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Its integral over a load path is the total amount of dilatational strain energy density stored in the material.
Many such materials show dilatational behavior under triaxial states of stress which the Mohr-Coulomb model does not include.
The forms are termed the deviatoric parts of the respective tensors, while are called the dilatational parts.
Carbon tetrachloride with a dilatational velocity of does not attack epoxies for example but can form carcinogenic vapours (trichloroethane is the next best choice).
In time-dependent form therefore we may expect one relation between the deviatoric stresses and strains and another, independent one between the dilatational parts.
When an elastic wave is obliquely incident at a fluid-solid interface, the refracted wave splits into two components: dilatational and transverse.
Similarly, by integrating the increment in elastic energy for unit volume change due to hydrostatic pressure, , the dilatational strain energy density is:
For the criticality to occur at an angle of incidence less than 90 , the shear velocity in the solid must be greater than the dilatational velocity in the coupling liquid.
According to this criterion, an upper limit to allowable strains is set either by a critical value Τ of the elastic energy density due to volume change (dilatational energy) or by a critical value Τ of the elastic energy density due to change in shape (distortional energy).