Localizing gradient damage model for anisotropic materials: Focusing on timber

Abstract

This paper presents a new damage model for transversely isotropic materials, with special focus on timber. The model proposed in this study is formulated by employing the localized gradient form of continuum damage theory. The model accounts for anisotropic damage through two damage variables, delineating damage parallel and perpendicular to the grain, representing isotropic damage within the cross-sectional plane. The conditions assumed in this work pertain to loading scenarios that occur within the plane. An additional fourth-order tensor transformation is incorporated to facilitate the conversion between the global and local reference frames, allowing for arbitrary spatial orientations of the material matrix. In this work we concentrate on damage arising from tensile and shear stresses. The model is implemented as a consistent linearized coupled (monolithic) problem.The performance verification of the model relies on numerous numerical examples, incorporating experimental benchmark problems. The outcomes demonstrate that the suggested damage model adeptly captures both the initiation of failure and the propagation of damage.