In this paper the normalized generalized stress and strain vectors in 9-D space are introduced. A method of constructing the eigen-compliance constants and material modes for the piezoelectric material is presented, which is applied to design a new failure criterion based upon the concept of strain energy modes. In this theory, normalized generalized stress and strain vectors can be additively decomposed into nine independent and non-interaction modal components
{\overline T}^{(i)}
and
{\overline S}^{(i)}
respectively, whose directions are called material modes, and the total strain energy is additively composed with nine independent modal energy components. Along each material mode, there is a modal energy given by
{\overline T}^{(i)}{\overline S}^{(i)}/2
and it is assumed that the role of different modal energies is different in the failure event. It is postulated that the failure will occur when one of the modal energies or an appropriate linear combination of these energy modes reaches a critical value. PZT-4 piezoelectric ceramic is used as a numerical example to demonstrate the adequacy of the theory with experiment for the piezoelectric failure problem. The calculated result seems to be in good qualitative agreement with experimental data.
