Soft matrix: probing local mechanical properties in amorphous solids

Understanding how amorphous solids yield under shear is central to predicting material failure, yet prescribing reliable local yielding criteria remains a fundamental challenge. Here we introduce the soft matrix method, which creates a minimally constrained and elastically coupled environment that allows localized regions of an amorphous solid to yield naturally. This method overcomes key limitations of earlier approaches and provides a robust platform for probing failure mechanisms in soft disordered materials. Using this framework, we analyze localized yielding by systematically varying the size of the local probe region in our microscopic simulations, and we uncover an intrinsic length scale (ζ) that governs local failure, showing that ζ grows with the age of the system. The age dependence appears not only in the distribution of local yield stresses but also in the pseudogap exponent θ, which quantifies the marginal stability of amorphous solids. These insights offer a pathway toward improved elastoplastic modeling of disordered materials.