Linear Spring

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Table of contents

1 Introduction 
2 Combined Estimation of Material Parameters and Unloaded Configurations 
2.1 Models
2.1.1 Linear Spring
2.1.2 Nonlinear Spring
2.1.3 Rivlin Cube
2.1.4 Tube
2.2 Forward Problem
2.2.1 A Method for Solving Nonlinear Problems
2.2.2 Linear Spring
2.2.3 Rivlin Cube
2.3 Inverse Problem
2.3.1 Methods for Minimizing a Cost Function
2.3.2 Methods for Computing Gradients and Hessians
2.3.3 Unloaded Configuration Estimation
2.3.4 Material Parameter Estimation
2.3.5 Combined Estimation of the Unloaded Configuration and Material Parameters
2.4 Finite Differences Approximation of the Derivative and Hessian Matrix
2.4.1 Computing the Gradient of Some Functions
3 Lung Mechanical Modeling 
3.1 Introduction
3.1.1 Lung Mesh
3.1.2 Thorax Mesh
3.1.3 Lung Porosity
3.1.4 Thorax Displacement Field
4 Discussion and Ongoing Research 
Bibliography