## 1 Introduction  
Bubbles near a horizontal rigid wall tend to generate high-speed jets directed toward the material during the rupture phase. In contrast, bubbles near a free interface will rupture along with the jet moving away from the interface. If the interface is neither \"free\" nor \"rigid\" (as is often the case in biomaterials), the resulting fluid dynamics can be complex. It is significant to know the direction of the jet, which can damage the tissue, or to predict it in advance to reduce the damage caused by the jet impact; this can have important implications for the support structures of offshore platforms [1]. Bubbles occur in many medical treatments, often as a result of high-intensity focused ultrasound, laser therapy, or shock wave lithotripsy. The physics of bubbles in the vicinity of elastic (soft) materials is even less well understood. Current research on bubbles near elastic walls is shown in the schematic Figure 1. Similarly to the research near rigid planes, some scholars have studied the dynamic state of bubbles near fixed elastic boundaries, as shown in Figure (a)a, where different materials are used as boundary conditions. These studies investigated bubble morphology and demonstrated bubbles' influence on the boundaries of materials with different properties. [PERSON] et al. [2, 3, 4] considered the elasticity of a solid wall and studied the interaction between cavitation collapse and elastic structure. Using the finite element and boundary element method to solve the problem, it was found that cavitation may form a \"mushroom-shaped\" shape when the liquid medium is elastic. [PERSON] [5] studied the growth and collapse shapes of bubbles near biomaterials; in some cases, the jet formed was directed away from the biomaterial, while in other cases, the jet was directed toward the biomaterial. In some cases, the bubble eventually splits into two parts, and regardless of whether opposite penetrating jets are formed, the jet's high maximum velocities (700-900 m/s) away from or toward the biomaterial are observed. [PERSON] and [PERSON] et al. [6], based on potential flow theory, applied the boundary element method (BEM) to calculate the dynamics of underwater explosion bubbles near the boundary and combined it with the finite element method to calculate the interaction structure between bubbles and elastic plastics. [PERSON] [7] used the BEM to solve some of the physics involved in these treatments to study the dynamics of bubbles near several biomaterials, whose behavior depends on the material properties of the biomaterials (Young's modulus, Poisson's ratio, and density). During the experiments, it was observed that the generated bubbles at certain moments formed jets in opposite directions. [PERSON] [8] studied the acoustic pressure waves and transient flow structures emitted by a single bubble near an elastic boundary based on particle image velocimetry (PIV). The results showed that the bubbles near the elastic boundary present \"mushroom-shaped\" bubbles and \"inverted cone-shaped\" bubbles. Near the rigid and elastic boundaries, the bubbles have opposite migration directions; that is, they are repelled by the elastic boundary and attracted by the rigid boundary. [PERSON] et al. [9] studied the damage caused by the collapse of a single cavitation bubble to aluminum foil and found that most of the damage was caused by the water hammer pressure during the microjet impact process. A single laser-induced cavitation bubble near agarose hydrogels with different degrees of elasticity was produced by [PERSON] [10]. The atomized part of a microjet can reach supersonic speeds up to 2000 m/s, while a fully developed liquid microjet travels at an average speed of up to 1000 m/s. In an experiment, [PERSON] [11] detected tangential stress on the elastic surface by measuring the displacement of the embedded particles and the deformation of the elastic structure. A corresponding numerical simulation was completed using the fluid-structure interaction volume solver in OpenFOAM-11.