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<p>In this article, an isotropic eikonal gradient-enhanced damage modeling technique for studying time-dependent fracture mechanisms in brittle/quasi-brittle solids is presented. As is consistent with the classical gradient damage theory, the eikonal-type gradient damage modeling framework is mesh-independent and simple to implement, as it does not require any numerical tracking algorithm for discontinuities in the displacement field during crack propagation. With the evolving interaction known as the damage-based transient internal length scale, eikonal damage formulations could overcome the drawbacks of spurious damage diffusion and incorrect damage initiation by the traditional gradient theory. More realistic failure behavior could be predicted by the eikonal-based damage models. In the work, the derived governing equations of the momentum and a smooth Rankine strain-based eikonal gradient-enhanced evolution for the motion of the body and evolution of the nonlocal equivalent strain (time-dependent fracture driving term) are effectively solved using the standard finite element method (FEM). For temporal discretization, a robust explicit solver of the central difference method integrated with the row-sum technique for mass lumping is adopted. The advantages and abilities of the present dynamic model are shown by considering a number of time-dependent crack propagation problems in two-dimensional (2D) and three- dimensional (3D) solids.</p>

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Dynamic crack growth analysis by an eikonal gradient damage model

  • 期刊论文

  • 发表日期：

    2025年10月10日

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  • Hung Thanh Tran

摘要

In this article, an isotropic eikonal gradient-enhanced damage modeling technique for studying time-dependent fracture mechanisms in brittle/quasi-brittle solids is presented. As is consistent with the classical gradient damage theory, the eikonal-type gradient damage modeling framework is mesh-independent and simple to implement, as it does not require any numerical tracking algorithm for discontinuities in the displacement field during crack propagation. With the evolving interaction known as the damage-based transient internal length scale, eikonal damage formulations could overcome the drawbacks of spurious damage diffusion and incorrect damage initiation by the traditional gradient theory. More realistic failure behavior could be predicted by the eikonal-based damage models. In the work, the derived governing equations of the momentum and a smooth Rankine strain-based eikonal gradient-enhanced evolution for the motion of the body and evolution of the nonlocal equivalent strain (time-dependent fracture driving term) are effectively solved using the standard finite element method (FEM). For temporal discretization, a robust explicit solver of the central difference method integrated with the row-sum technique for mass lumping is adopted. The advantages and abilities of the present dynamic model are shown by considering a number of time-dependent crack propagation problems in two-dimensional (2D) and three- dimensional (3D) solids.