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 threedimensional 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.

Restricted Trivariate Polycube Splines for Volumetric Data Modeling

“…It is more desirable in engineering design to have an integrated modeling framework that can represent geometry and material and conduct simulations simultaneously. Trivariate NURBS are used to model skeletal muscle with anisotropic attributes [4], on which NURBS-FEM analysis is directly conducted. Martin et al [6] parameterize a volumetric solid into a solid cylinder upon which a trivariate B-spline is constructed.…”

“…In the framework of isogeometric analysis [4], [5], trivariate tensor-product B-splines/NURBS are directly used to model smooth geometry and material attributes of solid objects for physical simulation. Martin et al [6] convert solid models to cylindrical trivariate B-splines by parameterizing models on solid cylinders.…”

Cylindrical element: Isogeometric model of continuum rod

“…When efficiency is of primary importance, it is critical to balance physical realism and computational efficiency. In [29,30], the present authors proposed to use NURBSbased isogeometric approach for muscle analysis. This method opens a pathway for a high-fidelity and high efficiency modeling of muscles.…”

Convergence analysis of Laplacian-based gradient elasticity in an isogeometric framework

“…Isogeometric Analysis [38] is an extension of finite element analysis where the spline-based shape functions used to approximate the geometry are used for the analysis as well. Although coined and standardised in [38], other works along the same lines exist [39,40]. The original drive behind isogeometric analysis was to integrate the design and analysis processes, which has the additional benefit of capturing the exact geometry, unlike standard finite element analysis.…”