Stress tensor deviatoric, dynamic

A strength value associated with a Hugoniot elastic limit can be compared to quasi-static strengths or dynamic strengths observed values at various loading strain rates by the relation of the longitudinal stress component under the shock compression uniaxial strain tensor to the one-dimensional stress tensor. As shown in Sec. 2.3, the longitudinal components of a stress measured in the uniaxial strain condition of shock compression can be expressed in terms of a combination of an isotropic (hydrostatic) component of pressure and its deviatoric or shear stress component. 

A more fundamental approach is to consider the rheological properties with dynamical properties. For a given rate-of-strain tensor E and moments of the orientation vector p, Batchelor (110) derived an expression for the bulk average deviatoric stress a for a suspension of non-Brownian fibers of large aspect ratio given by... 

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