On the relation between plasticity, friction, and geometry.
Plasticity refers to thermodynamically irreversible deformation associated with a change of configuration of materials. Friction is a phenomenological law that describes the forces resisting sliding between two solids or across an embedded dislocation. These two types of constitutive behaviors explain the deformation of a wide range of engineered and natural materials. Yet, they are typically described in distinct physical laws that cannot capture the continuum between distributed and localized deformation. Here, I describe a framework where friction appears as an end-member of plasticity for a high degree of localization. The proposed multiplicative form of rate-and-state friction regularizes the constitutive behavior at vanishing velocity. While simplified, the model highlights the importance of geometry in the constitutive behavior of solids. The frictional response can emerge from generalized plastic flow laws for high strain-rates when the deformed region collapses from three to two dimensions. That faults slide rather than open and plastic materials conserve volume during deformation seem to originate from the same deviatoric constraint in the constitutive behavior.
Publisher URL: http://arxiv.org/abs/1711.01954
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