The acuurate prediction of the time-dependent mechanical behavior and deformation mechanisms of second-phase reinforced alloys under size effects is critical for the development of high-strength ductile metals and alloys for dynamic applications. However, solving their responses using high-fidelity numerical methods is computationally expensive and, in many cases, impractical. To address this issue, a dual-scale incremental variational formulation is proposed that incorporates the influence of plastic gradients on plastic evolution characteristics, integrating a strain-rate-dependent strain gradient plasticity model and including plastic gradients in the inelastic dissipation potential. Subsequently, two minimization problems based on the energy dissipation mechanisms of strain gradient plasticity, corresponding to the macroscopic and microscopic structures, are solved, leading to the development of a homogenization-based dual-scale solution algorithm. Finally, the effectiveness of the variational model and tangent algorithm is validated through a series of numerical simulations. The contributions of this work are as follows: first, it advances the theory of self-consistent computational homogenization modeling based on the energy dissipation mechanisms of plastic strain rates and their gradients, along with the development of a rigorous multi-level finite element method (FE2) solution procedure; second, the proposed algorithm provides an efficient and accurate method for evaluating the time-dependent mechanical behavior of second-phase reinforced alloys under strain gradient effects, exploring how these effects vary with the strain rate, and investigating their potential interactions.
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