Slender beams are often employed as constituents in engineering materials and structures. Prior experiments on lattices of slender beams have highlighted their complex failure response, where the interplay between buckling and fracture plays a critical role. In this paper, we introduce a novel computational approach for modeling fracture in slender beams subjected to large deformations. We adopt a state-of-the-art geometrically exact Kirchhoff beam formulation to describe the finite deformations of beams in three-dimensions. We develop a discontinuous Galerkin finite element discretization of the beam governing equations, incorporating discontinuities in the position and tangent degrees of freedom at the inter-element boundaries of the finite elements. Before fracture initiation, we enforce compatibility of nodal positions and tangents weakly, via the exchange of variationally-consistent forces and moments at the interfaces between adjacent elements. At the onset of fracture, these forces and moments transition to cohesive laws modeling interface failure. We conduct a series of numerical tests to verify our computational framework against a set of benchmarks and we demonstrate its ability to capture the tensile and bending fracture modes in beams exhibiting large deformations. Finally, we present the validation of our framework against fracture experiments of dry spaghetti rods subjected to sudden relaxation of curvature.

翻译：细长梁常作为工程材料和结构中的组成部分。先前关于细长梁格子的实验揭示了其复杂的失效响应，其中屈曲与断裂的相互作用起到关键作用。本文提出了一种新的计算方法，用于模拟大变形条件下细长梁的断裂行为。我们采用最先进的几何精确Kirchhoff梁公式来描述梁在三维空间中的有限变形。我们开发了梁控制方程的不连续伽辽金有限元离散化方法，在有限单元间边界处引入位置和切向自由度的不连续性。在断裂起始前，我们通过相邻单元界面处交换变分一致的力和力矩，弱形式地强制节点位置和切向的相容性。在断裂发生时，这些力和力矩转变为模拟界面失效的内聚准则。我们进行了一系列数值试验，将计算框架与基准验证集进行对比，并展示了其捕捉大变形梁中拉伸和弯曲断裂模式的能力。最后，我们通过干意面棒突然释放曲率的断裂实验对本框架进行了验证。