I have a question that has troubled me for quite a while. Any kind of help would be greatly appreciated. I am computing the strain-energy density in a elastic solid when wave passes through. The formula I use is U=[I1^2+2(1+v)I2]/(2E), where U is the strain-energy density, I1 and I2 the first and second principal stress invariants, v poisson's ratio=0.3, E the Young's modulus. Since I1^2 must be positive, I2 might be negative behind the wave front. U might be negative. However, the textbook and many papers I ran into, says strain-energy density must be positive. Is it possible strain-energy density negative? What would the physical meaning of the negative strain-energy density be  if it exits?

 Thank you for reading.

Jacky 

Most fracture classes and texts focus on the following different approaches: Griffith's energy approach, Irwin's stress intensity factor approach, the Barenblatt-Dugdale strip yield model (and subsequently, cohesive zone modeling) and Rice's J-Integral approach. As a graduate student studying fracture mechanics, I have often wondered why there seems to be very little discussion in the community with regard to Sih's strain energy density approach. Are there any fundamental limitations to the approach or are there "other" reasons behind this? Your thoughts are appreciated.

Thanks,
Dhruv