Reduced finite element square techniques (RFE2): towards industrial multiscale fe software

Reduced order modeling techniques proposed by the authors are assessed for an industrial case study of a 3D reinforced composite laminate. Essentially, the main dominant strain micro-structural modes are obtained through standard reduced order modeling techniques applied over snapshots of a representative training strain space. Additionally, a reduced number of integration points is obtained by exactly integrating the main energy modes resulting from the training 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 micro-structural phases. Results are discussed in terms of the consistency of the multiscale analysis, tunability of the microscopic material parameters and speed up ratios comparing a high fidelity simulation and the multiscale reduced order model

Reduced finite element square techniques (RFE2): towards industrial multiscale fe software

Reduced order modeling techniques proposed by the authors are assessed for an industrial case study of a 3D reinforced composite laminate. Essentially, the main dominant strain micro-structural modes are obtained through standard reduced order modeling techniques applied over snapshots of a representative training strain space. Additionally, a reduced number of integration points is obtained by exactly integrating the main energy modes resulting from the training 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 micro-structural phases. Results are discussed in terms of the consistency of the multiscale analysis, tunability of the microscopic material parameters and speed up ratios comparing a high fidelity simulation and the multiscale reduced order model

Reduced finite element square techniques (RFE2): towards industrial multiscale fe software

Reduced order modeling techniques proposed by the authors are assessed for an industrial case study of a 3D reinforced composite laminate. Essentially, the main dominant strain micro-structural modes are obtained through standard reduced order modeling techniques applied over snapshots of a representative training strain space. Additionally, a reduced number of integration points is obtained by exactly integrating the main energy modes resulting from the training 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 micro-structural phases. Results are discussed in terms of the consistency of the multiscale analysis, tunability of the microscopic material parameters and speed up ratios comparing a high fidelity simulation and the multiscale reduced order model

Reduced finite element square techniques (RFE2): towards industrial multiscale fe software

Reduced order modeling techniques proposed by the authors are assessed for an industrial case study of a 3D reinforced composite laminate. Essentially, the main dominant strain micro-structural modes are obtained through standard reduced order modeling techniques applied over snapshots of a representative training strain space. Additionally, a reduced number of integration points is obtained by exactly integrating the main energy modes resulting from the training 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 micro-structural phases. Results are discussed in terms of the consistency of the multiscale analysis, tunability of the microscopic material parameters and speed up ratios comparing a high fidelity simulation and the multiscale reduced order model

Reduced finite element square techniques (RFE2): towards industrial multiscale fe software

Reduced order modeling techniques proposed by the authors are assessed for an industrial case study of a 3D reinforced composite laminate. Essentially, the main dominant strain micro-structural modes are obtained through standard reduced order modeling techniques applied over snapshots of a representative training strain space. Additionally, a reduced number of integration points is obtained by exactly integrating the main energy modes resulting from the training 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 micro-structural phases. Results are discussed in terms of the consistency of the multiscale analysis, tunability of the microscopic material parameters and speed up ratios comparing a high fidelity simulation and the multiscale reduced order model

High performance reduced order modeling techniques based on optimal energy quadrature: application to geometrically non-linear multiscale inelastic material modeling

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.Peer ReviewedPostprint (author's final draft

Reduced Finite Element square techniques (RFE2): towards industrial multiscale FE software

The FE2 method has gained a considerable interest within the simulation science community because of its generality and potential. Indeed, multiscale problems with complex micro-structures and constitutive behaviors can be tackled whereas classical homogenization techniques fail at predicting overall material properties. However, the multiplicative cost of different scale discretizations has significantly restricted their common use and distribution among industrial FE codes. The reduced order modeling techniques proposed in [1] and [2] are assessed for an industrial case study of a 3D reinforced composite laminate. Essentially, the main dominant strain microstructural modes are obtained through standard reduced order modeling techniques applied over snapshots of a representative training strain space. Additionally, a reduced number of integration points is obtained by exactly integrating the main energy modes resulting from the training 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 micro-structural phases. Different performance ratios between the full (high fidelity) and reduced simulations are obtained for a given user prescribed error. In fact, the ratio between the number of sampling points, i.e. integration points, of a standard FE2 and the reduced sampling points provided by the RFE2 technique scales with the complexity of the analyzed microscopic cells and, for relative errors below 1%, this ratio can easily reach three or four orders of magnitude when the amount of micro-structural sampling points is up to 106. Consequently, this technology results in feasible and affordable FE2 simulations suitable for industrial purposes.Postprint (published version

High performance reduced order modeling techniques based on optimal energy quadrature: application to geometrically non-linear multiscale inelastic material modeling

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

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

The authors have shown in previous contributions that reduced order modeling with optimal cubature applied to finite element square (FE2) techniques results in a reliable and affordable multiscale approach, the HPR-FE2technique. 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

Growth model for cholesterol accumulation in the wall of a simplified 3D geometry of the carotid bifurcation

Atherosclerosis is one of the leading causes of death in the first world countries nowadays. It is a vascular disease that affects medium and large size arteries, involving the formation of plaques within the artery wall. These plaques result from the accumulation of fat, cholesterol, cell debris, smooth muscle cells and other cells and substances, and may cause temporary or definitive lack of blood supply to an organ.This article proposes a model for cholesterol accumulation and plaque growth. The model is basically a mass balance of low density lipoproteins (LDL) in the intima. The inflow, outflow, oxidation, and consumption of LDL is modeled combining partial models and correlations available in the literature.The model was implemented into an open source finite volume code. Assuming steady blood flow, the code was used to predict lesion formation on a three-dimensional model of the carotid artery bifurcation, a location greatly studied for its role in supplying blood to some parts of the brain and for being related to strokes due to formation of atheromas. The simulation was carried out under physiologic conditions for blood pressure and LDL blood concentration.Results for LDL mass accumulation and intimal thickening over time, plaque shape, and location of thicker spots are reported, showing that the proposed model approximates reasonably well the intimal thickening obtained from post-mortem aortic fatty streaks and from B-mode ultrasonography of the carotid artery of healthy subjects reported by other authors.Fil: Gessaghi, Valeria Cristina. Universidad Nacional de la Pampa. Facultad de Ingeniería; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Raschi, Marcelo A.. Universidad Argentina de la Empresa. Facultad de Ingeniería y Ciencias Exactas; ArgentinaFil: Tanoni, Debora Y.. Universidad Argentina de la Empresa. Facultad de Ingeniería y Ciencias Exactas; ArgentinaFil: Perazzo, Carlos Alberto. Universidad Favaloro; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Larreteguy, Axel Eduardo. Universidad Argentina de la Empresa. Facultad de Ingeniería y Ciencias Exactas; Argentin