This paper presents a theory of continuum mechanics for strongly orthotropic materials that proposes a more informative asymmetric strain and rotation tensor. The infinitesimal strain tensor and, likewise, Green-Lagrange strains avoid rotational sensitivity by the use of effective shear strain averaging. The linear formulation of the proposed non-symmetric strain tensor field instead differentiates planar shear strains based on principal material direction and mechanical properties – adding determinacy to the otherwise geometric problem. The separation of in-plane shears also allows the formulation of a first order rotation tensor that gives change in principal property direction when applied to orthotropic materials – which is a new interpretation of rigid body rotation. Subsequent to the theory, a new extended Mohr’s plot and compliance tensor are presented. It is demonstrated in a numerical example that application of the proposed tensors yields the best solution when compared with an analytical model and three conventional solvers for a finite shear deformation
