Abstract
Off-axis Mohr circles are used to represent asymmetric second-order tensor quantities that describe deformation with homogeneous position gradients or flow with homogeneous velocity gradients. The validity of this representation is demonstrated. Several applications to problems of inhomogeneous deformation are explored by considering neighboring domains A and B that are homogeneously but differently deformed or flowing. The compatibility condition in Mohr space is that the circles for A and B should intersect in a point that represents the material line of the A/B boundary. In the first application it is assumed that the stretch tensor is known for each domain, and a Mohr construction is used to find the orientation of a compatible A/B boundary and the rotation of one domain with respect to the other. The second application is similar but involves the instantaneous state of a system. Non-parallel simple shearing at known rates is assumed in A and B, and a construction is used to find the instantaneous orientation of a compatible boundary and the spin of one domain with respect to the other. The third and fourth applications apply Mohr circles to problems of deformation interpolation and deformation averaging. In the former a deformation and shape is found for a domain C that lies between A and B, themselves incompatible, such that the A/C and C/B boundaries are both compatible.
Published Version
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