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

On the coherence of synthetic turbulence generation methods

Synthetic turbulence generation methods have been extensively used by engineers and scientists in the past ten years in order to impose initial conditions in a wide range of turbulent flow problems. The interest in synthetic methods relies in the fact that reliability of methodologies such as large eddy simulation (LES) or direct numerical simulation (DNS) strongly depends on how well the developed turbulence is characterized, which generally leads to computationally expensive simulations. In this work the methodology known as “modified discretizing and synthesizing random flow generation” (MDSRFG) jointly with a LES method is analyzed for its use in the study of bluff body aerodynamics. A comparison with other generation techniques, that are closely related by their features and their conceptual origins, is presented with particular emphasis on the correct representation of the coherence of the velocity field. The resulting wind loads on the model, along with the statistical characteristics of the flow, show that the MDSRFG technique allows to represent a field of spatially correlated velocities correctly.Publicado en: Mecánica Computacional vol. XXXV, no. 18Facultad de Ingenierí

On the coherence of synthetic turbulence generation methods

Synthetic turbulence generation methods have been extensively used by engineers and scientists in the past ten years in order to impose initial conditions in a wide range of turbulent flow problems. The interest in synthetic methods relies in the fact that reliability of methodologies such as large eddy simulation (LES) or direct numerical simulation (DNS) strongly depends on how well the developed turbulence is characterized, which generally leads to computationally expensive simulations. In this work the methodology known as “modified discretizing and synthesizing random flow generation” (MDSRFG) jointly with a LES method is analyzed for its use in the study of bluff body aerodynamics. A comparison with other generation techniques, that are closely related by their features and their conceptual origins, is presented with particular emphasis on the correct representation of the coherence of the velocity field. The resulting wind loads on the model, along with the statistical characteristics of the flow, show that the MDSRFG technique allows to represent a field of spatially correlated velocities correctly.Publicado en: Mecánica Computacional vol. XXXV, no. 18Facultad de Ingenierí

Thermodynamic consistent gradient-poroplasticity

Complex degradation processes of partial saturated media like soils during post-peak regime are strongly dependent on humidity, stress state, boundary conditions and material parameters, particularly porosity. To realistically and objectively describe the dramatic change from diffuse to localized failure mode or from ductile to brittle ones, accurate constitutive theories and numerical approaches are required. In this paper, a non-local gradient poroplastic model is proposed for partial saturated media based on thermodynamic concepts. A restricted non-local gradient theory is considered, following (Mroginski, et al. Int. J. Plasticity, 27:620-634) whereby the state variables are the only ones of non-local character. The non-local softening formulation of the proposed constitutive theory incorporates the dependence of the gradient characteristic length on both the governing stress and hydraulic conditions to realistically predict the size of the maximum energy dissipation zone. The material model employed in this work to describe the plastic evolution of porous media is the Modified Cam Clay, which is widely used in saturated and partially saturated soil mechanics. To evaluate the dependence of the transition point between ductile and brittle failure regime in terms of the hydraulic and stress conditions, the localization indicator for discontinuous bifurcation is formulated for both drained and undrained conditions, based on wave propagation criterion

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 Reviewe