mlsanityData to 14 Oct 2026

A numerical method for computing the overall response of nonlinear composites with complex microstructure

arXiv 2012.08962 ↗First posted 15 Dec 2020cs.CE physics.class-phcited by 18

Not on the map. Why?

Abstract (arXiv)

The local and overall responses of nonlinear composites are classically investigated by the Finite Element Method. We propose an alternate method based on Fourier series which avoids meshing and which makes direct use of microstructure images. It is based on the exact expression of the Green function of a linear elastic and homogeneous comparison material. First, the case of elastic nonhomogeneous constituents is considered and an iterative procedure is proposed to solve the Lippman-Schwinger equation which naturally arises in the problem. Then, the method is extended to non-linear constituents by a step-by-step integration in time. The accuracy of the method is assessed by varying the spatial resolution of the microstructures. The flexibility of the method allows it to serve for a large variety of microstructures. (C) 1998 Elsevier Science S.A.

Key facts. Cited by 18 papers in the map (data through 14 Oct 2026). First posted on arXiv 15 Dec 2020.

Builds on

No reference list yet.

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2021: 2; 2022: 0; 2023: 0; 2024: 3; 2025: 10; 2026: 3.

18 papers.

Sort:

By area:

  1. 2025FunDiff: Diffusion Models over Function Spaces for Physics-Informed Generative Modelingcited by 20
  2. 2024Micrometer: Micromechanics Transformer for Predicting Mechanical Responses of Heterogeneous Materialscited by 5
  3. 2025Learning Memory and Material Dependent Constitutive Lawscited by 5
  4. 2021Recurrent Localization Networks applied to the Lippmann-Schwinger Equationcited by 3
  5. 2025Universal Fourier Neural Operators for periodic homogenization problems in linear elasticitycited by 3
  6. 2021Cell division in deep material networks applied to multiscale strain localization modelingcited by 2
  7. 2024FFT-based surrogate modeling of auxetic metamaterials with real-time prediction of effective elastic properties and swift inverse designcited by 2
  8. 2025Physics-Informed Graph Neural Networks to Reconstruct Local Fields Considering Finite Strain Hyperelasticitycited by 2
  9. 2024Simulation-Free Determination of Microstructure Representative Volume Element Size via Fisher Scorescited by 1
  10. 2025Spectral Normalization and Voigt-Reuss net: A universal approach to microstructure-property forecasting with physical guaranteescited by 1
  11. 2025Reduced-order structure-property linkages for stochastic metamaterialscited by 1
  12. 2025Accelerating Conjugate Gradient Solvers for Homogenization Problems with Unitary Neural Operatorscited by 1
6 more
  1. 2025Temperature-Aware Recurrent Neural Operator for Temperature-Dependent Anisotropic Plasticity in HCP Materialscited by 0
  2. 2025MicroLad: 2D-to-3D Microstructure Reconstruction and Generation via Latent Diffusion and Score Distillationcited by 0
  3. 2025Robust inverse material design with physical guarantees using the Voigt-Reuss Netcited by 0
  4. 2026Systematic Performance Assessment of Deep Material Networks for Multiscale Material Modelingcited by 0
  5. 2026Bayesian Optimization of Genetic Algorithm Hyperparameters in a Multi-Fidelity Framework for Efficient Lattice Material Designcited by 0
  6. 2026A property-registry contract for retrieve-or-refuse thermal-mechanical lattice searchcited by 0