NURBS-based Galerkin method and application to skeletal muscle modeling

ABSTRACT

Non-Uniform Rational B-spline (NURBS) is often used to construct the free-form boundary representation of three-dimensional objects. In this paper, we propose a method for mechanical analysis for deformable bodies by combining NURBS geometric representation and the Galerkin method. The NURBS surface bounding a 3D body is extended to a trivariate NURBS solid by adding another parametric domain represented by additional control points. The displacement field of the body is constructed using the NURBS shape representation with the control point being the generalized coordinates. The interpolated displacement field is directly used to facilitate finite element formulation. In this manner, traditional FEM meshing is not required. In this work, the NURBS-FEM is applied to skeletal muscle modeling. Muscle is modeled as anisotropic, active hyperelastic solids. The directions of the contractile fibers can be uniform or along the tangent direction of NURBS curves. Typical contractive motions of isolated muscle are simulated.

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INDEX TERMS

Primary Classification:
  I. Computing Methodologies
  I.3 COMPUTER GRAPHICS
      I.3.5 Computational Geometry and Object Modeling

Keywords:
NURBS solid, finite element method, physically based deformable body modeling