalmers Univ Technol, Dept Math Sci, S-41296 Gothenburg, Sweden"
}
],
"doi": "10.1016/j.cma.2023.116593",
"issn": "0045-7825",
"keywords": [
"Algebraic connectivity",
"Discrete model",
"Multiscale method",
"Network model",
"Localized orthogonal decomposition",
"Upscaling"
],
"title": "Numerical Homogenization of Spatial Network Models",
"venue": {
"raw": "COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING"
},
"volume": "418",
"year": 2024
},
{
"_id": "6327dda690e50fcafd67df37",
"abstract": "Nonlinear balanced truncation is a model order reduction technique that reduces the dimension of nonlinear systems in a manner that accounts for either open- or closed -loop observability and controllability aspects of the system. A computational challenges that has so far prevented its deployment on large-scale systems is that the energy functions required for characterization of controllability and observability are solutions of various high -dimensional Hamilton-Jacobi- (Bellman) equations, which are computationally intractable in high dimensions. This work proposes a unifying and scalable approach to this challenge by considering a Taylor -series -based approximation to solve a class of parametrized Hamilton-Jacobi-Bellman equations that are at the core of nonlinear balancing. The value of a formulation parameter provides either open -loop balancing or a variety of closed -loop balancing options. To solve for the coefficients of Taylorseries approximations to the energy functions, the presented method derives a linear tensor system and heavily utilizes it to numerically solve structured linear systems with billions of unknowns. The strength and scalability of the algorithm is demonstrated on two semi-discretized partial differential equations, namely the Burgers and the Kuramoto-Sivashinsky equations.",
"authors": [
{
"_id": "63ae510f7d3ea0c54a781a8d",
"name": "Boris Kramer",
"org": "Univ Calif San Diego, Dept Mech & Aerosp Engn, La Jolla, CA 92093 USA"
},
{
"_id": "53f42bbadabfaedce54ab757",
"name": "Serkan Gugercin",
"org": "Virginia Tech, Dept Math, Blacksburg, VA 24061 USA"
},
{
"_id": "53f438dfdabfaedd74db81ad",
"name": "Jeff Borggaard",
"org": "Virginia Tech, Dept Math, Blacksburg, VA 24061 USA"
},
{
"_id": "6524aeba55b3f8ac4642a4e3",
"name": "Linus Balicki",
"org": "Virginia Tech, Dept Math, Blacksburg, VA 24061 USA"
}
],
"doi": "10.1016/j.cma.2024.117011",
"issn": "0045-7825",
"keywords": [
"Reduced-order modeling",
"Balanced truncation",
"Nonlinear manifolds",
"Hamilton-Jacobi-Bellman equation",
"Nonlinear systems"
],
"title": "Scalable Computation of Energy Functions for Nonlinear Balanced Truncation",
"venue": {
"raw": "Computer Methods in Applied Mechanics and Engineering"
},
"volume": "427",
"year": 2024
},
{
"_id": "633269fb90e50fcafd4913e6",
"abstract": "In recent years operator networks have emerged as promising deep learning tools for approximating the solution to partial differential equations (PDEs). These networks map input functions that describe material properties, forcing functions and boundary data to the solution of a PDE. This work describes a new architecture for operator networks that mimics the form of the numerical solution obtained from an approximate variational or weak formulation of the problem. The application of these ideas to a generic elliptic PDE leads to a variationally mimetic operator network (VarMiON). Like the conventional Deep Operator Network (DeepONet) the VarMiON is also composed of a sub-network that constructs the basis functions for the output and another that constructs the coefficients for these basis functions. However, in contrast to the DeepONet, the architecture of these sub-networks in the VarMiON is precisely determined. An analysis of the error in the VarMiON solution reveals that it contains contributions from the error in the training data, the training error, the quadrature error in sampling input and output functions, and a \"covering error\" that measures the distance between the test input functions and the nearest functions in the training dataset. It also depends on the stability constants for the exact solution operator and its VarMiON approximation. The application of the VarMiON to a canonical elliptic PDE and a nonlinear PDE reveals that for approximately the same number of network parameters, on average the VarMiON incurs smaller errors than a standard DeepONet and a recently proposed multiple-input operator network (MIONet). Further, its performance is more robust to variations in input functions, the techniques used to sample the input and output functions, the techniques used to construct the basis functions, and the number of input functions.",
"authors": [
{
"_id": "637254afec88d95668ccf55f",
"name": "Dhruv Patel",
"org": "Stanford Univ, Dept Mech Engn, Stanford, CA USA"
},
{
"_id": "62e48a25d9f204418d6a0ba6",
"name": "Deep Ray",
"org": "Univ Maryland, Dept Math, College Pk, MD USA"
},
{
"_id": "63af888784ab04bd7fb65276",
"name": "Michael R. A. Abdelmalik",
"org": "Eindhoven Univ Technol, Dept Mech Engn, Eindhoven, Netherlands"
},
{
"_id": "53f430ebdabfaeb1a7bb80a6",
"name": "Thomas J. R. Hughes",
"org": "Univ Texas Austin, Oden Inst Computat Engn & Sci, Austin, TX USA"
},
{
"_id": "53f436bfdabfaedce553252c",
"name": "Assad A. Oberai",
"org": "Univ Southern Calif, Dept Aerosp & Mech Engn, Los Angeles, CA 90007 USA"
}
],
"doi": "10.1016/j.cma.2023.116536",
"issn": "0045-7825",
"keywords": [
"Variational formulation",
"Deep neural operator",
"Deep operator network",
"Error analysis"
],
"title": "Variationally Mimetic Operator Networks",
"venue": {
"raw": "COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING"
},
"volume": "419",
"year": 2024
},
{
"_id": "6344dee690e50fcafd24e879",
"abstract": "Hybrid quantum mechanics/molecular mechanics (QM/MM) models play a pivotal role in molecular simulations. These models provide a balance between accuracy, surpassing pure MM models, and computational efficiency, offering advantages over pure QM models. Adaptive approaches have been developed to further improve this balance by allowing on -the -fly selection of the QM and MM subsystems as necessary. We propose a novel and robust adaptive QM/MM method for practical material defect simulations. To ensure mathematical consistency with the QM reference model, we employ machine -learning interatomic potentials (MLIPs) as the MM models (Chen et al., 2022 and Grigorev et al., 2023). Our adaptive QM/MM method utilizes a residual -based error estimator that provides both upper and lower bounds for the approximation error, thus indicating its reliability and efficiency. Furthermore, we introduce a novel adaptive algorithm capable of anisotropically updating the QM/MM partitions. This update is based on the proposed residual -based error estimator and involves solving a free interface motion problem, which is efficiently achieved using the fast marching method. We demonstrate the robustness of our approach via numerical tests on a range of crystalline defects comprising edge dislocations, cracks and di-interstitials.",
"authors": [
{
"_id": "64bfb90975f2d368227b888d",
"name": "Yangshuai Wang",
"org": "Univ British Columbia, 1984 Math Rd, Vancouver, BC, Canada"
},
{
"_id": "53f31d4edabfae9a84441861",
"name": "James R. Kermode",
"org": "Univ Warwick, Warwick Ctr Predict Modelling, Sch Engn, Coventry CV4 7AL, England"
},
{
"_id": "619325ac6750f83ab8797ded",
"name": "Christoph Ortner",
"org": "Univ British Columbia, 1984 Math Rd, Vancouver, BC, Canada"
},
{
"_id": "542a4f8cdabfae61d4968d4d",
"name": "Lei Zhang",
"org": "Shanghai Jiao Tong Univ, Inst Nat Sci, Sch Math Sci, Shanghai 200240, Peoples R China"
}
],
"doi": "10.1016/j.cma.2024.117097",
"issn": "0045-7825",
"keywords": [
"QM/MM coupling",
"Machine-learned interatomic potentials",
"A posteriori error estimate",
"Adaptive algorithm",
"Crystal defects"
],
"title": "A Posteriori Error Estimate and Adaptivity for QM/MM Models of Defects",
"venue": {
"raw": "COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING"
},
"volume": "428",
"year": 2024
},
{
"_id": "6348d42590e50fcafd5530ab",
"abstract": "We present a rate-independent model for isotropic elastic–orthotropic plastic material behaviour in a hyper-elasto-plastic setting at finite strains, which is based on a covariant formulation that includes plastic-deformation-induced evolution of orthotropy. The model relies on a treatment by Lu and Papadopoulos, who made use of the postulate of covariance for an anisotropic elasto-plastic solid and derived constitutive equations of evolving anisotropies at finite strains. The latter is tantamount to the notion of plastic spin. This treatment does not rely on a multiplicative decomposition of the deformation gradient. We test our model on in-plane sheet-metal forming processes, which are governed by the evolution of pre-existing preferred material orientations. Hence, we advocate an orthotropic yield criterion directed by evolving structural tensors to describe this material behaviour. Our formulation yields two key findings. Firstly, the covariant formulation of plasticity yields suitable evolution equations for the structural tensors characterising the symmetry group of the orthotropic yield function. Secondly, the constitutive equations for the plastic variables and the structural tensors, which are both symmetric second-order tensors, give results that are in good agreement with experimental and numerical findings from in-plane sheet forming processes.",
"authors": [
{
"_id": "53f44753dabfaee43ec816d5",
"name": "Christian C. Celigoj",
"org": "Graz Univ Technol, Inst Strength Mat, Kopernikusgasse 24-I, A-8010 Graz, Austria"
},
{
"_id": "53f380c2dabfae4b349f707b",
"name": "Manfred H. Ulz",
"org": "Graz Univ Technol, Inst Strength Mat, Kopernikusgasse 24-I, A-8010 Graz, Austria"
}
],
"doi": "10.1016/j.cma.2022.115567",
"issn": "0022-5096",
"keywords": [
"Postulate of covariance",
"Orthotropy",
"Evolving anisotropy",
"Plastic spin",
"Pulp fibres",
"Natural fibres"
],
"title": "An Orthotropic Plasticity Model at Finite Strains with Plasticity-Induced Evolution of Orthotropy Based on a Covariant Formulation",
"venue": {
"raw": "JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS"
},
"volume": "193",
"year": 2024
},
{
"_id": "6348d44b90e50fcafd5557cc",
"abstract": "A hydro-mechanical-damage fully coupled numerical method is developed for simulations of complicated quasi-brittle fracking in poroelastic media. A unified fluid continuity equation with crack-width dependent permeability, based on the Biot’s poroelastic theory, is used for simultaneous modeling of fluid flow in both fractures and porous media. The fluid pressure is coupled into the governing equations of the phase-field regularized cohesive zone model, which can automatically predict quasi-brittle multi-crack initiation, nucleation, and propagation without remeshing, crack tracking, or auxiliary fields as needed by other methods. An alternate minimization Newton–Raphson iterative algorithm is implemented within the finite element framework to solve the above three-fields coupled problem with nodal degrees of freedom of displacements, fluid pressures, and damages. The method is first validated by three problems with analytical solutions, a problem with experimental results, and a two-crack merging problem with numerical results in published literature, in terms of time evolutions of injected fluid pressures, crack widths and lengths, and final crack paths. Horizontal wellbore fracking problems with parallel hydraulic cracks and random natural fractures are then simulated, with the effects of spacing, number, and angle of perforations investigated in detail. It is found that the developed method is capable of modeling complex multi-crack fracking in both homogeneous media and heterogeneous media with natural fractures, and is thus promising for fracking design optimization of practical exploitation of shale gas and oil.",
"authors": [
{
"_id": "5614b61b45cedb3397a6310e",
"name": "Hui Li",
"org": "Wuhan Univ, Sch Civil Engn, Hubei Key Lab Geotech & Struct Safety, Wuhan 430027, Peoples R China"
},
{
"_id": "542a6a57dabfae2b4e10175d",
"name": "Zhenjun Yang",
"org": "Wuhan Univ, Sch Civil Engn, Hubei Key Lab Geotech & Struct Safety, Wuhan 430027, Peoples R China"
},
{
"_id": "56113f4f45ce1e596272d068",
"name": "Fengchen An",
"org": "China Univ Petr, Sch Safety & Ocean Engn, Beijing 102249, Peoples R China"
},
{
"_id": "53f42c7edabfaedce54b7e69",
"name": "Jianying Wu",
"org": "South China Univ Technol, State Key Lab Subtrop Bldg Sci, Guangzhou 510641, Peoples R China"
}
],
"doi": "10.1016/j.enggeo.2024.107502",
"issn": "0013-7952",
"keywords": [
"Phase field model",
"Dynamic fracture",
"Quasi-brittle fracture",
"Hydraulic fracturing",
"Pulsing fracking",
"Horizontal well"
],
"title": "Simulation of Dynamic Pulsing Fracking in Poroelastic Media by a Hydro-Damage-mechanical Coupled Cohesive Phase Field Model",
"venue": {
"raw": "ENGINEERING GEOLOGY"
},
"volume": "334",
"year": 2024
}
],
"log_id": "33Mf4NbmpwKQI9oLH5EQ9WmYp4b",
"msg": "",
"success": true,
"total": 10
}