An efficient hourglass control implementation for the uniform strain hexahedron using the Total Lagrangian formulation

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Abstract
The under‐integrated hexahedron is one of the best candidates for use in real‐time surgical simulations, because of its computational efficiency. This element requires a very efficient method of controlling the zero energy (hourglass) modes that arise from one‐point integration. An efficient implementation of the perturbation hourglass control method proposed by Flanagan and Belytschko for the uniform strain hexahedron is presented. The implementation uses the Total Lagrangian formulation and takes into consideration large deformations and rigid body motions. By using the Total Lagrangian formulation most of the necessary components for calculating the hourglass forces can be pre‐computed, leading to a significant reduction of the additional computation time required for hourglass control. The performance evaluation results show the very good accuracy and computational efficiency of the presented algorithm. Copyright © 2007 John Wiley & Sons, Ltd.