A localized mass-field damage model with energy decomposition: Formulation and FE implementation

Abstract

In this article, we present a new computational damage approach based on localized mass loss concept and its detailed finite element implementation for brittle fracture under quasi-static loading condition. Formulation of this approach is derived in a general way by means of finite deformation regime and nonlinear isotropic materials. The underlying idea of the theory lies in the fact that cracks are created by massive breakage of atomic bonds, diffusing in a volume of characteristic size, resulting in highly localized mass loss area, and nor geometric description of cracks are required. In degraded domain, the traditional law of conservation of mass is violated locally and that is replaced by the local mass-balance equation, accounting for mass flow in the area of degraded material. A coupled system of equilibrium and local mass-balance equations is thus introduced to govern deformation of the body and evolution of the mass density. In this setting, the failure, in contrast to conventional damage models, is thus driven by localized mass loss, which has physical meaning, nor internal parameters such as phase-field or damage variables are defined. We also introduce new constitutive laws for mass source and mass flux by means of energy decomposition, where only the positive part of strain energy density (SED) function involves in the degradation of mass, accounting for distinction of fracture behavior in tension and compression. The discrete forms of governing equations are solved by a staggered nonlinear algorithm. Importantly, equally linear interpolations for the standard finite elements are used for both displacements and mass density, nor mismatch of approximation exits, convenient in the implementation. In addition, we present a special detection technique to find so-called updated nodes, which aims to prevent numerically unstable issues caused by random distortions of deleted elements. The staggered algorithm is thus modified so that the displacements and mass density are updated separately. This detection technique is then integrated into the staggered algorithm. We also present a procedure for calibration of the required quantities used for the localized mass loss analysis. Numerical experiments for brittle fracture are studied to show the accuracy and performance of the developed damage approach.