High performance reduction technique for multiscale finite element modeling (HPR-FE2): Towards industrial multiscale FE software

Abstract

The authors have shown in previous contributions that reduced order modeling with optimal cubature applied to finite element square (FE 2 ) techniques results in a reliable and affordable multiscale approach, the HPR-FE 2 technique. Such technique is assessed here for an industrial case study of a generic 3D reinforced composite whose microstructure is represented by two general microcells accounting for different deformation mechanisms, microstrucural phases and geometry arrangement. Specifically, in this approach the microstrain modes used for building the reduced order model (ROM) are obtained through standard proper orthogonal decomposition (POD) techniques applied over snapshots of a representative sampling strain space. Additionally, a reduced number of integration points is obtained by exactly integrating the main free energy modes resulting from the sampling energy snapshots. The outcome consists of a number of dominant strain modes integrated over a remarkably reduced number of integration points which provide the support to evaluate the constitutive behavior of the microstructural phases. It is emphasized that stresses are computed according to the selected constitutive law at the reduced integration points and, therefore, the strategy inherits advantageous properties such as model completeness and customization of material properties. Overall results are discussed in terms of the consistency of the multiscale analysis, customization of the microscopic material parameters and speedup ratios compared to high-fidelity finite element (HF) simulations.

Training deep material networks to reproduce creep loading of short fiber-reinforced thermoplastics with an inelastically-informed strategy

“…The method was extended to reduce mechanics at interfaces [26,27], at finite strains [28,29] and in space-time [30], as well. Further data-driven approaches were exploited, for instance based on clustering [31][32][33] or proper orthogonal decomposition [34,35].…”

Experimental, Computational, and Dimensional Analysis of the Mechanical Performance of Fused Filament Fabrication Parts

“…Periodic Boundary Conditions (BCs) were applied at pairs of opposing faces of the RVE [ 45 ]: where and are pairs of points that belong to opposite faces of the RVE, which was considered to have a cubic geometry for this work. The whole procedure is depicted in Figure 7 and detailed in Algorithm 1, and additional details were given in [ 46 , 47 , 48 , 49 , 50 , 51 , 52 , 53 ]. The computational tool used for the in-fill homogenization was the in-house software Kratos Multiphysics [ 54 ].…”

A Statistical Finite Element Method Integrating a Plurigaussian Random Field Generator for Multi-scale Modelling of Solute Transport in Concrete

“…Whilst this has the advantage of avoiding the need for constitutive equations, this comes at an increased computational cost that can be prohibitive (Lange et al 2021). Recently, a number of researchers addressed this issue through techniques such as model reduction, GPU programming, and replacement of lower-scale solutions with machine learning-based surrogate models (Fritzen and Hodapp 2016;Raschi et al 2021;Rocha et al 2021). HMM and EFM are similar approaches that employ a macro-scale model with large time steps, in which the primary variables evolve through the solution of a micro-scale model over smaller time steps (Tretiak et al 2022).…”