Special Modeling Approaches for Anisotropic and Heterogeneous Materials

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Solid Mechanics Seminar, 13:30-17:00, Wednesday, 25 June 2014

Special Modeling Approaches for Anisotropic and Heterogeneous Materials

13:30-14:30 Petr Krysl (University of California, San Diego, USA): Finite Element Methods for Deformation of Anisotropic Elastic Solids

Joint work of Petr Krysl, Steve Oberrecht and Jan Novák

Anisotropic elasticity has been addressed in the finite element literature relatively infrequently. It is generally assumed that methods that work for isotropic materials will continue to do so even when significant anisotropy (for instance in the form of constraints due to stiff reinforcing fibers) is introduced. We find that to be overly optimistic and we illustrate the failures with examples. We also propose some approaches that can improve the response of commonly used hexahedra and tetrahedra. In particular, (a) B-bar methods for low- and high-order elements based on three-field variational principles and (b) mean-strain hexahedra are reformulated to allow for arbitrarily constrained anisotropic materials.

14:30-15:00 Jaroslav Vondřejc (CTU in Prague, University of West Bohemia): An FFT-based Galerkin Method for Homogenization of Periodic Media

The homogenized material parameters are calculated by using an FFT-based Galerkin Method, which can be understood as an alternative to conventional Finite Elements. The main advantage of the method lies in a fact that primal and dual formulation maintain identical mathematical structure which allows to evaluate guaranteed bounds on homogenized properties. The convergence rates of the properties are studied together with the effectiveness of various solvers for related algebraic systems.

15:30-16:00 Martin Doškář (CTU in Prague): On Modelling of Heterogeneous Materials by Means of Wang Tiling

The aim of the talk is to present a technique of modelling heterogeneous materials that is based on the concept of Wang tilings. The attention is drawn to the ability of the method to reduce long-range order spatial artefacts in reconstructions of random material systems. Efficient tools of compressing microstructural information within Wang tiles inspired by techniques of Computer Graphics will be outlined along with an application of the approach in homogenization of elastic properties.

16:00-16:30 Lukáš Zrůbek (CTU in Prague): Synthesis of Microstructural Fields with the Help of Wang Tiles

This talk is devoted to the method of Wang tilings used to generate aperiodic microstructure-informed enrichment functions. Acquired constructions are self-equilibrated and correspond with spatial statistics of underlying microstructures. The use of synthetized enrichments is seen in numerical simulations of disordered material systems in Generalized and Hybrid Finite Element environments.

16:30-17:00 Martin Horák (CTU in Prague): Enhanced Trefftz Finite Element Method

Analysis of composite materials with inclusions is of interest in many engineering applications. However, the conventional finite element method may be cumbersome as the finite element mesh must resolve all heterogeneity details. In this talk we present an alternative approach based on the Trefftz finite element formulation enhanced by synthesized microstructure informed enrichment functions, thereby avoiding the detailed discretization. Moreover, possible extension of the Trefftz finite element method to isogeometric analysis will be discussed.