Modified internal state variable models of plasticity using nonlocal integrals in damage and gradients in dislocation density

To enhance material performance at different length scales, this study strives to develop a reliable analytical and computational tool with the help of internal state variables spanning micro and macro-level behaviors. First, the practical relevance of a nonlocal damage integral added to an internal state variable (BCJ) model is studied to alleviate numerical instabilities associated within the post-bifurcation regime. The characteristic length scale in the nonlocal damage, which is mathematical in nature, can be calibrated using a series of notch tensile tests. Then the same length scale from the notch tests is used in solving the problem of a high-velocity (between 89 and 107 m/s) rigid projectile colliding against a 6061-T6 aluminum-disk. The investigation indicates that incorporating a characteristic length scale to the constitutive model eliminates the pathological mesh-dependency associated with material instabilities. In addition, the numerical calculations agree well with experimental data. Next, an effort is made rather to introduce a physically motivated length scale than to apply a mathematical-one in the deformation analysis. Along this line, a dislocation based plasticity model is developed where an intrinsic length scale is introduced in the forms of spatial gradients of mobile and immobile dislocation densities. The spatial gradients are naturally invoked from balance laws within a consistent kinematic and thermodynamic framework. An analytical solution of the model variables is derived at homogenous steady state using the linear stability and bifurcation analysis. The model qualitatively captures the formation of dislocation cell-structures through material instabilities at the microscopic level. Finally, the model satisfactorily predicts macroscopic mechanical behaviors - e.g., multi-strain rate uniaxial compression, simple shear, and stress relaxation - and validates experimental results.