## 1 Introduction
They found that deformation occurred not only when the bubble collapsed but also strongly during the initial expansion of the bubble. [PERSON] et al. [12; 13] experimentally investigated the interaction of laser-induced cavitation bubbles with elastic boundaries, the elastic material consisted of polyacrylamide (PAA) gel, whose elastic properties could be controlled by varying the water content of the sample to simulate various biological tissues. For softer samples,  
Figure 1: Schematicof the study of bubbles near an elastic wall (the blue circle is the bubble). (**a**) Fixed boundary, (**b**) Movable boundary, (**c**) Sperical boundary, (**d**) Fixed film, (**e**) Fluid boundary, (**f**) Fixed beam. the liquid jet was directed away from the boundary. If the bubble was generated near the boundary, the material was detached from the sample during bubble collapse. These processes play an important role in the efficiency and side effects of pulsed laser surgery in the human body. In [PERSON]'s [14] experiments, the sample consisted of a piece of polymethyl methacrylate (PMMA) material and a thin polyethylene (PE) elastic membrane; this geometry is frequently encountered in ophthalmology. The evolution of the bubbles generated within the gap can be described as a characteristic combination of the rigid boundary and elastic membrane cases, depending on the relative sizes of the gap and the bubbles and their relative positions. As shown in Figure 1b, [PERSON], [PERSON], and [PERSON] [15] numerically studied the dynamics of underwater explosion bubbles interacting with a movable plate with the basic characteristics of a sandwich structure using the boundary element method. Three different states of bubble behavior were distinguished, and the sandwich plate can provide larger deformations and larger maximum deformation speeds, which is beneficial for changing the jet direction away from the plate. [PERSON] et al. [11; 16] studied the spatial evolution of a single bubble near the rigid and elastic boundaries. When the dimensionless parameter \(\gamma<1.5\), the jet effect dominated by high-speed jets and the mixed impact form can lead to asymmetric deformation and cause greater local damage to the elastic plate. [PERSON] [17] (the experimental structure is shown in Figure 1c) proposed that high-speed liquid jets are usually observed in the collapse stage of cavitation bubbles and proposed a surprising reflection flow (away from the boundary) that is formed in the early expansion stage of the bubble near the curved elastic boundary, which has not been reported before. The elastic boundary is not only defined as an ordinary fixed boundary with a certain thickness, a film-like boundary composed of a film and two liquids of different densities, but also as a typical and common elastic boundary (as shown in Figure 1d,e). [PERSON] and [PERSON] et al. [18; 19] used a low voltage of 55 V to generate spark bubbles and used numerical and experimental methods to explore the pulsation characteristics of bubbles near the elastic membrane. They found that the bubbles were coupled with the elastic membrane during movement, and disturbances occurred on the bubble surface, causing the bubbles to tear during collapse. They concluded that the distance between the bubbles and the elasticity of the membrane are two parameters that affect the movement of the bubbles. [PERSON] et al. [20; 21] also used a high-speed camera to study the interaction between bubbles and elastic membranes caused by electric sparks and found that bubbles showed a \"mushroom-shaped\" shape due to deformation during the contraction stage and rebound of the elastic boundary also occurred. [PERSON] [22] generated cavitation bubbles by focusing a high-energy laser beam near an elastic membrane immersed in water, which corresponds to a situation often encountered in ophthalmology. Cavitation bubbles located in the center of the membrane produce less damage than bubbles slightly further away.