The Stress Tensor 



In the absence of viscosity the acoustic stress tensor* 

 in a fluid is given by 



Hh = K®hh (8) 



where 6 - h is the unit tensor (which has unit value for I = k 

 and vanishes for i 4- h). Relation (8) is a compact statement 

 for the isotropy of the normal stress in an inviscid fluid. 



For an elastic solid which is in a state of strain relative 

 to an equilibrium state, the associated elastic stress is 

 given by the non-isotropic tensor 



t. 7 = |j 2?.. + \ ® 5,, (9) 



yk a TsK o vk 



Here 2L ^ is the strain (or deformation) tensor 





where s^ is the components of the vector displacement s 

 relative to the relaxed (equilibrium) state and \± is the 

 first Lame parameter. The elastic tensor is symmetric 

 in the sense that t^ = t^, which implies that there are 

 basically three different shear stress terms and three 

 different normal stress terms. Relation (9) would be 



*The stress tensor t^ as employed here is such that tensile 

 stresses t , t 23 , t 33 are positive or pressures negative. 

 The conventional indicial notation is employed, where i, k 

 can take on values 1,2, 3 independently. 



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