In this paper, a method is proposed for extracting fracture parameters in anisotropic thermoelasticity cracking via interaction integral method within the framework of extended finite element method (XFEM). The proposed method is applied to linear thermoelastic crack problems. The numerical results of the stress intensity factors (SIFs) are presented and compared with those reported in related references. The good agreement of the results obtained by the developed method with those obtained by other numerical solutions proves the applicability of the proposed approach and confirms its capability of efficiently extracting thermoelasticity fracture parameters in anisotropic materials.

In this paper, a method for extracting stress intensity factors (SIFs) in orthotropic thermoelasticity fracture by the extended finite element method (XFEM) and interaction integral method is present. The proposed method is utilized in linear elastic crack problems. The numerical results of the SIFs are presented and compared with those obtained using boundary element method (BEM). The good accordance among these two methods proves the applicability of the proposed approach and conforms its capability of efficiently extracting thermoelasticity fracture parameters in orthotropic material.

Subsurface flows are influenced by the presence of faults and large fractures which actas preferential paths or barriers for the flow. In literature models were proposed tohandle fractures in a porous medium as objects of codimension 1. In this work we considerthe case of a network of intersecting fractures, with the aim of deriving physicallyconsistent and effective interface conditions to impose at the intersection betweenfractures. This new model accounts for the angle between fractures at the intersectionsand allows for jumps of pressure across intersections. This fact permits to describe theflow when fractures are characterized by different properties more accurately with respectto other models that impose pressure continuity. The main mathematical properties of themodel, derived in the two-dimensional setting, are analyzed. As concerns the numericaldiscretization we allow the grids of the fractures to be independent, thus in generalnon-matching at the intersection, by means of the extended finite element method(XFEM). This increases the flexibility of the method in the case of complexgeometries characterized by a high number of fractures.

This paper is devoted to the introduction of a new variant of the extendedfinite element method (Xfem) for the approximation of elastostatic fractureproblems. This variant consists in a reduced basis strategy for the definitionof the crack tip enrichment. It is particularly adapted when the asymptoticcrack-tip displacement is complex or even unknown. We give a mathematical resultof quasi-optimal a priori error estimate and some computational tests includinga comparison with some other strategies.