Formation of jets from hemispherical shaped charge liners

Accurately predicting shaped charge jet formation remains a central challenge in detonation physics as analytic models developed for conical liners do not readily extend to alternative geometries used in some modern designs. Hemispherical liners exhibit a distinct collapse process, converging toward a near-common point rather than a moving stagnation region and producing a layered jet. While jet formation theories for conical liners are well established, comparable analytic descriptions for hemispherical liners remain limited. Consequently, researchers often rely on continuum-based simulations, which are accurate but computationally intensive and can obscure influential collapse and jet formation mechanisms. To advance current understanding, we introduce an analytic framework describing the collapse and jet formation process of a constant-wall-thickness hemispherical liner driven by a planar detonation wave. Treating the liner as an incompressible perfect fluid and applying mass and momentum conservation, equations are derived to predict the velocity field and associated mass distribution of a layered jet. Using methods analogous to existing approaches for approximating initial collapse velocities yields a fully self-contained analytic model for hemispherical liner jet formation. The model is evaluated against continuum-based simulations with varying parameters to quantify accuracies and identify valid ranges. When collapse velocity profiles are well characterized, the model accurately predicts jet behavior relative to simulations neglecting liner material strength, supporting its validity. Liner material strength, however, influences jet characteristics across all investigated materials, motivating an empirical correction. Incorporating these insights and an additional empirical correction, the model demonstrates good agreement with experimental data, representing an initial step toward validation.