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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. 

Predicting the fracture behavior of macroscale components containing microscopic porosity relies on multiscale damage models which typically ignore the manufacturing-induced spatial variabilities in porosity. This simplification is made due to the prohibitive computational costs associated with explicitly modeling spatially varying microstructures in a macroscopic component. To address this challenge, we propose a data-driven framework that integrates a mechanistic reduced-order model (ROM) with a calibration scheme based on latent map Gaussian processes (LMGPs). 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 construct a multi-fidelity LMGP to inversely estimate the damage parameters of an ROM as a function of microstructure and clustering 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. 

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.