AI 中文总结
本文提出一种宏观连续介质理论，将脆性断裂形核与扩展视为约束能量最小化问题，通过九项实验验证其适用于各向同性弹性脆性材料。
AI 中文摘要
本文提出了一种宏观（或连续介质）理论，旨在描述在单调、准静态但其他方面任意的机械载荷下，名义上弹性脆性材料中裂纹何时、何地以及为何形核和扩展。受近期研究见解的启发，所提出的尖锐理论假设：裂纹仅在材料强度表面被超过的区域形核和扩展，其演化由势能（弹性能量减去外力所做的功）与表面能量之和的最小化决定。尽管该理论适用于具有任意弹性（线性或非线性）和任意材料对称性（各向同性或各向异性）的材料，但此处的研究范围仅限于最基础的各向同性弹性脆性材料情况。为了验证，该理论与一组九项测试进行了对比，这些测试涵盖了关于断裂形核和扩展的全部既定实验知识——即所谓的“弹性脆性断裂九圆”——测试对象包括一种硬质材料（硅酸盐玻璃）和一种软质材料（合成橡胶）。
英文摘要
This paper presents a macroscopic, or continuum, theory aimed at describing when, where, and why cracks nucleate and propagate in nominally elastic brittle materials under monotonic, quasi-static, but otherwise arbitrary mechanical loads. Motivated by recent insights, the proposed sharp theory posits that: \emph{cracks nucleate and propagate exclusively in regions where the strength surface of the material is exceeded, with their evolution dictated by the minimization of the sum of the potential --- the elastic energy minus the work done by the externally applied forces --- and surface energies.} While the theory applies to materials with any elasticity (linear or nonlinear) and any material symmetry (isotropic or anisotropic), attention is restricted here to the most basic case of isotropic elastic brittle materials. For demonstration purposes, the theory is confronted with a set of nine tests that span the entire range of well-settled experimental knowledge on fracture nucleation and propagation --- the so-called ``Nine Circles of Elastic Brittle Fracture'' --- on both a hard material (a silicate glass) and a soft material (a synthetic rubber).
