Abstract

The presentation is aimed to cover areas related to modeling of material behaviour using different numerical schemes. Special emphasis is laid on homogenization procedures and multi- scale approaches that include inelastic microstructural deformations and development of inter- face cracks. In detail the inelastic responses of polycrystals is investigated including induced anisotropy and nonlinear hardening. The necessary numerical procedures will be discussed and examples from different areas are introduced. 

Included in this presentation is the design of macroscopic constitutive equations with only few parameters that are obtained from homogenization of polycrystal assemblies. The results are validated at micro and macro scale by means of experiments. These include as well results from microstructural observation as from classical pullout tests. Typical and important industrial applications range from ceramic to ductile materials.

Abstract

In previous works, the nonlinear localization was first presented and studied in the case of large displacements but only for globally stable structural responses. In this paper, the parallelization of this computational strategy using a Balancing Domain Decomposition by Constrains (BDD-C) is presented. Finally, a validation of this implementation is carried out in lineal elasticity, verifying the ''speed-up'' and the numerical extensibility.

Abstract

Abstract

Nowadays, many open-source numerical codes are available to solve physical problems in structural mechanics, fluid flow, heat transfer, and neutron diffusion. However, even if these codes are often highly specialized in the numerical simulation of a particular type of physics, none of them allows simulating complex systems involving all the physical problems mentioned above. In this work we present a numerical framework, based on the SALOME platform, developed to perform multiscale and multiphysics simulations involving all the mentioned physical problems. In particular, the developed numerical platform includes the multigrid finite element in-house code FEMuS for heat transfer, fluid flow, turbulence and fluid-structure modeling; the open-source finite volume CFD software OpenFOAM; the multiscale neutronic code DONJON-DRAGON; and a system-scale code used for thermal-hydraulic simulations. Efficient data exchange among these codes is performed within computer memory by using the MED libraries, provided by the SALOME platform.

Abstract

Many multiscale simulation problems require a many-to-one coupling between different scales. For such coupled problems, researchers oftentimes focus on the coupling methodology, but largely ignore software engineering and high-performance computing aspects. This can lead to inefficient use of hardware resources, on the one hand, but also inefficient use of human resources as solutions to typical technical coupling problems are constantly reinvented. This work proposes a flexible and application-agnostic software framework to couple independent simulation codes in a many-to-one fashion. To this end, we introduce a prototype of a new lightweight software component called Micro Manager, which allows us to reuse the coupling library preCICE for two-scale coupled problems. We demonstrate the applicability of the framework by a two-scale coupled heat conduction problem.

Abstract

In this article, we analyze some residual-based stabilization techniques for the transient Stokes problem when considering anisotropic time–space discretizations. We define an anisotropic time–space discretization as a family of time–space partitions that does not satisfy the condition h2⩽Cδt with C uniform with respect to h and δt. Standard residual-based stabilization techniques are motivated by a multiscale approach, approximating the effect of the subscales onto the large scales. One of the approximations is to consider the subscales quasi-static (neglecting their time derivative). It is well known that these techniques are unstable for anisotropic time–space discretizations. We show that the use of dynamic subscales (where the subscales time derivatives are not neglected) solves the problem, and prove optimal convergence and stability results that are valid for anisotropic time–space discretizations. Also the improvements related to the use of orthogonal subscales are addressed.

Abstract

The log-conformation reformulation, originally proposed by Fattal and Kupferman (2004), allows computing incompressible viscoelastic problems with high Weissenberg numbers which are impossible to solve with the typical three-field formulation. By following this approach, in this work we develop a new stabilized finite element formulation based on the logarithmic reformulation using the Variational Multiscale (VMS) method as stabilization technique, together with a modified log-conformation formulation. Our approach follows the term-by-term stabilization proposed by Castillo and Codina (2014) for the standard formulation, which is more effective when there are stress singularities. The formulation can be used when the relaxation parameter is set to zero, and permits a direct steady numerical resolution. The formulation is validated in the classical benchmark flow past a cylinder and in the well-known planar contraction 4:1, achieving very accurate, stable and mesh independent results for highly elastic fluids.

Abstract

This paper presents two procedures, based on the numerical multiscale theory, developed to predict the mechanical non-linear response of composite materials under monotonically increasing loads. Such procedures are designed with the objective of reducing the computational cost required in these types of analysis. Starting from virtual tests of the microscale, the solution of the macroscale structure via Classical First-Order Multiscale Method will be replaced by an interpolation of a discrete number of homogenized surfaces previously calculated. These surfaces describe the stress evolution of the microscale at fixed levels of an equivalent damage parameter (). The information required for these surfaces to conduct the analysis is stored in a Data Base using a json format. Of the two methods developed, the first one uses the pre-computed homogenized surface just to obtain the material non-linear threshold, and generates a Representative Volume Element (RVE) once the material point goes into the nonlinear range; the second method is completely off-line and is capable of describing the material linear and non-linear behavior just by using the discrete homogenized surfaces stored in the Data Base. After describing the two procedures developed, this manuscript provides two examples to validate the capabilities of the proposed methods

Abstract

En los últimos años el estudio del comportamiento de los materiales a nivel microscópico ha aumentado significativamente en términos de diseño de materiales de altas prestaciones. A pesar de los recientes avances de ordenadores de elevado rendimiento, la aplicación de métodos numéricos multiescala para simular grandes estructuras aún requiere costes computacionales prohibitivos. Éste trabajo presenta un procedimiento capaz de predecir la respuesta mecánica no-lineal de los materiales compuestos con el fin de reducir el coste computacional necesario para el análisis numérico de estructuras complejas. La solución de la estructura macroscópica a través del método multiescala de primer orden (FE2) se sustituirá por un modelo discreto obtenido de un análisis del comportamiento de un Volumen Representativo Elemental (RVE) del material. A través de las definiciones de un parámetro de daño equivalente (deq), función del esfuerzo global en la microescala, se realizarán una serie de ensayos virtuales en control de deformación, almacenando el estado de tensión-deformación alcanzado por ciertos niveles de deq en una base de datos. Analizando la evolución de la fractura en los materiales compuestos se puede observar como el régimen no-lineal se alcanza solo en algunos elementos de la estructura. Es por ello que se plantea un procedimiento, el Discrete Multiscale Threshold Surface (DMTS), en el que el análisis del RVE sirve para obtener la superficie en la que empieza el daño (deq >0). Esta ley permite saber si para un determinado estado tenso-deformacional el material ha dañado, sin necesidad de resolver el micro-modelo. Una vez iniciado el daño, se propone de generar de forma adaptiva un RVE con el que obtener el comportamiento dañado del material. Luego, el método FE2 se utilizará solo en los puntos de integración que hayan dañado. Este trabajo demuestra que el método FE2 puede ser remplazado por un Modelo Discreto Multiescala, representativo del material compuesto, obteniendo mejoras computacionales significativas.

Abstract

In this study, resin permeability of plain-woven composites is analyzed using a three-scale homogenization method. To this end, the three-scale homogenization method is developed to analyze the resin flow through both the structures of fiber bundles and the inside of fiber bundles, and also the mesoscopic and macroscopic resin permeability. To evaluate the validity of this method, resin permeability and characteristic flow velocity of plain-woven glass fiber-reinforced plastic (GFRP) are analyzed. The results show that the present method successfully analyzes the resin permeability of plain-woven composites.