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.

现象学应变梯度可塑性建模的一个普遍信念是，在本构环境中包括标量变量的梯度会导致尺寸依赖的各向同性硬化，而二阶张量的梯度会导致尺寸依赖的运动硬化。本文表明，也可以使用基于标量的梯度理论进行尺寸依赖的运动硬化。为此，开发了一个包含等效塑性应变梯度的新模型，并将其与两种基于标量的参考理论和基于张量的理论进行了比较。首先提出了使用简单单调加载条件的理论研究，以评估所提出模型解决与现有基于标量的梯度理论相关的一些问题的能力。然后提供了在循环载荷条件下的模拟，以研究所得硬化的性质。这些仿真表明，与现有的基于张量的应变梯度可塑性理论相比，所提出的模型能够以更合理的成本产生尺寸相关的运动硬化效应。