Multiscale design of nonlinear materials using reduced-order modeling

David R. Brandyberry, Xiang Zhang, Philippe H. Geubelle

Research output: Contribution to journalArticlepeer-review


A two-step optimization method is proposed for the efficient multiscale design of heterogeneous materials whose nonlinear macroscopic response is driven by volumetric and interfacial damage taking place at the microstructural level. The Eigendeformation-based reduced-order Homogenization Method (EHM) is used in a reduced-order design phase, allowing for a preliminary design that combines multiple initial configurations with a gradient-based optimization method. The preliminary design is then adopted to initialize a high-fidelity optimization phase based on the Interface-Enriched Generalized Finite Element Method (IGFEM) to arrive at the final design. The analytic sensitivities of EHM with respect to nonlinear material properties are derived to drive the gradient-based algorithm. Several multiscale optimization problems of increasing complexity are presented to illustrate the efficiency of the proposed method using an objective function based on stress error relative to a desired stress–strain response.

Original languageEnglish (US)
Article number115388
JournalComputer Methods in Applied Mechanics and Engineering
StatePublished - Sep 1 2022
Externally publishedYes


  • Cohesive model
  • Composite materials
  • Continuum damage
  • Eigendeformation-based reduced-order homogenization model
  • Generalized FEM

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • General Physics and Astronomy
  • Computer Science Applications


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