Numerical Determination of the Mean Value of an Elasticity Tensor by Integration over the Rotation Group with Haar Measure
Kossi Atchonouglo *
Departement de Physique, Universite de Lome, Facule des Sciences, BP 1515 Lome, Togo.
Claude Vallee
Institut P', Universite de Poitiers, CNRS - ENSMA, UPR 3346, BP 30179, 86962 Futuroscope - Chasseneuil Cedex, France.
Zi-Qiang Feng
School of Mechanics and Engineering, Southwest Jiaotong University, Chengdu, China and Universite d'Evry - Val d'Essonne - L.M.E., EA3332, 40 Rue du Pelvoux, 91020 Evry Cedex, France.
Jamal Chaoufi
Departement de Physique, Universite d'Agadir, Faculte des Sciences, Cite Dakhla, B.P. 8106, 80000 Agadir, Morocco.
*Author to whom correspondence should be addressed.
Abstract
Let A be a 3D symmetric elasticity tensor not necessary isotropic. If μ is an invariant measure on SO(3), then μ is a convex combinaison of the Haar measure. The nearest isotropic elasticity tensor is obtained by integrating the tensor A on the rotation group SO(3). For the numerical approach, we integrate the elasticity tensor on the unit ordinary ball B(0, 1).
Keywords: Elasticity tensor, Finite elements, identi cation