Multidimensional coupling in a human knee model

List of Symbols 1 Introduction 2 Biomechanics of the Human Knee 2.1 Structure and Function of the Human Knee Joint 2.2 Bones 2.3 Ligaments 2.4 The Attachment of Ligaments to Bone 2.5 The Problem of Getting Material Parameters 3 Two-Body Contact Problems on Domains with Curved Boundaries 3.1 Linear Elasticity 3.2 Two-Body Contact in Linear Elasticity 3.3 Discretization Using Mortar Elements 3.4 The Truncated Nonsmooth Newton Multigrid Algorithm 3.5 Implementing the Contact Mapping 3.6 Creating and Using Parametrized Boundaries 3.7 Hierarchical A Posteriori Error Estimation 3.8 Contact between the Human Femur and Tibia 4 Cosserat Rods as Models for Ligaments 4.1 Riemannian Manifolds, Lie Groups, and SO(3) 4.2 Cosserat Rods 4.3 Geodesic Finite Element Spaces 4.4 Riemannian Trust-Region Solvers 4.5 A Trust-Region Solver for the Cosserat Rod with Hyperelastic Material 4.6 Numerical Results 5 Coupling Rods and Three-Dimensional Objects 5.1 Homogeneous Coupling in Nonlinear Elasticity 5.2 Heterogeneous Coupling Conditions 5.3 A Dirichlet–Neumann Algorithm 5.4 Existence of Solutions of the Heterogeneous Problem 5.5 Numerical Results 6 Software Issues and Numerical Results 6.1 The Distributed and Unified Numerics Environment (Dune) 6.2 Two-Body Contact and Ligaments A The Derivatives of the Strains of a Cosserat Rod Bibliography

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