chapter
Modelling (B)
Pages 46

Finally, the energy dissipated in the process zone is given by (with v = w / w c)

3*7r = ^ f t w j pc0 = 0.2945f tw j pc0. (19)

w ( u ) = a0f p^ u 3/2 + a i ^ u 5/2 + a ^ l i l u 712. (20)

cr(u) = A[3a0R}^2( l — u) l l 2J0(u) + 5 a i l £ l 2( \ - u ) l l 2J i (u ) + l a 2R b^ 2{ l - u ) 1^ 2J2{u)\, (21)

where, for brevity R = £pd0, and A = E ' / ( i n ) . From the condition tha t w = w c at u = 1, we get

where k\ = a i R / a 0, k2 = a2R 2/ao.