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**Structured extended finite element methods for solids defined by implicit surfaces.**
*(English)*
Zbl 1038.74041

Summary: A paradigm is developed for generating structured finite element models from solid models by means of implicit surface definitions. The implicit surfaces are defined by radial basis functions. Internal features, such as material interfaces, sliding interfaces and cracks are treated by enrichment techniques developed in the extended finite element method. Methods for integrating the weak form for such models are proposed. These methods simplify the generation of finite element models. Results presented for several examples show that the accuracy of this method is comparable to the accuracy of standard unstructured finite element methods.

### MSC:

74S05 | Finite element methods applied to problems in solid mechanics |

### Keywords:

radial basis functions; material interfaces; sliding interfaces, cracks; enrichment techniques; unit cells; representative volume elements### Software:

XFEM
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\textit{T. Belytschko} et al., Int. J. Numer. Methods Eng. 56, No. 4, 609--635 (2003; Zbl 1038.74041)

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