| This work presents numerical methods based on the Non-Uniform Rational B-Spline (NURBS), Reproducing Kernel (RK), and Radial Basis Function (RBF), for seamless integration of geometric representation and numerical discretization for modeling skeletal muscle deformation.;The constitutive model of skeletal muscle was formulated using a transversely isotropic hyperelasticity with active force-length characteristics. Numerical studies support some experimental findings and suggest that the pennation angle plays a significant role in the aponeurosis and muscle deformation.;The effectiveness of NURBS in representing the topologically complicated muscle-tendon geometry has been demonstrated in 3D trivariate solids. We also proposed a NURBS-based displacement-pressure mixed formulation to approximate properly the incompressibility of skeletal muscle. Numerical tests demonstrated that this mixed formulation resolves the pressure oscillation and incompressible locking, and yields optimal rates of convergence for displacement and pressure solutions.;In the RK based method, the active contour model based on the variational level set formulation was introduced for automatic boundary identification from image pixels. We also used RK functions as the approximation of the level set function and solved the level set equation for boundary detection by collocation methods. The same set of RK functions was adopted for solving equilibrium equations. By considering the interaction of multiple muscles, we developed a level set algorithm for detecting the contact surface in conjunction with the frictional kernel contact algorithm. This approach allows modeling multi-body contact purely based on point data without using the conventional finite element based contact algorithms.;Based on the RBF, we proposed a subdomain collocation method for solving heterogeneous elasticity problems. The original heterogeneous problem domain was divided into subdomains. In each subdomain, RBFs with their source points located in the same subdomain approximate the solution. We showed both numerically and theoretically that both Neumann and Dirichlet boundary conditions should be imposed on the interface to achieve the optimum convergence. The radial basis collocation method (RBCM) was also employed to model hyperelastic materials under large deformation. Numerical examples showed that the weighted RBCM yield solutions that are more accurate but with less degrees of freedom compared to the solutions obtained from finite element methods. |
