Penetration of a flexible and steerable needle into a soft target material is a complex problem to be modelled, involving several mechanical challenges. In the present paper, an adaptive finite element algorithm is developed to simulate the penetration of a steerable needle in brain-like gelatine material, where the penetration path is not predetermined. The geometry of the needle tip induces asymmetric tractions along the tool–substrate frictional interfaces, generating a bending action on the needle in addition to combined normal and shear loading in the region where fracture takes place during penetration. The fracture process is described by a cohesive zone model, and the direction of crack propagation is determined by the distribution of strain energy density in the tissue surrounding the tip. Simulation results of deep needle penetration for a programmable bevel-tip needle design, where steering can be controlled by changing the offset between interlocked needle segments, are mainly discussed in terms of penetration force versus displacement along with a detailed description of the needle tip trajectories. It is shown that such results are strongly dependent on the relative stiffness of needle and tissue and on the tip offset. The simulated relationship between programmable bevel offset and needle curvature is found to be approximately linear, confirming empirical results derived experimentally in a previous work. The proposed model enables a detailed analysis of the tool–tissue interactions during needle penetration, providing a reliable means to optimise the design of surgical catheters and aid pre-operative planning.

将柔性且可操纵的针刺入柔软的目标材料是要建模的复杂问题，涉及多个机械挑战。在本文中，开发了一种自适应有限元算法，以模拟可操纵针在脑样明胶材料中的穿透路径，其中该穿透路径未预先确定。针尖的几何形状会沿工具-基底的摩擦界面产生不对称的牵引力，从而在针刺上产生弯曲作用，此外在穿透过程中发生断裂的区域中会同时承受法向载荷和剪切载荷的共同作用。断裂过程由内聚区模型描述，裂纹扩展的方向由尖端周围组织中应变能密度的分布确定。可以通过改变互锁的针段之间的偏移来控制转向的可编程斜角针头设计的深针刺入仿真结果，主要是针对刺入力与位移的关系，以及对针尖轨迹的详细描述。结果表明，这种结果在很大程度上取决于针和组织的相对刚度以及针尖偏移。发现可编程斜角偏移和针曲率之间的模拟关系近似为线性，从而证实了先前工作中通过实验得出的经验结果。提出的模型可以对针刺入过程中工具与组织的相互作用进行详细分析，从而为优化外科导管的设计和辅助术前计划提供可靠的手段。