High performance reduced order modeling techniques based on optimal energy quadrature: application to geometrically non-linear multiscale inelastic material modeling
Rights accessOpen Access
European Commission's projectCOMP-DES-MAT - Advanced tools for computational design of engineering materials (EC-FP7-320815)
A High-Performance Reduced-Order Model (HPROM) technique, previously presented by the authors in the context of hierarchical multiscale models for non linear-materials undergoing infinitesimal strains, is generalized to deal with large deformation elasto-plastic problems. The proposed HPROM technique uses a Proper Orthogonal Decomposition procedure to build a reduced basis of the primary kinematical variable of the micro-scale problem, defined in terms of the micro-deformation gradient fluctuations. Then a Galerkin-projection, onto this reduced basis, is utilized to reduce the dimensionality of the micro-force balance equation, the stress homogenization equation and the effective macro-constitutive tangent tensor equation. Finally, a reduced goal-oriented quadrature rule is introduced to compute the non-affine terms of these equations. Main importance in this paper is given to the numerical assessment of the developed HPROM technique. The numerical experiments are performed on a micro-cell simulating a randomly distributed set of elastic inclusions embedded into an elasto-plastic matrix. This micro-structure is representative of a typical ductile metallic alloy. The HPROM technique applied to this type of problem displays high computational speed-ups, increasing with the complexity of the finite element model. From these results, we conclude that the proposed HPROM technique is an effective computational tool for modeling, with very large speed-ups and acceptable accuracy levels with respect to the high-fidelity case, the multiscale behavior of heterogeneous materials subjected to large deformations involving two well-separated scales of length.
CitationCaicedo, M., Mroginski, J., Toro, S., Raschi, M., Huespe, A., Oliver, J. High performance reduced order modeling techniques based on optimal energy quadrature: application to geometrically non-linear multiscale inelastic material modeling. "Archives of computational methods in engineering", Setembre 2019, vol. 26, núm. 4, p. 771-792.
All rights reserved. This work is protected by the corresponding intellectual and industrial property rights. Without prejudice to any existing legal exemptions, reproduction, distribution, public communication or transformation of this work are prohibited without permission of the copyright holder