Power law distributed fluctuations are known to accompany terminal failure in disordered brittle solids. The associated intermittent scale-free behavior is of interest from the fundamental point of view as it emerges universally from an intricate interplay of threshold-type nonlinearity, quenched disorder, and long-range interactions. We use the simplest mean-field description of such systems to show that they can be expected to undergo a transition between brittle and quasi-brittle (ductile) responses. While the former is characterized by a power law distribution of avalanches, in the latter, the statistics of avalanches is predominantly Gaussian. The realization of a particular regime depends on the variance of disorder and the effective rigidity represented by a combination of elastic moduli. We argue that the robust criticality, as in the cases of earthquakes and collapsing porous materials, indicates the self-tuning of the system towards the boundary separating brittle and ductile regimes.

已知幂律分布波动伴随终端无序脆性固体的失效。从基本的角度来看，相关的间歇性无标度行为很有趣，因为它普遍来自阈值型非线性、淬灭无序和长程相互作用的复杂相互作用。我们使用此类系统最简单的平均场描述来表明它们可以预期在脆性和准脆性（韧性）响应之间发生转变。前者以雪崩的幂律分布为特征，而在后者中，雪崩的统计主要是高斯分布。特定状态的实现取决于无序的方差和弹性模量组合所代表的有效刚度。我们认为鲁棒临界性，如在地震和坍塌多孔材料的情况下，