Localizing gradient damage model with smoothed stress based anisotropic nonlocal interactions

Abstract

In this paper, a localizing gradient damage model with smoothed stress based anisotropic nonlocal interactions is proposed, which overcomes the limitations of conventional damage models for the accurate prediction of localized failure of quasi-brittle materials. The proposed model uses a modified anisotropic nonlocal interaction domain, which also accounts the decrease in nonlocal interactions during the softening regime. The modification in the nonlocal interaction domain is done by introducing a normalized anisotropic interaction kernel and a damage dependent interaction function in the constitutive framework. The normalized anisotropic interaction kernel governs the orientation of the nonlocal interaction domain, depending on the principal stress state, whereas the interaction function controls the intensity of the nonlocal interactions. Due to these enhancements in the interaction behavior, an anisotropic behavior is introduced in the nonlocal interactions. The proposed model employs a thermomechanical micromorphic procedure, where an additional microforce balance equation is introduced in the constitutive framework apart from the standard equilibrium equation. To enable the use of low order finite elements, an integral nonlocal smoothening technique is employed to obtain a smoothed stress field for the better prediction of diffusive interaction domain. For the numerical implementation purpose, the performance and the accuracy of the proposed model are tested against mode-I, mode-II and mixed mode type of failure problems under plane deformation condition.