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