Energetic Constraints and Kinetic Closure in Dynamic Rupture: An Analytical Framework for Earthquake Source Physics

Abstract

Dynamic fracture and earthquake rupture propagation are governed by the balance between elastic energy release, fracture resistance, and elastodynamic wave radiation. In this study, we present a compact energetic framework that synthesizes established results from dynamic fracture mechanics and earthquake source theory into a physically transparent formulation. The framework couples bulk elastodynamics with an energetic admissibility condition and employs a phenomenological kinetic closure to relate energy excess to rupture speed, providing an explicit description of rupture evolution without prescribing detailed frictional constitutive laws. Within this setting, elastodynamic radiation constrains rupture velocity through mode‑dependent dynamic energy corrections, leading to asymptotic saturation within sub‑Rayleigh rupture regimes. Analytical relations are derived linking rupture speed to stress drop, rupture size, and fracture energy, yielding interpretable scaling trends for dynamically propagating ruptures. The proposed framework is intended as an analytical reference for interpreting rupture dynamics and energy partitioning, and for benchmarking numerical and constitutive models of earthquake rupture.