Multiscale analysis of composite structures with goal-oriented mesh adaptivity and reduced order homogenization

Ju, Xiaozhe; Mahnken, Rolf; Xu, Yangjian; Liang, Lihua; Cheng, Chun; Zhou, W.

doi:10.1016/j.compstruct.2022.115699

Cited by 4 publications

(2 citation statements)

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“…For a generalization of the NTFA, the work 16 proposed a potential‐based reduced order homogenization method (pRBMOR), where additional computational costs are compensated via a GPU acceleration 17 . In our previous works, the NTFA was extended to consider softening effects and strength difference 18,19 and goal‐oriented adaptivities 20,21 . Subsequently, the work 22 proposed a so‐called self‐consistent clustering analysis (SCCA), where the micro‐domain is decomposed into several uniform subdomains via a clustering analysis.…”

Section: Introductionmentioning

confidence: 99%

“…17 In our previous works, the NTFA was extended to consider softening effects and strength difference 18,19 and goal-oriented adaptivities. 20,21 Subsequently, the work 22 proposed a so-called self-consistent clustering analysis (SCCA), where the micro-domain is decomposed into several uniform subdomains via a clustering analysis. The recent works [23][24][25] combined the NTFA with a clustering algorithm and proposed a new cluster-based reduced order model called CNTFA, containing a large variety of mesoscale models in a unified framework.…”

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Efficient nonlinear homogenization of bones using a cluster‐based model order reduction technique

Ju,

Zhou,

Liang

et al. 2023

Numer Methods Biomed Eng

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We present a reduced order model for efficient nonlinear homogenization of bones, accounting for strength difference effects and containing some well‐known plasticity models (like von Mises or Drucker‐Prager) as special cases. The reduced order homogenization is done by using a cluster‐based model order reduction technique, called cluster‐based nonuniform transformation field analysis. For an offline phase, a space–time decomposition is performed on the mesoscopic plastic strain fields, while a clustering analysis is employed for a spatial decomposition of the mesoscale RVE model. A volumetric‐deviatoric split is additionally introduced to capture the enriched characteristics of the mesoscopic plastic strain fields. For an online analysis, the reduced order model is formulated in a unified minimization problem, which is compatible with a large variety of material models. Both cortical and trabecular bones are considered for numerical experiments. Compared to conventional FE‐based RVE computations, the developed reduced order model renders a considerable acceleration rate beyond , while maintaining a sufficient accuracy level.

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Section: Introductionmentioning

confidence: 99%

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confidence: 99%

Efficient nonlinear homogenization of bones using a cluster‐based model order reduction technique

Ju,

Zhou,

Liang

et al. 2023

Numer Methods Biomed Eng

Self Cite

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A cluster‐based incremental potential approach for reduced order homogenization of bones

Ju,

Xu,

et al. 2024

Numer Methods Biomed Eng

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We develop a cluster‐based model order reduction (called C‐pRBMOR) approach for efficient homogenization of bones, compatible with a large variety of generalized standard material (GSM) models. To this end, the pRBMOR approach based on a mixed incremental potential formulation is extended to a clustered version for a significantly improved computational efficiency. The microscopic modeling of bones falls into a mixed incremental class of the GSM framework, originating from two potentials. An offline phase of the C‐pRBMOR approach includes both a clustering analysis spatially decomposing the micro‐domain within an RVE and a space–time decomposition of the microscopic plastic strain fields. A comparative study on two different clustering approaches and two algorithms for mode identification is additionally conducted. For an online analysis, a cluster‐enhanced version of evolution equations for the reduced variables is derived from an effective incremental variational formulation, rendering a very small set of nonlinear equations to be numerically solved. Several numerical examples show the effectiveness of the C‐pRBMOR approach. A striking acceleration rate beyond 104 against conventional FE computations and that beyond 103 against the original pRBMOR approach are observed.

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Mesh‐ and model adaptivity for NTFA and full‐field elasto‐plastic homogenization based on downwind and upwind approximations

Tchomgue Simeu,

Mahnken

2024

Proc Appl Math and Mech

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To increase the quality of computational results for heterogeneous materials like fiber‐reinforced composites with Prandtl–Reuss‐type material laws, goal‐oriented measures of the adaptive finite element method coupled to model adaptivity is established. The former is an adaptive mesh refinement on the macroscale, which allows to control the spatial discretization errors. The latter is an efficient combination of a numerically low cost nonuniform transformation field analysis (NTFA) and numerically high cost full‐field elasto‐plastic homogenization methods on the microscale. The present contribution deals with the application of the concept of downwind and upwind approximations to a goal‐oriented a posteriori error estimator based on duality techniques by means of reduced order homogenization schemes like NTFA, and with accuracy and numerical efficiency of the proposed goal‐oriented adaptive framework. NTFA consists of an offline phase and an online phase. During the offline phase, some relevant information of the micro system under consideration is precomputed allowing a reduced set of equations to be solved in the online phase. Thus, NTFA leads to a quite efficient homogenization method but less accurate compared to the full‐field homogenization method which is characterized with a high computational demand for accounting nonlinear microstructural mechanisms. Due to nonlinearities and time‐dependency of plasticity, the estimation of error transport and error generation are obtained with a backward‐in‐time dual method despite a high demand on memory capacity. In this contribution, the dual problem is solved with a forward‐in‐time dual method that allows estimating the full error during the resolution of the primal problem without the need for extra memory capacity. Several numerical examples illustrate the effectiveness of the proposed adaptive approach based on downwind and upwind approximations.

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Multiscale analysis of composite structures with goal-oriented mesh adaptivity and reduced order homogenization

Cited by 4 publications

References 60 publications

Efficient nonlinear homogenization of bones using a cluster‐based model order reduction technique

Efficient nonlinear homogenization of bones using a cluster‐based model order reduction technique

A cluster‐based incremental potential approach for reduced order homogenization of bones

Mesh‐ and model adaptivity for NTFA and full‐field elasto‐plastic homogenization based on downwind and upwind approximations

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