Hyperelastic Inclusions in a Linear Elastic and Isotropic Material Matrix

Comprehensive validation studies, involving spherical and prolate spheroidal hyperelastic inclusions under complex internal eigenstrain and external loading conditions, demonstrate that our method significantly enhances prediction accuracy compared to classical linear-elastic approaches. Furthermore, the framework exhibits exceptional flexibility in seamlessly integrating externally derived explicit Eshelby tensor solutions, obviating the need for cumbersome integral evaluations. \textcolor{red}{To overcome the limitations imposed by the isotropic matrix assumption, we can incorporate formulations based on spectral invariants or numerical evaluation schemes of the Eshelby tensor into the framework}.

Originally motivated by the complex geomechanical problems encountered in kerogen-rich shale formations critical to unconventional energy exploitation, our method’s broader applicability is evident across diverse fields, such as biomedical engineering, composite material design, and smart material development. Thus, this study not only advances the fundamental theoretical understanding of nonlinear inclusion mechanics but also provides a versatile, practical tool for predictive modeling in numerous scientific and engineering applications.