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An X-FEM and level set computational approach for image-based modelling: application to homogenization. (English) Zbl 1235.74297

Summary: The advances in material characterization by means of imaging techniques require powerful computational methods for numerical analysis. The present contribution focuses on highlighting the advantages of coupling the extended finite elements method and the level sets method, applied to solve microstructures with complex geometries. The process of obtaining the level set data starting from a digital image of a material structure and its input into an extended finite element framework is presented. The coupled method is validated using reference examples and applied to obtain homogenized properties for heterogeneous structures. Although the computational applications presented here are mainly two-dimensional, the method is equally applicable for three-dimensional problems.

MSC:

74S05 Finite element methods applied to problems in solid mechanics
74Q15 Effective constitutive equations in solid mechanics

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