On Non-Local Flow Theories that Preserve the Classical Structure of Incremental Boundary Value Problems

A new non-local inelastic constitutive theory is proposed. The model retains the algebraic nature of the flow rules of conventional theories. This feature, which is in contrast to other recently proposed non-local theories, allows the problem of incremental equilibrium to be stated without extra boundary conditions or higher-order stresses. The general idea is presented both in the context of a J-2 flow theory and a single crystal plasticity theory. It is also demonstrated that reaction-diffusion type equations in the slip variables can be accommodated within the rate-independent crystal plasticity theory presented here.

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