Question: For the Flamant problem with only normal loading, explore the strain energy in a semicircular area of radius R centered at the loading point. Refer

For the Flamant problem with only normal loading, explore the strain energy in a semicircular area of radius R centered at the loading point. Refer to the discussion in Section 5.8, and use relation (6.1.10) to explicitly determine the strain energy. Comment on whether the expression is singular or not as R→0.

Equation 6.1.10

U(a) = 1+v 2E 1+v (0 + 03 + 0  + 213y + 232 +2x) - 2 (0x+0 +0 2E ijo ij V 2E jjkk (6.1.10)

Data from section 5.8

Before leaving this chapter, we wish to briefly discuss a somewhat unpleasant feature of our elasticity

Dislocation Line

result in non-elastic failure behavior. All of this implies that such unbounded elastic behaviors coming from

where K is a constant coming from terms that depend on elastic constants and the stress-strain dis- tribution


U() 1+7 2E u 2E jjkk ijij 1+v =!#(c+8+m +2c,+2+2c)-2(0,+0,+0)* 2E (6.1.10)

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