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1. Data-Driven Calibration of Multifidelity Multiscale Fracture Models Via Latent Map Gaussian Process

   https://doi.org/10.1115/1.4055951  

   Deng, Shiguang; Mora, Carlos; Apelian, Diran; Bostanabad, Ramin (January 2023, Journal of Mechanical Design)

   Abstract Fracture modeling of metallic alloys with microscopic pores relies on multiscale damage simulations which typically ignore the manufacturing-induced spatial variabilities in porosity. This simplification is made because of the prohibitive computational expenses of explicitly modeling spatially varying microstructures in a macroscopic part. To address this challenge and open the doors for the fracture-aware design of multiscale materials, we propose a data-driven framework that integrates a mechanistic reduced-order model (ROM) with a calibration scheme based on random processes. Our ROM drastically accelerates direct numerical simulations (DNS) by using a stabilized damage algorithm and systematically reducing the degrees of freedom via clustering. Since clustering affects local strain fields and hence the fracture response, we calibrate the ROM by constructing a multifidelity random process based on latent map Gaussian processes (LMGPs). In particular, we use LMGPs to calibrate the damage parameters of an ROM as a function of microstructure and clustering (i.e., fidelity) level such that the ROM faithfully surrogates DNS. We demonstrate the application of our framework in predicting the damage behavior of a multiscale metallic component with spatially varying porosity. Our results indicate that microstructural porosity can significantly affect the performance of macro-components and hence must be considered in the design process. 

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2. Reduced-order multiscale modeling of plastic deformations in 3D alloys with spatially varying porosity by deflated clustering analysis

   https://doi.org/10.1007/s00466-022-02177-8  

   Deng, Shiguang; Soderhjelm, Carl; Apelian, Diran; Bostanabad, Ramin (April 2022, Computational Mechanics)

   Abstract Aluminum alloys are increasingly utilized as lightweight materials in the automobile industry due to their superior capability in withstanding high mechanical loads. A significant challenge impeding the large-scale use of these alloys in high-performance applications is the presence of manufacturing-induced, spatially varying porosity defects. In order to understand the impacts of these defects on the macro-mechanical properties of cast alloys, multiscale simulations are often required. In this paper, we introduce a computationally efficient reduced-order multiscale framework to simulate the behavior of metallic components containing process-induced porosity under irreversible nonlinear deformations. In our approach, we start with a data compression scheme that significantly reduces the number of unknown macroscale and microscale variables by agglomerating close-by finite element nodes into a limited number of clusters. Then, we use deflation methods to project these variables into a lower-dimensional space where the material’s elastoplastic behaviors are approximated. Finally, we solve for the unknown variables and map them back to the original, high-dimensional space. We call our method deflated clustering analysis and by comparing it to direct numerical simulations we demonstrate that it accurately captures macroscale deformations and microscopic effective responses. To illustrate the effect of microscale pores on the macroscopic response of a cast component, we conduct multi-scale simulations with spatially varying local heterogeneities that are modeled with a microstructure characterization and reconstruction algorithm. 

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3. A multiscale phase field fracture approach based on the non-affine microsphere model for rubber-like materials

   https://doi.org/10.1016/j.cma.2023.115982  

   Arunachala, Prajwal Kammardi; Abrari Vajari, Sina; Neuner, Matthias; Linder, Christian (May 2023, Computer Methods in Applied Mechanics and Engineering)

   - (Ed.)

   Rubber-like materials have a broad scope of applications due to their unique properties like high stretchability and increased toughness. Hence, computational models for simulating their fracture behavior are paramount for designing them against failures. In this study, the phase field fracture approach is integrated with a multiscale polymer model for predicting the fracture behavior in elastomers. At the microscale, damaged polymer chains are modeled to be made up of a number of elastic chain segments pinned together. Using the phase field approach, the damage in the chains is represented using a continuous variable. Both the bond stretch internal energy and the entropic free energy of the chain are assumed to drive the damage, and the advantages of this assumption are expounded. A framework for utilizing the non-affine microsphere model for damaged systems is proposed by considering the minimization of a hypothetical undamaged free energy, ultimately connecting the chain stretch to the macroscale deformation gradient. At the macroscale, a thermodynamically consistent formulation is derived in which the total dissipation is assumed to be mainly due to the rupture of molecular bonds. Using a monolithic scheme, the proposed model is numerically implemented and the resulting three-dimensional simulation predictions are compared with existing experimental data. The capability of the model to qualitatively predict the propagation of complex crack paths and quantitatively estimate the overall fracture behavior is verified. Additionally, the effect of the length scale parameter on the predicted fracture behavior is studied for an inhomogeneous system. 

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4. Closure Learning for Nonlinear Model Reduction Using Deep Residual Neural Network

   https://doi.org/10.3390/fluids5010039  

   Xie, Xuping; Webster, Clayton; Iliescu, Traian (March 2020, Fluids)

   null (Ed.)

   Developing accurate, efficient, and robust closure models is essential in the construction of reduced order models (ROMs) for realistic nonlinear systems, which generally require drastic ROM mode truncations. We propose a deep residual neural network (ResNet) closure learning framework for ROMs of nonlinear systems. The novel ResNet-ROM framework consists of two steps: (i) In the first step, we use ROM projection to filter the given nonlinear system and construct a spatially filtered ROM. This filtered ROM is low-dimensional, but is not closed. (ii) In the second step, we use ResNet to close the filtered ROM, i.e., to model the interaction between the resolved and unresolved ROM modes. We emphasize that in the new ResNet-ROM framework, data is used only to complement classical physical modeling (i.e., only in the closure modeling component), not to completely replace it. We also note that the new ResNet-ROM is built on general ideas of spatial filtering and deep learning and is independent of (restrictive) phenomenological arguments, e.g., of eddy viscosity type. The numerical experiments for the 1D Burgers equation show that the ResNet-ROM is significantly more accurate than the standard projection ROM. The new ResNet-ROM is also more accurate and significantly more efficient than other modern ROM closure models. 

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5. Rupture Dynamics of Cascading Earthquakes in a Multiscale Fracture Network

   https://doi.org/10.1029/2023JB027578  

   Palgunadi, Kadek Hendrawan; Gabriel, Alice‐Agnes; Garagash, Dmitry Igor; Ulrich, Thomas; Mai, Paul Martin (March 2024, Journal of Geophysical Research: Solid Earth)

   Abstract Fault‐damage zones comprise multiscale fracture networks that may slip dynamically and interact with the main fault during earthquake rupture. Using 3D dynamic rupture simulations and scale‐dependent fracture energy, we examine dynamic interactions of more than 800 intersecting multiscale fractures surrounding a listric fault, emulating a major listric fault and its damage zone. We investigate 10 distinct orientations of maximum horizontal stress, probing the conditions necessary for sustained slip within the fracture network or activating the main fault. Additionally, we assess the feasibility of nucleating dynamic rupture earthquake cascades from a distant fracture and investigate the sensitivity of fracture network cascading rupture to the effective normal stress level. We model either pure cascades or main fault rupture with limited off‐fault slip. We find that cascading ruptures within the fracture network are dynamically feasible under certain conditions, including: (a) the fracture energy scales with fracture and fault size, (b) favorable relative pre‐stress of fractures within the ambient stress field, and (c) close proximity of fractures. We find that cascading rupture within the fracture network discourages rupture on the main fault. Our simulations suggest that fractures with favorable relative pre‐stress, embedded within a fault damage zone, may lead to cascading earthquake rupture that shadows main fault slip. We find that such off‐fault events may reach moment magnitudes up toM_w ≈ 5.5, comparable to magnitudes that can be otherwise hosted by the main fault. Our findings offer insights into physical processes governing cascading earthquake dynamic rupture within multiscale fracture networks. 

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