Title: Dual Role for Heterogeneity in Dynamic Fracture Show Chinese title

Title: 动态断裂中异质性的双重作用

Abstract: We approach the problem of heterogeneous dynamic fracture by considering spatiotemporal perturbations to planar crack fronts. Front propagation is governed by local energy balance between the elastic energy per unit area available to fracture, G, and the dissipation in creating new surfaces. G is known analytically as a perturbation series in the crack front fluctuation. For dissipation that monotonically increases with the crack speed, we derive an equation of motion for crack fronts that is second-order accurate. In the linear order, heterogeneity does not change the net speed of fracture. In the second order, nonlinear interactions of the front and the heterogeneous landscape populate an intermediate-scale fluctuation spectrum. We find that, when dissipation weakly grows with velocity, nonlinearities globally amplify dissipation and reduce the crack speed. Strong velocity dependence, however, mitigates toughening effects and may facilitate fracture. Show Chinese abstract

Abstract: 我们通过考虑平面裂纹前沿的时空扰动来解决异质动态断裂问题。 前沿传播由单位面积可用的弹性能量G与产生新表面的耗散之间的局部能量平衡所控制。 G已知为裂纹前沿波动的摄动级数。 对于随裂纹速度单调增加的耗散，我们推导出一个二阶精度的裂纹前沿运动方程。 在一级近似下，异质性不会改变断裂的净速度。 在二级近似下，前沿与异质景观的非线性相互作用会产生中间尺度的波动谱。 我们发现，当耗散随速度弱增长时，非线性全局地放大耗散并降低裂纹速度。 然而，强速度依赖性会减弱增韧效应，并可能促进断裂。