Scalar-based strain gradient plasticity theory to model size-dependent kinematic hardening effects
Résumé
A common belief in phenomenological strain gradient plasticity modeling is that including the
gradient of scalar variables in the constitutive setting leads to size-dependent isotropic hardening, whereas
the gradient of second-order tensors induces size-dependent kinematic hardening. The present paper
shows that it is also possible to produce size-dependent kinematic hardening using scalar-based gradient
theory. For this purpose, a new model involving the gradient of the equivalent plastic strain is developed
and compared with two reference scalar-based and tensor-based theories. Theoretical investigations using
simple monotonic loading conditions are first presented to assess the ability of the proposed model to solve
some issues related to existing scalar-based gradient theories. Simulations under cyclic loading conditions
are then provided to investigate the nature of the resulting hardening. These simulations show that the
proposed model is capable of producing size-dependent kinematic hardening effects at more affordable
costs, compared to existing tensor-based strain gradient plasticity theories
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