A continuum damage model for piezoelectric materials

• 来源期刊: 力学学报（英文版）
• 年，卷（期）: 2008,（2）
• 页码范围: 171-179
• 页数: 9页
• 语种: 英文
• DOI: 10.1007/s10409-008-0133-y

摘要

In this paper, a constitutive model is proposed for piezoelectric material solids containing distributed cracks.The model is formulated in a framework of continuum damage mechanics using second rank tensors as internal variables. The Helmhotlz free energy of piezoelectric mate-rials with damage is then expressed as a polynomial including the transformed strains, the electric field vector and the ten-sorial damage variables by using the integrity bases restricted by the initial orthotropic symmetry of the material. By using the Talreja's tensor valued internal state damage variables as well as the Helmhotlz free energy of the piezoelectric mate-rial, the constitutive relations of piezoelectric materials with damage are derived. The model is applied to a special case of piezoelectric plate with transverse matrix cracks. With theKirchhoff hypothesis of plate, the free vibration equationsof the piezoelectric rectangular plate considering damage isestablished. By using Galerkin method, the equations are sol-ved. Numerical results show the effect of the damage on the free vibration of the piezoelectric plate under the close-circuit condition, and the present results are compared with those of the three-dimensional theory.