ANALYSIS OF ROTATION AND STRESS RATE IN DEFORMING BODIES

When a solid element experience large deformations, the components of stress will, in general, vary as a result of material rotation. These changes occur even in the absence of additional strain, and need to be accounted for in formulating constitutive laws that involve the rate of change of stress. In this paper the correction terms are extended to the case when material axes become strongly skewed. An expression for the rate of material rotation as an explicit function of vorticity, rate of deformation and stretch is derived. It is then shown that the rate of change of stress depends on the rate of material rotation. As an example, expressions for material rotation and stress are derived for a hypoelastic material undergoing uniform, rectilinear, shear. The shear stress is compared with a solution that neglects skewing of the axes, and it is found that, for the example, skewing may be neglected for strains less than 0.4. Finally, the use of these relations in numerical calculations involving finite deformation is discussed. © 1979 Springer-Verlag.