Local numerical homogenization in modeling of heterogeneous visco-elastic materials

Marek Klimczak, Witold Cecot

Cracow University of Technology, ul. Warszawska 24, 31-155 Kraków.

DOI:

https://doi.org/10.7494/cmms.2013.2.0434

Abstract:

The main objective of this paper is to present the prospects of application of local numerical homogenization to visco-elastic problems. Local numerical homogenization is one of the computational homogenization methods, proposed by Jhurani in 2009 for linear problems. Its main advantage is that it can be used in the case of modeling of heterogeneous materials with neither distinct scales separation nor periodic microstructure. The main idea of the approach is to replace of a group of many small finite elements by one macro element. The coarse element stiffness matrix is computed on the basis of the fine element matrices. In such a way one obtains a coarse mesh approximation of the time consuming fine mesh solution. In this paper we use the Burgers model to describe inelastic deformations, however any other constitutive equations may be applied. In the 1D case the Burgers model is interpreted as a combination of a spring and a dashpot and it is mainly used for bituminous materials (e.g. binders or asphalt mix). Because of rheological effects a transient analysis is necessary. Integration of local numerical homogenization with Burgers model should improve modeling of heterogeneous visco-elastic materials. The approach we propose can reduce the computational cost of the analysis without deterioration of the modeling reliability. We present numerical results of 1D and 2D analysis for selected problems that provide comparison between the ‘brute force’ FEM approach and local numerical homogenization in application to modeling of heterogeneous visco-elastic materials in order to validate the technique.

Cite as:

Klimczak, M., & Cecot, W. (2013). Local numerical homogenization in modeling of heterogeneous visco-elastic materials. Computer Methods in Materials Science, 13(2), 226 – 230. https://doi.org/10.7494/cmms.2013.2.0434

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