Eulerian finite volume framework for extreme multiphase plastic deformation

Predicting the mechanical behavior of polycrystalline materials under extreme loading conditions remains challenging due to the limitations of traditional Lagrangian approaches, which struggle with severe mesh distortion at high strain rates and large deformations. This work presents a finite volume Eulerian formulation for modeling multiphase plasticity under extreme conditions, with applications to stress wave propagation and high strain-rate deformation. The approach integrates a crystal plasticity framework within an Eulerian frame of reference, employing a cell-centered finite volume discretization for its naturally conservative properties during field advection. A multi-phase diffuse interface representation captures complex grain-scale interactions and slip system activation in heterogeneous microstructures. Benchmark simulations demonstrate that the numerically computed wave propagation speed matches analytical predictions to high accuracy, and crystallographic updates are validated for large rigid body rotations. Application to polycrystalline shock loading reveals strain localization patterns and up to 35.6% velocity attenuation through plastic dissipation. Three-dimensional simulations of α − β titanium microstructures demonstrate the framework’s capability to resolve complex strain partitioning between phases with different crystal structures. The methodology provides a robust numerical framework for investigating material behavior under conditions where Lagrangian approaches fail, offering new insights into the interplay between microstructural heterogeneity and high strain-rate plasticity.