The contribution presents an analysis of a rate-independent non-local damage model, recently proposed by (Mielke and Roubicek, 2006). An analytical as well as numerical solution of a simple one-dimensional bifurcation problem is performed, demonstrat
ing that, for the elementary localization test, the model is free of pathological features.
This paper presents an approach to constructing microstructural enrichment functions to local fields in non-periodic heterogeneous materials with applications in Partition of Unity and Hybrid Finite Element schemes. It is based on a concept of aperio
dic tilings by the Wang tiles, designed to produce microstructures morphologically similar to original media and enrichment functions that satisfy the underlying governing equations. An appealing feature of this approach is that the enrichment functions are defined only on a small set of square tiles and extended to larger domains by an inexpensive stochastic tiling algorithm in a non-periodic manner. Feasibility of the proposed methodology is demonstrated on constructions of stress enrichment functions for two-dimensional mono-disperse particulate media.
The focus of this paper is on the analysis of the Conjugate Gradient method applied to a non-symmetric system of linear equations, arising from a Fast Fourier Transform-based homogenization method due to (Moulinec and Suquet, 1994). Convergence of th
e method is proven by exploiting a certain projection operator reflecting physics of the underlying problem. These results are supported by a numerical example, demonstrating significant improvement of the Conjugate Gradient-based scheme over the original Moulinec-Suquet algorithm.
In this short note, we present a new technique to accelerate the convergence of a FFT-based solver for numerical homogenization of complex periodic media proposed by Moulinec and Suquet in 1994. The approach proceeds from discretization of the govern
ing integral equation by the trigonometric collocation method due to Vainikko (2000), to give a linear system which can be efficiently solved by conjugate gradient methods. Computational experiments confirm robustness of the algorithm with respect to its internal parameters and demonstrate significant increase of the convergence rate for problems with high-contrast coefficients at a low overhead per iteration.
One of the key aspects governing the mechanical performance of composite materials is debonding: the local separation of reinforcing constituents from matrix when the interfacial strength is exceeded. In this contribution, two strategies to estimate
the overall response of particulate composites with rigid-brittle interfaces are investigated. The first approach is based on a detailed numerical representation of a composite microstructure. The resulting problem is discretized using the Finite Element Tearing and Interconnecting method, which, apart from computational efficiency, allows for an accurate representation of interfacial tractions as well as mutual inter-phase contact conditions. The candidate solver employs the assumption of uniform fields within the composite estimated using the Mori-Tanaka method. A set of representative numerical examples is presented to assess the added value of the detailed numerical model over the simplified micromechanics approach.
