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Geometry and mechanics of two-dimensional defects in amorphous materials

Significance Modeling defects, or localized strain carriers, are a central challenge in the formulation of elasto-plastic theory of amorphous solids. Whereas in crystalline solids defects are identified as local deviations from the crystal order, it is not clear how, or even if, equivalent intrinsic entities can be defined in amorphous solids. This work presents a new way of defining and describing localized intrinsic geometrical defects in amorphous solids and for computing the stresses within defected bodies. The methods and results that are presented here can be integrated into phenomenological theories of plasticity and can be applied to biomechanical problems that involve strain localization. We study the geometry of defects in amorphous materials and their elastic interactions. Defects are defined and characterized by deviations of the material’s intrinsic metric from a Euclidian metric. This characterization makes possible the identification of localized defects in amorphous materials, the formulation of a corresponding elastic problem, and its solution in various cases of physical interest. We present a multipole expansion that covers a large family of localized 2D defects. The dipole term, which represents a dislocation, is studied analytically and experimentally. Quadrupoles and higher multipoles correspond to fundamental strain-carrying entities. The interactions between those entities, as well as their interaction with external stress fields, are fundamental to the inelastic behavior of solids. We develop analytical tools to study those interactions. The model, methods, and results presented in this work are all relevant to the study of systems that involve a distribution of localized sources of strain. Examples are plasticity in amorphous materials and mechanical interactions between cells on a flexible substrate.