Control of heat flux using computationally designed metamaterials

To gain control over the diffusive heat flux in a given domain, one has to design metamaterials with a specifc distribution of the generally anisotropic thermal conductivity throughout the domain. Until now, the appropriate conductivity distribution was usually determined using transformation thermodynamics. By this way, only a few particular cases of heat flux control in simple domains having simple boundary conditions were studied. As a more general approach, we propose to define the heat control problem as an optimization problem where we minimize the error in guiding the heat flux in a given way, taking as design variables the parameters that define the variable microstructure of the metamaterial. Anisotropic conductivity is introduced by using a metamaterial made of layers of two materials with highly dfferent conductivities, the thickness of the layers and their orientation throughout the domain are the current design variables. As an application example we design a device that thermally shields the region it encloses, while it keeps unchanged the flux outside it.Preprin

Strain injection techniques in dynamic fracture modeling

A computationally affordable modeling of dynamic fracture phenomena is performed in this study by using strain injection techniques and Finite Elements with Embedded strong discontinuities (E-FEM). In the present research, classical strain localization and strong discontinuity approaches are considered by injecting discontinuous strain and displacement modes in the finite element formulation without an increase of the total number of degrees of freedom. Following the Continuum Strong Discontinuity Approach (CSDA), stress–strain constitutive laws can be employed in the context of fracture phenomena and, therefore, the methodology remains applicable to a wide number of continuum mechanics models. The position and orientation of the displacement discontinuity is obtained through the solution of a crack propagation problem, i.e. the crack path field, based on the distribution of localized strains. The combination of the above mentioned approaches is envisaged to avoid stress-locking and directional mesh bias phenomena. Dynamic simulations are performed increasing the loading rate up to the appearance of crack branching, and the variation in terms of failure modes is investigated as well as the influence of the strain injection together with the crack path field algorithm. Objectivity of the presented methodology with respect to the spatial and temporal discretization is analyzed in terms of the dissipated energy during the fracture process. The dissipation at the onset of branching is studied for different loading rate conditions and is linked to the experimental maximum velocity observed before branching takes place.Fil: Lloberas Valls, Oriol. Universidad Politecnica de Catalunya; España. Centre Internacional de Metodes Numerics en Enginyeria; EspañaFil: Huespe, Alfredo Edmundo. Centre Internacional de Metodes Numerics en Enginyeria; España. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Centro de Investigaciones en Métodos Computacionales. Universidad Nacional del Litoral. Centro de Investigaciones en Métodos Computacionales; ArgentinaFil: Oliver, J.. Centre Internacional de Metodes Numerics en Enginyeria; España. Universidad Politecnica de Catalunya; EspañaFil: Dias, I.F.. Laboratório Nacional de Engenharia Civil; Portuga

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

Crack-path field and strain-injection techniques in computational modeling of propagating material failure

The work presents two new numerical techniques devised for modeling propagating material failure, i.e. cracks in fracture mechanics or slip-lines in soil mechanics. The first one is termed crack-path-field technique and is conceived for the identification of the path of those cracks, or slip-lines, represented by strain-localization based solutions of the material failure problem. The second one is termed strain-injection, and consists of a procedure to insert, during specific stages of the simulation and in selected areas of the domain of analysis, goal oriented specific strain fields via mixed finite element formulations. In the approach, a first injection, of elemental constant strain modes (CSM) in quadrilaterals, is used, in combination of the crack-path-field technique, for obtaining reliable information that anticipates the position of the crack-path. Based on this information, in a subsequent stage, a discontinuous displacement mode (DDM) is efficiently injected, ensuring the required continuity of the crack-path across sides of contiguous elements. Combination of both techniques results in an efficient and robust procedure based on the staggered resolution of the crack-path-field and the mechanical failure problems. It provides the classical advantages of the “intra-elemental” methods for capturing complex propagating displacement discontinuities in coarse meshes, as E-FEM or X-FEM methods, with the non-code-invasive character of the crack-path-field technique. Numerical representative simulations of a wide range of benchmarks, in terms of the type of material and the failure problem, show the broad applicability, accuracy and robustness of the proposed methodology. The finite element code used for the simulations is open-source and available at http://www.cimne.com/compdesmat/.Postprint (published version

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

Numerical modeling of the fracture process in reinforced concrete by means of the continuum strong discontinuity approach. Part I: formulation

En general, las estructuras de concreto reforzado como vigas, columnas y muros están conformadas por entramados complejos de barras de acero embebidas en una matriz de concreto, las cuales exhiben múltiples fisuras ante la aplicación de cargas externas elevadas. Este artículo presenta la formulación de un modelo numérico cuyo objetivo es describir el proceso de fractura en elementos de concreto reforzado a partir de la fracción volumétrica del concreto y del acero. El modelo utiliza un campo enriquecido de la deformación para describir la formación y propagación de fisuras en un material compuesto, tal como lo establecen la metodología de discontinuidades fuertes de continuo y la teoría de mezclas. El material compuesto está constituido por una matriz de concreto y uno o dos paquetes de barras de acero ortogonales entre sí. El acero y el concreto se representan con modelos de plasticidad unidimensional y de daño escalar con tracción y compresión diferenciada, respectivamente. La acción pasador y los efectos del deslizamiento entre las barras y la matriz, se describen con modelos adicionales que relacionan el esfuerzo y la deformación de los materiales componentes. Finalmente, se concluye que el modelo propuesto se puede implementar con facilidad en el método de los elementos finitos, dado que permanecen muchas características del procedimiento numérico no lineal convencional. Asimismo, el modelo permite analizar el problema en la escala macroscópica, lo cual elude la construcción de mallas de elementos finitos de cada material componente y de sus efectos de interacción, reduciendo así el costo computacional.Reinforced concrete structures generally refers to beams, columns and walls which are constituted by complex lattices of steel bars embedded in a concrete matrix, exhibiting multiple cracks due to high external loads. This paper presents the formulation of a numerical model aimed at describing the fracture process in reinforced concrete, from the volumetric ratio of concrete and steel. Crack formation and propagation in a composite material is described in the model by an enhanced strain field, such as that established in the continuum strong discontinuity approach and mixture theory. The composite material is constituted by a concrete matrix and one or two steel bar orthogonal packages. The steel and concrete are represented by a one-dimensional plasticity model and a scalar damage model having different tension and compression strength, respectively. The dowel action and the bond-slip effects between the bars and the matrix are described with additional models relating component material stress and strain. It is concluded that the proposed model can easily be implemented in the finite element method, due to several conventional nonlinear numerical process characteristics which remain. The model would also allow the problem to be analysed at macroscopic scale, thereby avoiding a finite element mesh having to be constructed for each component material and its interaction effects and reducing computational costs.Fil: Linero Segrera, Dorian Luis. Universidad Nacional de Colombia; ColombiaFil: Oliver, Javier. Universidad Politecnica de Catalunya; EspañaFil: Huespe, Alfredo Edmundo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Santa Fe. Instituto de Desarrollo Tecnológico para la Industria Química (i); Argentin

A study on finite elements for capturing strong discontinuities

This is the peer reviewed version of the following article: [Oliver, J., Huespe, A.E. and Samaniego, E. (2003), A study on finite elements for capturing strong discontinuities. Int. J. Numer. Meth. Engng., 56: 2135-2161. doi:10.1002/nme.657], which has been published in final form at https://onlinelibrary.wiley.com/doi/abs/10.1002/nme.657. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.The work focuses on the presently existing families of finite elements with embedded discontinuities and explores the possibilities of obtaining symmetric statically consistent finite elements that alleviate the stress-locking problem. For this purpose, mixed (reduced integration) and assumed enhanced strain techniques are applied to the basic symmetric four-noded element. Numerical simulations show the effectiveness of the proposed measures.Peer ReviewedPostprint (author's final draft