Abstract
Theoretical mechanics, as presented in Chapter 2, only provides differential equations describing the properties and behavior of materials. Resolution methods are necessary to obtain temporal descriptions of the state variables as required for the simulation. The assumption of complete linearity is a great advantage because it allows the solution of the complete dynamic problem, and leads to the exact response of the system. However, for a physically realistic simulation, all the non-linearities of a material deformation must be taken into account. In this case, solutions can only be approximated using incremental-iterative procedures after spatial and temporal discretizations. The common approach for this purpose is to combine a finite element discretization of the geometry together with a finite difference discretization of time and an updated Lagrangian iterative scheme based on the Newton—Raphson method. Basics of these methods are presented in this chapter for helping to understand how complex non-linear deformation processes and material constitutive relations may be applied to soft tissue simulation.
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© 1998 Springer-Verlag Berlin Heidelberg
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Maurel, W., Thalmann, D., Wu, Y., Thalmann, N.M. (1998). Resolution Methods. In: Biomechanical Models for Soft Tissue Simulation. Esprit Basic Research Series. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-03589-4_3
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DOI: https://doi.org/10.1007/978-3-662-03589-4_3
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