The reduced model multiscale method (R3M) for the non-linear homogenization of hyperelastic media at finite strains

By Julien Yvonnet, Qi-Chang He. Journal of Computational Physics, 2007

340 citations recorded by the source corpus.

Subfields: Biomedical Engineering, Computational Theory and Mathematics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/f8831f6871f1409712a5bbe294418b88bcf4109c

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Biomedical Engineering

1. Wing Kam Liu
2. Zeliang Liu
3. S. Oller
4. X. Martínez
5. F. Otero
6. Miguel A. Bessa
7. Kun Wang
8. V. Kouznetsova

In Computational Theory and Mathematics

1. WaiChing Sun
2. Kun Wang
3. Wing Kam Liu
4. Zeliang Liu
5. X. Martínez
6. F. Otero
7. S. Oller
8. Mark Fleming

In Mechanics of Materials

1. Wing Kam Liu
2. X. Martínez
3. F. Otero
4. S. Oller
5. Kun Wang
6. Zeliang Liu
7. Alfredo Huespe
8. WaiChing Sun

Citations in the corpus

• Multiscale structural topology optimization with an approximate constitutive model for local material microstructure (2015, neutral): “Most of the existing ROMs constructed using reduction strategies such as Proper Orthogonal Decomposition (POD) [24,25], Proper Generalized Decomposition (PGD) [26–28], material map model [29,30], eigendeformation-based reduction [31,32], Nonuniform Transformation Field Analysis (NTFA) [33–36], and N”
• A review of predictive nonlinear theories for multiscale modeling of heterogeneous materials (2017, background): “Yvonnet and He [271] proposed a POD based model for both homogenization and localization of hyperelastic composites.”
• A framework for data-driven analysis of materials under uncertainty: Countering the curse of dimensionality (2017, methodology): “Successful applications of the NTFA [58–60], POD [54,55,61,62] and PGD [63] demonstrate the usefulness of these approaches.”
• High-performance model reduction techniques in computational multiscale homogenization (2014, methodology): “In the specific context of two-scale homogenization, it has been recently explored by Boyaval [10], Yvonnet and He [61] and Monteiro et al. [50].”
• A multilevel projection‐based model order reduction framework for nonlinear dynamic multiscale problems in structural and solid mechanics (2017, methodology): “The PMOR approach proposed in [16] was subsequently extended in [17] to formulations with periodic boundary conditions for the microstructure model using the Lagrange multiplier approach.”
• A multiscale multi-permeability poroplasticity model linked by recursive homogenizations and deep learning (2018, methodology): “The surrogate model can be simply a phenomenological model [8,58], a reduced-order sub-scale model [57,70,71] or a data-driven model [15].”
• An efficient multi-scale method for non-linear analysis of composite structures (2015, methodology): “In order to improve the computational cost of the multi-scale homogenization some strategies use model-order reduction techniques [37, 38, 39].”
• Numerically explicit potentials for the homogenization of nonlinear elastic heterogeneous materials (2009, background): “However, their main shortcoming is that the computational cost is still high even though use is made of techniques like model reduction [22], [23] or parallel computing [17] to reduce it.”
• Multiscale Computational Homogenization: Review and Proposal of a New Enhanced-First-Order Method (2016, methodology): “adaptive strategies to solve the micro-scale problem only the minimum number of times necessary [93, 124], adaptive sub-incremental strategies to ensure the convergence of the multiscale solution in the presence of several sources of non-linearity [100, 110], model-order reduction techniques [41, 64”
• Self-consistent clustering analysis: An efficient multi-scale scheme for inelastic heterogeneous materials (2016, methodology): “Furthermore, the40 representative unit cells need to be subjected to irreversible deformation to obtain the plastic modes (as in41 POD) which leads to an extensive exploration of the deformation space at the offline stage.42 In this article a new approach is proposed where the above-mentioned limita”
• Microstructural material database for self-consistent clustering analysis of elastoplastic strain softening materials (2018, methodology): “However, both NTFA and POD methods require extensive a priori simulations for interpolating nonlinear inelastic material behaviors, and the offline stages need to be recomputed for different combinations of material constituents.”