# Solid volumetric deformable muscle model for computer animation using weighted residual method

This source preferred by Lihua You and Jian Jun Zhang

**Authors: **You, L.H., Zhang, J.J. and Comninos, P.

**Journal:** Computer Methods in Applied Mechanics and Engineering

**Volume:** 190

**Pages:** 853-863

**ISSN:** 0045-7825

**DOI:** 10.1016/S0045-7825(99)00448-X

One of the most important yet expensive tasks in realistic character animation is to represent the body deformation, i.e. the deformation of the muscles. Because of the complexity of the geometry and deformable behaviours of such muscle tissues, three-dimensional (3D) finite element analysis (FEA) is usually employed. FEA however, requires enormous computing power, and often is impractical for computer animation where computational cost needs to be balanced with modelling accuracy. In this sense, it differs from engineering analysis where accuracy is often paramount for many applications, such as in aviation industry. Proposed in this paper is a 3D solid volumetric deformable muscle model which is almost as accurate as the FEA, but requires only a fraction of the computing cost. In this model, the muscle tissues are assumed to be elastic bodies with isotropic behaviour. The governing equations are derived and a weighted residual method is introduced to solve these equations. Suitable trial functions are proposed which satisfy the deformation compatibility and equilibrium equations. Using the least squares technique, the residual values on the boundaries are formulated and minimized to determine the unknown constants in the trial functions. In order to validate our model, the numerical results produced by our model are compared with the finite element computation and it is found that the two results closely agree with each other.

This data was imported from Scopus:

**Authors: **You, L.H., Zhang, J.J. and Comninos, P.

**Journal:** Computer Methods in Applied Mechanics and Engineering

**Volume:** 190

**Issue:** 8-10

**Pages:** 853-863

**ISSN:** 0045-7825

**DOI:** 10.1016/S0045-7825(99)00448-X

One of the most important yet expensive tasks in realistic character animation is to represent the body deformation, i.e. the deformation of the muscles. Because of the complexity of the geometry and deformable behaviours of such muscle tissues, three-dimensional (3D) finite element analysis (FEA) is usually employed. FEA however, requires enormous computing power, and often is impractical for computer animation where computational cost needs to be balanced with modelling accuracy. In this sense, it differs from engineering analysis where accuracy is often paramount for many applications, such as in aviation industry. Proposed in this paper is a 3D solid volumetric deformable muscle model which is almost as accurate as the FEA, but requires only a fraction of the computing cost. In this model, the muscle tissues are assumed to be elastic bodies with isotropic behaviour. The governing equations are derived and a weighted residual method is introduced to solve these equations. Suitable trial functions are proposed which satisfy the deformation compatibility and equilibrium equations. Using the least squares technique, the residual values on the boundaries are formulated and minimized to determine the unknown constants in the trial functions. In order to validate our model, the numerical results produced by our model are compared with the finite element computation and it is found that the two results closely agree with each other.

This data was imported from Web of Science (Lite):

**Authors: **You, L.H., Zhang, J.J. and Comninos, P.

**Journal:** COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

**Volume:** 190

**Issue:** 8-10

**Pages:** 853-863

**ISSN:** 0045-7825

**DOI:** 10.1016/S0045-7825(99)00448-X