A new energy-based local damage model for dynamic analysis of cracks

A new energy-based local damage model for dynamic analysis of cracks

Authors: Hung Thanh Tran

Journal: Computational Mechanics

Link: https://doi.org/10.1007/s00466-024-02547-4

Abstract: This contribution presents a novel dynamic local damage model based on strain energy density (SED) for time-dependent crack propagation modeling. The developed technique is derived in detail, and its implicit dynamic finite element implementation at small strain is provided for localized failure in brittle/quasi-brittle media under impact loading conditions. The aim of this work is to offer a consistent numerical framework entirely based on energy for dynamic crack growth analysis, focusing on simplicity and effectiveness. For that, the classical scalar strain-based damage formulation is converted to the energy-based one. Other related parameters of the model are also described in terms of energy. Thus, unlike the traditional strain-based local damage technique where the strain tensor is typically transformed into a scalar equivalent strain to define the damage variable, in this work, the internal damage law is directly governed by the positive reference SED, which is already a scalar field. To enhance the capabilities of the formulated model, the spectral decomposition of the strain tensor is utilized to distinguish between cracks occurring under tensile and compressive modes. Additionally, the well-known crack band theory is applied to address mesh-biased issues. Inheriting the characteristics of classical scalar smeared damage theory, the present method eliminates the need for any tracking algorithm or additional ad-hoc criteria for crack growth. Furthermore, only a single equation of motion needs to be solved for the governing equation, which further enhances the robustness, performance, and numerical effectiveness of the developed damage-simulating technique. Numerical experiments are conducted to demonstrate the ability and performance of the introduced formulation for time-dependent fracture analysis.