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strain energy density

How to do such integration with dummy indicials for strain energy density?

Submitted by pengfei_guo on
strain energy density
tensorial analysis
The integration puzzles me is
Integrate C_ijkl e_kl de_ij  (from 0 to e_ij )= 1/2 C_ijkl e_ij e_kl
which is the well known strain energy density of elasticity and much like the energy in a spring as
Integrate k x dx  (from 0 to x ) = 1/2 k x x.
By the way, this integration appears at page 226 in the book "Nonlinear Finite Elements for Continua and Structures" by T Belytschko, B Moran, WK Liu, 1999, the book just directly throws out the result without any details.

Is negative strain energy density possible?

Submitted by JackyLuo on
strain energy density

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.

Sih's Strain Energy Density Approach in Fracture - why is it not very popular?

Submitted by yoursdhruly on
education
fracture
strain energy density
Sih

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.

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