An explicit formulation of a three-dimensional material damping model with transverse isotropy

A constitutive three-dimensional (3D) damping model is derived for transversely isotropic material symmetry, using the augmented Hooke's law Intl. J. Solids Struct. 32 (1995) 2835] as a starting point. The proposed material model is tested numerically, via finite-element techniques, on a laminate structure built from stacked aluminium and Plexiglas plates. Effective 3D transversely isotropic material properties are given in terms of homogeneous material damping functions in connection with homogenised elastic laminate properties. Comparisons made between the results from the elastic (undamped) eigenvalue problem of the detailed (layerwise) model of the laminate and the effective 3D elastic model show that the homogenised model is reasonably accurate, in terms of predicted elastic eigenfrequencies for the first 20 modes. The dynamic homogenisation process, with damping included, is evaluated in terms of forced vibration response for the laminate structure, using effective transversely isotropic frequency dependent material properties. The dynamic 3D effective homogeneous material model is found to simulate very closely the detailed model in the studied frequency interval for the numerical test case.