Debao Zhou, Yun Peng, Jing Bai, and Ryan G. Rosandich
Dynamic contact, viscoelastic, generalized force, stress distribution
Contact of a hard tool with soft tissues is very common in medical researches and clinical applications. To visualize the stress, in this work, we develop a set of analytical equations to compute the 3D stress distribution of a viscoelastic material under generalized force. Based on the facts that many researchers have demonstrated that soft tissues, such as liver, kidney, and so on, can be approximated as linear viscoelastic materials, and that in many cases only small deformation exists, we derive our solution from the classic elastic contact problem and apply the correspondence principle to address the linear viscoelastic problem. Such a method has the advantages of analytic form of solutions and thus avoids using the commonly used finite element method (FEM). In our model, the loading owns an arbitrary profile in space and time and comprises of both tangential and vertical components. To verify its efficiency as a replacement of FEM, we compare the results from our method and from FEM commercial software, with positive results obtained. A number of clinical cases are simulated, such as evaluating the effects of blade sharpness and slicing angle on the initial contact of needle insertion or punching. The results provide quantifiable insights to differentiate the difficulties of fracture initiation under various slicing angles or loading magnitudes.
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