is described by a nonlocal damage model. The nonlocal formulation serves as an efficient localization limiter and leads to objective results, However, fine grids are necessary to resolve the bands of localized strains, and stress oscillations often appear in low-order…
is described by a nonlocal damage model. The nonlocal formulation serves as an efficient localization limiter and leads to objective results, However, fine grids are necessary to resolve the bands of localized strains, and stress oscillations often appear in low-order elements due to a mismatch between the interpolation of local and nonlocal quantities. This calls for innovative adaptative procedures that go beyond the commonly used h- adaptivity, The extended finite element method (X-FEM) is used to adaptively enrich the standard displacement approximation by incorporating special shape functions, A numerical example illustrating the new approach demonstrates the performance and accuracy of the method. It is shown that satisfactory results can be obtained even on a very coarse mesh with only a few added degrees of freedom corresponding to an enrichment by a regularized Heaviside function. INTRODUCTION interpolation of local and nonlocal quantities (Jirasek Quasibrittle materials, such as concrete, rock, tough and Patzak 2000). As shown by Jirasek (2001), p- ceramics, or ice, are characterized by the development adaptive methods based on an increase of the poly- of nonlinear fracture process zones, which can be nomial order of finite element shape functions lead to macroscopically described as regions of highly local- only a partial improvement. The undesired stress os- ized strains.