دانلود رایگان مقاله اعتبار سنجی شبیه سازی برای رویکرد تغییراتی شکستگی

1. Introduction

The modeling of crack geometry (path) has been one of the most challenging and elusive aspects of fracture mechanics and has captured the interest of scientists in different disciplines for many years. The difficulty in this endeavor is two-fold: deriving proper models capable of predicting potentially complex unknown crack paths, and coming up with numerical schemes capable of dealing with the unknown crack geometry without remeshing. The later issue has been tackled with some success by methods based on enriching the approximation space through cohesive [1,2] or extended [3,4] finite elements, or non-local approximations based on phase-fields [5–7], level sets [8,9] or eigendeformation [10]. Francfort and Marigo’s variational approach to fracture [11–13] aims at addressing both issues simultaneously by providing a rigorous model derived from Griffith’s concept of energy restitution between bulk and surface energies, and providing an efficient numerical implementation capable of handling complex unknown crack path. Over the last decade, this approach was applied to many areas including elastic fracture [12,14,15], thermoelastic fracture [16,17], thin-film fracture [18–20], thin-shells [21], electro-mechanical fracture [22,23], or dynamic fracture [24–27] to name a few. A major difficulty associated with the variational approach to fracture is the reliance on global energy minimization, which can sometimes result in unrealistic crack paths by making equally admissible “near” and “far” points in configuration space. In this paper, we propose a variant of the backtracking algorithm from [15] that allows a more thorough exploration of “near” states. While most of the literature focuses on verification simulations, or numerical investigations of the properties of such models or algorithms, we focus on the quantitative validation of our method. We use available well-documented experimental data to illustrate the ability of this deep backtracking algorithm, combined with the regularized expression of the variational fracture energy to accurately predict crack paths in realistic situations.

5. Conclusions] In this article, we performed several validation experiments for the variational approach to fracture [13], implemented through a regularized energy, focusing on situations where complex crack paths arise. We highlighted the adequacy of this approach for quantitative prediction of crack paths, without a priori hypotheses. We improved significantly on the backtracking algorithm by devising a variant exploring more states in configuration space. In four distinct problems, we performed numerical simulations predicting crack paths that are consistent with experiments and the most accepted numerical literature. When nucleation of a crack with non-zero length is observed, the critical loading upon which cracks nucleate is shown to depends significantly on the regularization parameter ϵ of the regularized energy. This phenomenon should highlight the importance of the extensive study of gradient damage models in the one-dimensional case [30], and how it can be leveraged in numerical simulations, as in [17].