Generalized dynamic domain-independent interaction integral in the transient fracture investigation of magneto-electro-elastic composites

Abstract

The domain-independent interaction integral (DII-integral) is a powerful tool for dealing with crack issues of nonhomogeneous materials, due to its feature of being independent of the scale of integration domain, regardless of the nonhomogeneous properties and complex material interfaces. As an important part of the interaction integral (I-integral), the auxiliary field conditions required to establish the dynamic DII-integral have not been clearly clarified so far. For the first time, this work rigorously proves and gives the requirements of the auxiliary fields for building the dynamic DII-integral in anisotropic linear elastic, piezoelectric (PE), piezomagnetic (PM) and MEE materials, respectively, and a theoretical framework is derived for designing the dynamic DII-integral for new functional materials in the future. This proof guarantees the successful utilization of DII-integral to investigate the transient response in cracked composites without employing homogenized material parameters, while considering internal microstructure and complex interfaces. Using the extended finite element method (XFEM) as a pre-processing technique, the accuracy of the DII-integral is verified by comparing available references. Then, the domain-independence is confirmed with multiple integration domains, especially for those containing interfaces. Finally, the arrangements of PE/PM layers, locations and distributions of PE/PM particles affecting dynamic IFs are systematically investigated. Simultaneously, illustrations of elastic wave in cracked MEE composites are depicted to better understand the dynamic fracture response.