Elijah N. Borodin

Plastic deformation in crystalline solids arises from discrete microstructural rearrangements driven by energy exchange and crystallographic constraints. Conventional continuum plasticity models, even when enriched with crystal anisotropy, rely on prescribed flow rules and struggle to represent the emergence of internal length and time scales during the early stages of plastic flow. Here, we propose a fully discrete statistical framework for crystalline plasticity based on polytopal cell complexes (PCCs), in which elementary plastic events are represented as probabilistic microslips defined on crystallographically admissible face–edge pairs. The framework captures several physically interpretable features associated with non-equilibrium plastic flow, including strain-rate sensitivity, stress-dependent activation of slip systems, discrete activation spectra arising from crystallographic topology and the appearance of a minimum representative volume (MRV) for statistically stable plastic activity. Characteristic relaxation times (CRTs) and effective deformation rates arise naturally from the dynamics of internal energy dissipation, providing an intrinsic mapping between stochastic evolution and physical time. While the present study is restricted to illustrative simulations of face-centred cubic (FCC) single crystals under relatively simple loading conditions, the results demonstrate the potential of the proposed discrete framework for mesoscale investigations of crystallographically constrained stochastic plasticity.

Changes in dislocation density and material grain size commonly remain neglected in numerical simulations of plasticity and fracture. However, for a wide range of intense high-strain-rate and severe plastic deformation (SPD) regimes, such microstructural changes become a determining factor governing the mechanical response of materials. This study proposes a novel microstructure-informed dynamical model for high-rate severe plastic deformation inside adiabatic shear bands (ASB). When integrated into FEM simulations of SHPB dynamic tests on S355 mild steel, the model provides a level of physical fidelity and predictive detail that standard empirical frameworks, such as the Johnson-Cook model, fail to capture. Crucially, this framework facilitates the effective direct integration of EBSD microscopy data into FEM-based numerical simulations, enabling the prediction of spatial gradients in dislocation density, grain size, and yield strength near shear bands. The developed discrete methodology offers a possibility for detailed microstructural studies of the transition from the recrystallised fine-grain structure in the ASB region to the undeformed area, revealing similarities in the governing recrystallisation mechanisms. The experimentally observed transformation zone size, affected by post-dynamic recrystallisation (PDRX), is much larger than the width of the adiabatic shear band itself. While typically only the temperature increase and thermal conductivity are taken into account, the simulations show that the area of very high dislocation density can exceed the ASB width by a factor of 3, serving as a second driving force of PDRX.

Agglomerations of carbon‐based inclusions and the low adhesion of inclusion‐matrix interfaces are commonly viewed as detrimental to the strength and fracture toughness of ceramic composites. While large, high‐power agglomerations indeed promote microcracking, our computations show that moderate agglomeration levels can enhance energy dissipation through Y‐junctions in inclusion networks. Focusing on high‐temperature Zr‐based reduced graphene oxide/ceramic nanocomposites, we use a polytopal cell complex (PCC) framework to analyze macrocrack bridging for 12 graphene precursor powders with distinct log‐normal size distributions. The simulations quantify how inclusion fraction, strip‐length statistics, and agglomeration power jointly determine the topology of percolation networks and their contribution to fracture resistance. The results rationalize experimental observations that uniform‐size precursor powders reduce harmful clustering while maximizing bridging. Dislocation‐based estimates indicate that, even under ideal architectures, crack‐bridging toughening is theoretically limited to a factor of 2–3, exceeding but consistent with the 30%–50% improvements typically reported.

Microstructural changes in solids, driven by energy flows, do not develop in a static continuous space, such as the space considered in conventional plasticity models. The applied forces create an evolving internal energy landscape, which is constrained by crystallography but has characteristic spatial and temporal scales that form dynamically. To describe this view, we replace a common model for the evolution of dislocation substructure in metals with the evolution of microscopic slips in a combinatorial structure referred to as a polytopal cell complex (PCC). The micro-slips are associated with the 2-cells (faces) of the PCC and are driven by the minimisation of a properly defined Lagrangian. The approach provides a comprehensive statistical and thermodynamic description of plastic flow development. It allows the investigation of energy levels associated with different slip systems and reveals the microscopic mechanisms that result in the phenomenon of strain rate sensitivity.