The effect of quasi-static pressure on strain growth in an elastic ring

Regarding strain growth, the influence of quasi-static pressure on the strain growth of a plane-strain ring is investigated using a simplified pressure model that incorporates quasi-static pressure, combining with Mathieu equation, SDoF equation and numerical simulation. The results demonstrate that after considering quasi-static pressure, the mechanism of strain growth in a plane-strain ring remains as a nonlinear coupling between bending and breathing modes. It is inadequate to accurately predict the generation of bending mode solely based on the initial velocity in Mathieu equation. If pure triangular pulse fails to excite strain growth, it is still possible for the plane-strain ring to experience strain growth caused by quasi-static pressure. Furthermore, higher peak pressures of triangular pulses correspond to smaller magnitudes of quasi-static pressure required to trigger the bending mode. The compression displacement significantly affects the response and strain growth in a planestrain ring. When considering quasi-static pressure effects, observing strain growth becomes more likely when compression displacement exists; conversely, without compression displacement, likelihood of strain growth occurrence diminishes. These findings have implications for designing cylindrical and spherical explosion containers.