The study of elasticity, plasticity and failure in non-crystalline solids has greatly benefitted from the application of atomic scale simulation. This "colloquium paper" reviews the ways in which a variety of computational approaches have been used to elucidate the atomic scale phenomena that control the mechanics of amorphous solids. The constitutive theories that have been developed for describing mechanical response are briefly reviewed, as well as the prospects for testing the assumptions of these theories using simulation. We list what we believe to be the most pressing open questions for substantiating these theoretical approaches, and ultimately for understanding and predicting the mechanical responses of amorphous solids.
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