Computational Biomechanics for Medicine Soft Tissues and the Musculo
One of the greatest challenges for mechanical engineers is to extend the success of computational mechanics to fields outside traditional engineering, in particular to biology, biomedical sciences, and medicine. The proposed workshop will provide an oppor
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Abstract This study presents an approach to modeling the tearing of tissue in two dimensions taking into account both material and geometrical nonlinearities. The approach is based on the total Lagrangian explicit dynamics (TLED) algorithm and realigns edges in the mesh along the path of the tear by node relocation. As such, no new elements are created during the propagation of the tear. The material is assumed to be isotropic, and the tearing criterion is based on the maximum nodeaveraged principal stress. Preliminary results show that the approach is capable of handling both isotropic and anisotropic tears. Keywords Tissue tearing · Tissue cutting · Total Lagrangian · Explicit dynamics · Soft tissue
1 Introduction Simulations of tearing and cutting of tissue for use in computer-integrated surgery often pose significant challenges not only because of material and geometrical nonlinearities, but also due to the need to modify the mesh in real-time. Much of the literature on cutting and tearing of soft tissue and other soft materials has focused on the geometrical aspects of the problem. Broadly, three approaches have been put forth: element deletion (e.g., [1]), mesh division (e.g., [2]), and mesh adaptation (e.g., [3–5]). While the first approach violates mass conservation principles, the second leads to an increase in the number of elements and nodes, a decrease in the size of the smallest element, and, consequently, a decrease in the time step size for explicit methods. The last approach, in which nodes are relocated to align element edges with the tear or cut, also leads to a decrease in the size of the smallest element but no new elements are introduced. A hybrid of the latter approaches has also been proposed [6].
K. Vemaganti () University of Cincinnati, Cincinnati, OH, USA e-mail: [email protected]
A. Wittek et al. (eds.), Computational Biomechanics for Medicine: Soft Tissues and the Musculoskeletal System, DOI 10.1007/978-1-4419-9619-0 7, c Springer Science+Business Media, LLC 2011
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Most published works use a spring-mass model or isotropic linear elastic model to represent the material response of soft tissue and completely ignore its well-known nonlinear response. Also often ignored is the large deformation undergone by soft tissue. A recent exception to this trend is the anisotropic tearing model investigated by [7]. Nonetheless, tearing/cutting approaches that fully account for material and geometrical nonlinearities are not currently available. In this study, we develop an approach to modeling tissue tearing based on the total Lagrangian explicit dynamics (TLED) algorithm developed by Miller et al. [8]. The TLED algorithm is an efficient numerical algorithm for computing deformations of very soft tissues and easily handles both geometrical and material nonlinearities. It is based on the total Lagrangian formulation, where stresses and strains are measured with respect to the original configuration. This allows for the pre-computation of certain spatial deriva
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