Numerical modeling of 3-D inclusions and voids by a novel adaptive XFEM

•A novel adaptive XFEM using hexahedron elements for inclusions and voids of composite materials is presented.•A posteriori error estimation based on recovery strain allows ones to obtain a desired accuracy with one or two trials.•Variable-node hexahedron transition elements are used to treat the mismatching problems of different meshes.•Single and multiple inclusions and voids in composites are modeled accurately and efficiently. This paper describes an adaptive numerical framework for modeling arbitrary inclusions and holes in three-dimensional (3-D) solids based on a rigorous combination of local enriched partition-of-unity method, a posterior error estimation scheme, and the variable-node hexahedron elements. In this new setting, a posteriori error estimation scheme driven by a recovery strain procedure in terms of extended finite element method (XFEM) is taken for adaptive purpose (local mesh refinement). Refinement is only performed where it is needed, e.g., the vicinity of the internal boundaries, through an error indicator. To treat the mismatch of different meshes-scale in 3-D, the variable-node hexahedron elements based on the generic point interpolation are thus integrated into the present formulation. The merits of the proposed approach such as its accuracy, effectiveness and performance are demonstrated through a series of representative numerical examples involving single and multiple inclusions/holes in 3-D with different configurations. The obtained numerical results are compared with reference solutions based on analytical and standard non-adaptive XFEM methods.