Computational certification under limited experiments

Abstract

Summary A computational certification framework under limited experimental data is developed. By this approach, a high‐fidelity model (HFM) is first calibrated to limited experimental data. Subsequently, the HFM is employed to train a low‐fidelity model (LFM). Finally, the calibrated LFM is utilized for component analysis. The rational for utilizing HFM in the initial stage stems from the fact that constitutive laws of individual microphases in HFM are rather simple so that the number of material parameters that needs to be identified is less than in the LFM. The added complexity of material models in LFM is necessary to compensate for simplified kinematical assumptions made in LFM and for smearing discrete defect structure. The first‐order computational homogenization model, which resolves microstructural details including the structure of defects, is selected as the HFM, whereas the reduced‐order homogenization is selected as the LFM. Certification framework illustration, verification, and validation are conducted for ceramic matrix composite material system comprised of the 8‐harness weave architecture. Blind validation is performed against experimental data to validate the proposed computational certification framework.

Data‐physics driven reduced order homogenization

“…The basic idea of these approaches is to apply data-driven methods to supplement or completely replace RVE based models by single-scale phenomenological models. Among these approaches [36][37][38][39][40][41][42][43][44][45][46][47][48][49][50][51][52] machine learning techniques, such as neural networks (NNs), have been successfully employed. By this approach fully connected neural network is trained to map from the coarse-scale strain into the coarse-scale stress 37,43,44,49 for path-independent problems.…”

Hierarchical Rve-Based Multiscale Modeling of Nonlinear Heterogeneous Materials Using the Finite Volume Method

“…Thus, reduced-order models have been actively studied. Some important reduced-order methods include the Voronoi cell method (Ghosh and Moorthy, 1995), spectral method (Aboudi, 1982), network approximation method (Berlyand and Kolpakov, 2001), fast Fourier transforms (Moulinec and Suquet, 1998), mesh-free reproducing kernel particle method (Chen et al, 1996), finite-volume direct-averaging micromechanics (Cavalcante et al, 2011), transformation field analysis (Dvorak, 1990), methods of cells (Paley and Aboudi, 1992), methods based on control theory including balanced truncation (Moore, 1981), optimal Hankel norm approximation (Glover, 1984), proper orthogonal decomposition (Krysl et al, 2001;Yvonnet and He, 2007), data-driven-based reduced-order methods (Bhattacharjee and Matouš, 2016;Fish et al, 2018;Le et al, 2015), and non-uniform transformation field methods (Fritzen and Böhlke, 2011;Michel and Suquet, 2004). Principally, the multiscale simulations could be based on a combination of these two categories, using concurrent and information passing methods in a hybrid way.…”

A second‐order reduced asymptotic homogenization approach for nonlinear periodic heterogeneous materials

“…Thus, the development of reduced order models for a heterogeneous continuum has been an active research area. Among noteworthy reduced order methods are the Voronoi cell method, 62,63 the spectral method, 64 the network approximation method, 65 the fast Fourier transforms, 66,67 the mesh-free reproducing kernel particle method, 68,69 the finite-volume direct averaging micromechanics, 70 the transformation field analysis, 71,72 the methods of cells 64 or its generalization, 73 methods based on control theory including balanced truncation, 74,75 the optimal Hankel norm approximation, 76 the proper orthogonal decomposition, 77,78 data-driven-based reduced order methods, [79][80][81][82] the reduced order homogenization methods for two scales 83,84 and more than two-scales, 85,86 and the nonuniform transformation field methods. [87][88][89] For a recent comprehensive review of various homogenization-like method, we refer to the works of Fish 90 and Geers et al 91 The primary objective of this manuscript is to develop an efficient computational framework for analyzing nonlinear periodic materials with large microstructure that combines nonlinear higher-order asymptotic homogenization methods that do not require higher-order continuity of the coarse-scale solution with an efficient model reduction scheme.…”

“…Thus, the development of reduced order models for a heterogeneous continuum has been an active research area. Among noteworthy reduced order methods are the Voronoi cell method, the spectral method, the network approximation method, the fast Fourier transforms, the mesh‐free reproducing kernel particle method, the finite‐volume direct averaging micromechanics, the transformation field analysis, the methods of cells or its generalization, methods based on control theory including balanced truncation, the optimal Hankel norm approximation, the proper orthogonal decomposition, data‐driven–based reduced order methods, the reduced order homogenization methods for two scales and more than two‐scales, and the nonuniform transformation field methods . For a recent comprehensive review of various homogenization‐like method, we refer to the works of Fish and Geers et al…”