Table 1 Energy equations used in the 2D and 3D models
Energy term | 2D | 3D |
|---|---|---|
Total energy | \(E = E_{l} + E_{b} + E_{a} \quad (2)\) | \(E = E_{L} + E_{A} + E_{B} + E_{V} \quad (3)\) |
Stretch resistance | \(E_{l} = \mathop \sum \limits_{i = 1}^{N} \frac{{k_{l} }}{2}(l_{i} - l_{0,i} )^{2} \quad (4)\) | \(E_{L} = \mathop \sum \limits_{i = 1}^{{N_{e} }} \frac{{k_{L} }}{2}(l_{i} - l_{0,i} )^{2}\quad (5)\) |
Surface area incompressibility | \(E_{A} = \mathop \sum \limits_{i = 1}^{{N_{t} }} \frac{{k_{A} }}{2}\left( {A_{i} - A_{0,i} } \right)^{2}\quad (6)\) | |
Bending resistance | \(E_{b} = \mathop \sum \limits_{i = 1}^{N} \frac{{k_{b} }}{2}\tan^{2} \left( {\frac{{\theta_{i} - \theta_{0,i} }}{2}} \right)\quad (7)\) | \(E_{B} = \mathop \sum \limits_{i = 1}^{{N_{e} }} \frac{{k_{B} }}{2}\tan^{2} \left( {\frac{{\theta_{i} - \theta_{0,i} }}{2}} \right)\quad (8)\) |
Volumetric incompressibility | \(E_{a} = \frac{{k_{a} }}{2}\left( {\frac{{A - A_{ref} }}{{A_{ref} }}} \right)^{2} \quad (9)\) | \(E_{V} = \frac{{k_{V} }}{2}\left( {\frac{{V - V_{ref} }}{{V_{ref} }}} \right)^{2}\quad (10)\) |