Dimensional hyper-reduction of nonlinear finite element models via empirical cubature

We present a general framework for the dimensional reduction, in terms of number of degrees of freedom as well as number of integration points (“hyper-reduction”), of nonlinear parameterized finite element (FE) models. The reduction process is divided into two sequential stages. The first stage consists in a common Galerkin projection onto a reduced-order space, as well as in the condensation of boundary conditions and external forces. For the second stage (reduction in number of integration points), we present a novel cubature scheme that efficiently determines optimal points and associated positive weights so that the error in integrating reduced internal forces is minimized. The distinguishing features of the proposed method are: (1) The minimization problem is posed in terms of orthogonal basis vector (obtained via a partitioned Singular Value Decomposition) rather that in terms of snapshots of the integrand. (2) The volume of the domain is exactly integrated. (3) The selection algorithm need not solve in all iterations a nonnegative least-squares problem to force the positiveness of the weights. Furthermore, we show that the proposed method converges to the absolute minimum (zero integration error) when the number of selected points is equal to the number of internal force modes included in the objective function. We illustrate this model reduction methodology by two nonlinear, structural examples (quasi-static bending and resonant vibration of elastoplastic composite plates). In both examples, the number of integration points is reduced three order of magnitudes (with respect to FE analyses) without significantly sacrificing accuracy.Peer ReviewedPostprint (published version

Multiscale modeling of prismatic heterogeneous structures based on a localized hyperreduced-order method

This work aims at deriving special types of one-dimensional Finite Elements (1D FE) for efficiently modeling heterogeneous prismatic structures, in the small strains regime, by means of reduced-order modeling (ROM) and domain decomposition techniques. The employed partitioning framework introduces “fictitious” interfaces between contiguous subdomains, leading to a formulation with both subdomain and interface fields. We propose a low-dimensional parameterization at both subdomain and interface levels by using reduced-order bases precomputed in an offline stage by applying the Singular Value Decomposition (SVD) on solution snapshots. In this parameterization, the amplitude of the fictitious interfaces play the role of coarse-scale displacement unknowns. We demonstrate that, with this partitioned framework, it is possible to arrive at a solution strategy that avoids solving the typical nested local/global problem of other similar methods (such as the FE method). Rather, in our approach, the coarse-grid cells can be regarded as special types of finite elements, whose nodes coincides with the centroids of the interfaces, and whose kinematics are dictated by the modes of the “fictitious” interfaces. This means that the kinematics of our coarse-scale FE are not pre-defined by the user, but extracted from the set of “training” computational experiments. Likewise, we demonstrate that the coarse-scale and fine-scale displacements are related by inter-scale operators that can be precomputed in the offline stage. Lastly, a hyperreduced scheme is considered for the evaluation of the internal forces, allowing us to deal with possible material nonlinearities.This work has received support from the Spanish Ministry of Economy and Competitiveness, through the “Severo Ochoa Programme for Centres of Excellence in R&D” (CEX2018-000797-S)”. A. Giuliodori also gratefully acknowledges the support of “Secretaria d’Universitats i Recerca de la Generalitat de Catalunya i del Fons Social Europeu” through the FI grant (00939/2020), and J.A. Hernández the support of, on the one hand, the European High-Performance Computing Joint Undertaking (JU) under grant agreement No. 955558 (the JU receives, in turn, support from the European Union’s Horizon 2020 research and innovation program and from Spain, Germany, France, Italy, Poland, Switzerland, Norway), and the European Union’s Horizon 2020 research and innovation program under Grant Agreement No. 952966 (project FIBREGY).Peer ReviewedPostprint (published version

Numerical modeling of crack formation in power compaction processes

Powder metallurgy (P/M) is an important technique of manufacturing metal parts from metal in powdered form. Traditionally, P/M processes and products have been designed and developed on the basis of practical rules and trial-and-error experience. However, this trend is progressively changing. In recent years, the growing efficiencies of computers, together with the recognition of numerical simulation techniques, and more specifically, the finite element method , as powerful alternatives to these costly trial-and-error procedures, have fueled the interest of the P/M industry in this modeling technology. Research efforts have been devoted mainly to the analysis of the pressing stage and, as a result, considerable progress has been made in the field of density predictions. However, the numerical simulation of the ejection stage, and in particular, the study of the formation of cracks caused by elastic expansion and/or interaction with the tool set during this phase, has received less attention, notwithstanding its extreme relevance in the quality of the final product. The primary objective of this work is precisely to fill this gap by developing a constitutive model that attempts to describe the mechanical behavior of the powder during both pressing and ejection phases, with special emphasis on the representation of the cracking phenomenon. The constitutive relationships are derived within the general framework of rate-independent, isotropic, finite strain elastoplasticity. The yield function is defined in stress space by three surfaces intersecting nonsmoothly, namely, an elliptical cap and two classical Von Mises and Drucker-Prager yield surfaces. The distinct irreversible processes occurring at the microscopic level are macroscopically described in terms of two internal variables: an internal hardening variable, associated with accumulated compressive (plastic) strains, and an internal softening variable, linked with accumulated (plastic) shear strains. The innovative part of our modeling approach is connected mainly with the characterization of the latter phenomenological aspect: strain softening. Incorporation of a softening law permits the representation of macroscopic cracks as high gradients of inelastic strains (strain localization). Motivated by both numerical and physical reasons, a parabolic plastic potential function is introduced to describe the plastic flow on the linear Drucker-Prager failure surface. A thermodynamically consistent calibration procedure is employed to relate material parameters involved in the softening law to fracture energy values obtained experimentally on Distaloy AE specimens. The discussion of the algorithmic implementation of the model is confined exclusively to the time integration of the constitutive equations. Motivated by computational robustness considerations, a non-conventional integration scheme that combines advantageous features of both implicit and explicit method is employed. The basic ideas and assumptions underlying this method are presented, and the stress update and the closed-form expression of the algorithmic tangent moduli stemming from this method are derived. This integration scheme involves, in turn, the solution at each time increment of the system of equations stemming from a classical, implicit backward-Euler difference scheme. An iterative procedure based on the decoupling of the evolution equations for the plastic strains and the internal variables is proposed for solving these return-mapping equations. It is proved that this apparently novel method converges unconditionally to the solution regardless of the value of the material properties. To validate the proposed model, a comparison between experimental results of diametral compression tests and finite element predictions is carried out. The validation is completed with the study of the formation of cracks due to elastic expansion during ejection of an overdensified thin cylindrical part. Both simulations demonstrate the ability of the model to detect evidence of macroscopic cracks, clarify and provide reasons for the formation of such cracks, and evaluate qualitatively the influence of variations in the input variables on their propagation. Besides, in order to explore the possibilities of the numerical model as a tool for assisting in the design and analysis of P/M uniaxial die compaction (including ejection) processes, a detailed case study of the compaction of an axially symmetric multilevel part in an advanced CNC press machine is performed. Special importance is given in this study to the accurate modeling of the geometry of the tool set and the external actions acting on it (punch platen motions). Finally, the potential areas for future research are identified.Postprint (published version

High-performance model reduction procedures in multiscale simulations

Technological progress and discovery and mastery of increasingly sophisticated structural materials have been inexorably tied together since the dawn of history. In the present era — the so-called Space Age —-, the prevailing trend is to design and create new materials, or improved existing ones, by meticulously altering and controlling structural features that span across all types of length scales: the ultimate aim is to achieve macroscopic proper- ties (yield strength, ductility, toughness, fatigue limit . . . ) tailored to given practical applications. Research efforts in this aspect range in complexity from the creation of structures at the scale of single atoms and molecules — the realm of nanotechnology —, to the more mundane, to the average civil and mechanical engineers, development of structural materials by changing the composition, distribution, size and topology of their constituents at the microscopic/mesoscopic level (composite materials and porous metals, for instance).Postprint (published version

Multi-scale (FE2) analysis of material failure in cement/aggregate-type composite structures

The work propases a FP multiscale approach to computational modeling of material failure in concreteMlike structures, made of cement/aggregate-type composite materials. Keeping the approach in a classical homogenization setting, a multiscale model is proposed, which naturally provides a microscopic length-scale to be exported to the macrostructure. There, this length scale is used as regularization parameter in the context of the Continuum Strong Discontinuity Approach to material failure, and finite elements with embedded strong discontinuities (E~ FE M). The resulting technique allows robust modeling of crack propagation at the structural scale, accounting for the mesostructure morphology, supplies proper energy dissipation and solutions independent of the finite element and RVE sizes. Application toa number of examples, in the range from light-aggregate concrete to regular concrete, shows the potentiality of the method.Postprint (published version

Reduced order modeling strategies for computational multiscale fracture

The paper proposes some new computational strategies for affordably solving multiscale fracture problems through a FE2 approach. To take into account the mechanical effects induced by fracture at the microstructure level the Representative Volume Element (RVE), assumed constituted by an elastic matrix and inclusions, is endowed with a large set of cohesive softening bands providing a good representation of the possible microstructure crack paths. The RVE response is then homogenized in accordance with a model previously developed by the authors and upscaled to the macro-scale level as a continuum stress–strain constitutive equation, which is then used in a conventional framework of a finite element modeling of propagating fracture. For reduced order modeling (ROM) purposes, the RVE boundary value problem is first formulated in displacement fluctuations and used, via the Proper Orthogonal Decomposition (POD), to find a low-dimension space for solving the reduced problem. A domain separation strategy is proposed as a first technique for model order reduction: unconventionally, the low-dimension space is spanned by a basis in terms of fluctuating strains, as primitive kinematic variables, instead of the conventional formulation in terms of displacement fluctuations. The RVE spatial domain is then decomposed into a regular domain (made of the matrix and the inclusions) and a singular domain (constituted by cohesive bands), the required RVE boundary conditions are rephrased in terms of strains and imposed via Lagrange multipliers in the corresponding variational problem. Specific low-dimensional strain basis is then derived, independently for each domain, via the POD of the corresponding strain snapshots. Next step consists of developing a hyper-reduced model (HPROM). It is based on a second proposed technique, the Reduced Optimal Quadrature (ROQ) which, again unconventionally, is determined through optimization of the numerical integration of the primitive saddle-point problem arising from the RVE problem, rather than its derived variational equations, and substitutes the conventional Gauss quadrature. The ROQ utilizes a very reduced number of, optimally placed, sampling points, the corresponding weights and placements being evaluated through a greedy algorithm. The resulting low-dimensional and reduced-quadrature variational problem translates into very relevant savings on the computational cost and high computational speed-ups. Particular attention is additionally given to numerical tests and performance evaluations of the new hyper-reduced methodology, by “a-priori” and “a-posteriori” error assessments. Moreover, for the purposes of validation of the present techniques, a real structural problem exhibiting propagating fracture at two-scales is modeled on the basis of the strain injection-based multiscale approach previously developed by the authors. The performance of the proposed strategy, in terms of speed-up vs. error, is deeply analyzed and reported.Peer ReviewedPostprint (published version

Two-scale topology optimization in computational material design: an integrated approach

In this work, a new strategy for solving multiscale topology optimization problems is presented. An alternate direction algorithm and a precomputed offline microstructure database (Computational Vademecum) are used to efficiently solve the problem. In addition, the influence of considering manufacturable constraints is examined. Then, the strategy is extended to solve the coupled problem of designing both the macroscopic and microscopic topologies. Full details of the algorithms and numerical examples to validate the methodology are provided.Peer ReviewedPostprint (published version

Productive performance of grasslands with different combinations of orchard grass (Dactylis glomerata L.), perennial ryegrass (Lolium perenne L.) and white clover (Trifolium repens L.)

En la zona central de México existen sistemas de producción animal que tienen como componente importante el uso de praderas puras y asociadas. El objetivo de esta investigación fue evaluar cuatro asociaciones, dos gramíneas y una leguminosa, sembradas en diferentes proporciones. Los tratamientos consistieron de las siguientes asociaciones: 20-40-40, 00-50-50, 40-20-40, y 50-00-50 % de ovillo (Ov), ballico perenne (Ba) y trébol blanco (Tr), respectivamente. Los tratamientos se distribuyeron aleatoriamente en 12 parcelas experimentales de 9 por 8 m, de acuerdo con un diseño de bloques completamente al azar con tres repeticiones. Se evaluó rendimiento de materia seca, tasa de crecimiento, composición botánica y morfológica y altura de la planta. En rendimiento anual las asociaciones que presentaron mayor rendimiento fueron; 40-20-40 y 20-40-40 con 20,182 y 19,146 kg MS ha-1, respectivamente y la menor, la asociación 00-50-50 con 15,896 kg MS ha-1. La asociación; 40-20-40 es la que mayor tasa de crecimiento anual presentó con 56 kg MS ha-1 d-1. Independientemente de la estación, en composición botánica y morfológica las asociaciones; 20-40-40, 40-20-40 y 50-00-50 fue la que mayor hoja de ovillo presentó con un promedio de 50%. La estación de invierno fueron las que mayor porcentaje de hoja de ballico presentó para la asociación 00-50-50 con 32%. Independientemente de la asociación, en la estación de primavera fue donde se obtuvo mayor altura con un promedio de 37 cm y la menor fue en invierno con un promedio de 15 cm. En conclusión, la asociación; 40-20-40 fue mejor en rendimiento anual, tasa de crecimiento y altura y la menor fue la asociación 00-50-50.In central Mexico there animal production systems whose major component using pure and associated grasslands. The objective of this research was to evaluate four associations, two grasses and legume planted in different proportions. Treatments consisted of the following associations: 20-40-40, 00-50-50, 40-20-40, and 50-00-50% of orchard grass (Ov), perennial ryegrass (Ba) and white clover (Tr) respectively. The treatments were randomly distributed in 12 experimental plots of 9 and 8 m, according to a design of a randomized complete block with three replications. Dry matter yield, growth rate, botanical and morphological composition and plant height were evaluated. In the association's annual yield higher performance were presented; 40-20-40 and 20-40-40 with 20.182 and 19.146 kg DM ha-1 respectively and the lowest 00-50-50 association with 15.896 kg DM ha-1. The Association; 40-20-40 is the highest annual growth rate presented with 56 kg DM ha-1 d-1. Regardless of the season, botanical and morphological composition associations; 20-40-40, 40-20-40 and 50-00-50 which was higher clew sheet presented with an average of 50 %, the winter season were the highest percentage of ryegrass sheet presented to the association 00-50-50 to 32%. Regardless of the association in the spring season it was where greater height was obtained with an average of 37 cm and the lowest was in winter with an average of 15 cm. In conclusion the association; 40-20-40 was better in annual yield growth rate and lower height and the association was 00-50-50.Fil: Rojas García, Adelaido Rafael.Fil: Hernández Garay, Alfonso. Colegio de Postgraduados. Campus Montecillo (México)Fil: Ayala, Walter.Fil: Mendoza Pedroza, Sergio Iban. Universidad Autónoma Chapingo (México)Fil: Cancino, Santiago Joaquín. Colegio de Postgraduados. Campus Montecillo (México)Fil: Vaquera Huerata, Humberto. Colegio de Postgraduados. Campus Montecillo (México)Fil: Ortega, Mario Alberto Santiago. Colegio de Postgraduados. Campus Montecillo (México

Comportamiento productivo de praderas con distintas combinaciones de ovillo (Dactylis glomerata L.), ballico perenne (Lolium perenne L.) y trébol blanco (Trifolium repens L.)

In central Mexico there animal production systems whose major component using pure and associated grasslands. The objective of this research was to evaluate four associations, two grasses and legume planted in different proportions. Treatments consisted of the following associations: 20-40-40, 00-50-50, 40-20-40, and 50-00-50% of orchard grass (Ov), perennial ryegrass (Ba) and white clover (Tr) respectively. The treatments were randomly distributed in 12 experimental plots of 9 and 8 m, according to a design of a randomized complete block with three replications. Dry matter yield, growth rate, botanical and morphological composition and plant height were evaluated. In the association's annual yield higher performance were presented; 40-20-40 and 20-40-40 with 20.182 and 19.146 kg DM ha-1 respectively and the lowest 00-50-50 association with 15.896 kg DM ha-1. The Association; 40-20-40 is the highest annual growth rate presented with 56 kg DM ha-1 d-1. Regardless of the season, botanical and morphological composition associations; 20-40-40, 40-20-40 and 50-00-50 which was higher clew sheet presented with an average of 50 %, the winter season were the highest percentage of ryegrass sheet presented to the association 00-50-50 to 32%. Regardless of the association in the spring season it was where greater height was obtained with an average of 37 cm and the lowest was in winter with an average of 15 cm. In conclusion the association; 40-20-40 was better in annual yield growth rate and lower height and the association was 00-50-50.En la zona central de México existen sistemas de producción animal que tienen como componente importante el uso de praderas puras y asociadas. El objetivo de esta investigación fue evaluar cuatro asociaciones, dos gramíneas y una leguminosa, sembradas en diferentes proporciones. Los tratamientos consistieron de las siguientes asociaciones: 20-40-40, 00-50-50, 40-20-40, y 50-00-50 % de ovillo (Ov), ballico perenne (Ba) y trébol blanco (Tr), respectivamente. Los tratamientos se distribuyeron aleatoriamente en 12 parcelas experimentales de 9 por 8 m, de acuerdo con un diseño de bloques completamente al azar con tres repeticiones. Se evaluó rendimiento de materia seca, tasa de crecimiento, composición botánica y morfológica y altura de la planta. En rendimiento anual las asociaciones que presentaron mayor rendimiento fueron; 40-20-40 y 20-40-40 con 20,182 y 19,146 kg MS ha-1, respectivamente y la menor, la asociación 00-50-50 con 15,896 kg MS ha-1. La asociación; 40-20-40 es la que mayor tasa de crecimiento anual presentó con 56 kg MS ha-1 d-1. Independientemente de la estación, en composición botánica y morfológica las asociaciones; 20-40-40, 40-20-40 y 50-00-50 fue la que mayor hoja de ovillo presentó con un promedio de 50%. La estación de invierno fueron las que mayor porcentaje de hoja de ballico presentó para la asociación 00-50-50 con 32%. Independientemente de la asociación, en la estación de primavera fue donde se obtuvo mayor altura con un promedio de 37 cm y la menor fue en invierno con un promedio de 15 cm. En conclusión, la asociación; 40-20-40 fue mejor en rendimiento anual, tasa de crecimiento y altura y la menor fue la asociación 00-50-50

Gestión del conocimiento. Perspectiva multidisciplinaria. Volumen 7

El libro “Gestión del Conocimiento. Perspectiva Multidisciplinaria”, volumen 7, de la Colección Unión Global, es resultado de investigaciones. Los capítulos del libro, son resultados de investigaciones desarrolladas por sus autores. El libro es una publicación internacional, seriada, continua, arbitrada de acceso abierto a todas las áreas del conocimiento, que cuenta con el esfuerzo de investigadores de varios países del mundo, orientada a contribuir con procesos de gestión del conocimiento científico, tecnológico y humanístico que consoliden la transformación del conocimiento en diferentes escenarios, tanto organizacionales como universitarios, para el desarrollo de habilidades cognitivas del quehacer diario. La gestión del conocimiento es un camino para consolidar una plataforma en las empresas públicas o privadas, entidades educativas, organizaciones no gubernamentales, ya sea generando políticas para todas las jerarquías o un modelo de gestión para la administración, donde es fundamental articular el conocimiento, los trabajadores, directivos, el espacio de trabajo, hacia la creación de ambientes propicios para el desarrollo integral de las instituciones