A computational approach based on the integration of the equivalent-eigenstrain concept with the eXtended Finite Element Method for general-shaped inclusions embedded in ceramic materials

Tempering and firing practices decrease the strength of ceramic materials such as those used for traditional pottery, due to thermal expansion mismatch between temper particles and ceramic matrix [1]. We study stress concentration around sharp temper inclusions where damaged zones have a toroidal shape (Figure 1) [2]. For this purpose, a variational formulation based on Eshelby's equivalent eigenstrain approach [3] is developed. In this approach, the toroidal damaged zone is treated as an inclusion surrounded by a "regularized" layer of finite width simulating an imperfect interface. The regularized layer is treated as an equivalent eigenstrain [4]. The associated numerical formulation is obtained by means of the regularized eXtended Finite Element Method. This method is suitable for general shaped inclusions because it describes interfaces implicitly through the level set method, while making discretization independent of the interface geometry. In the present work, three-dimensional simulations have been performed on a specimen with a toroidal inclusion for variable Young moduli and Poisson coefficients of the matrix and the inclusion. Figs. 1 e 2 show the stress σzz for a tensile specimen with a hard and a soft torus inclusion, respectively, subjected to a tensile pressure pz of 1MPa applied over the top, with Poisson coefficient of 0.2 for both matrix and inclusion. In Fig.1 and 2, a perfect interface between torus and matrix has been assumed. One fourth of the specimen has been studied because symmetries of loading and geometry have been exploited.