The principal contribution of this dissertation is a theory of Strongly Orthotropic Continuum Mechanics that is derived entirely from an assertion of geometric strain indeterminacy. Implementable into the finite element method, it can resolve widespread kinematic misrepresentations and offer unique and purportedly exact strain-induced energies by removing the assumptions of strain tensor symmetry. This continuum theory births the proposal of a new class of physical tensors described as the Intrinsic Field Tensors capable of generalising the response of most classical mechanical metrics, a number of specialised formulations and the solutions shown to be kinematically intermediate. A series of numerical examples demonstrate Euclidean objectivity, material frame-indifference, patch test satisfaction, and agreement between the subsequent Material Principal Co-rotation and P??I??C decomposition methods that produce the intermediary stress/strain fields. The encompassing theory has wide applicability owing to its fundamental divergence from conventional mechanics, it offers non-trivial outcomes when applied to even very simple problems and its use of not the Eulerian, Lagrangian but the Intrinsic Frame generates previously unreported results in strongly orthotropic continua.

The principal contribution of this dissertation is a theory of Strongly Orthotropic Continuum Mechanics that is derived entirely from an assertion of geometric strain indeterminacy. Implementable into the finite element method, it can resolve widespread kinematic misrepresentations and offer unique and purportedly exact strain-induced energies by removing the assumptions of strain tensor symmetry. This continuum theory births the proposal of a new class of physical tensors described as the Intrinsic Field Tensors capable of generalising the response of most classical mechanical metrics, a number of specialised formulations and the solutions shown to be kinematically intermediate. A series of numerical examples demonstrate Euclidean objectivity, material frame-indifference, patch test satisfaction, and agreement between the subsequent Material Principal Co-rotation and P??I??C decomposition methods that produce the intermediary stress/strain fields. The encompassing theory has wide applicability owing to its fundamental divergence from conventional mechanics, it offers non-trivial outcomes when applied to even very simple problems and its use of not the Eulerian, Lagrangian but the Intrinsic Frame generates previously unreported results in strongly orthotropic continua.