Analytical solution of Mises elastoplastic solid spherical cavity expansion model considering initial hole and elastoplastic continuity

The cavity expansion model (CEM) holds significant engineering value for high-speed impact and blast analysis, yet its theoretical development suffers from three critical limitations: failure to quantify the influence of elastic strain accumulation on initial cavity size, solution discontinuity caused by conceptual confusion between elastic/plastic compressibility, and inadequate applicability of traditional solutions to non-zero initial cavity conditions. This study establishes a unified theoretical framework within the Eulerian framework based on the quasi-static spherical CEM, simultaneously considering both compressibility and incompressibility during the plastic phase. By introducing initial cavity size and elastic pre-strain, we derived a general analytical solution enabling continuous elastic-plastic transition, supported by numerical validation. The results demonstrate that incorporating both elastic compressibility and initial cavity size under plastic incompressibility assumptions yields continuous analytical solutions. For cavity wall pressure evolution, the improved theory shows closer alignment with numerical solutions in pre-critical pressure regimes, accurately captures momentum conservation characteristics under high-pressure conditions, and resolves longstanding ambiguities in volumetric compressibility concepts.