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| The non-linear motion equations of deformation are open problem for rational mechanics. For this research, the deformation is defined as the base vector transformation of commoving dragging coordinator system in geometrical field theory. As a logic conclusion, the strain and stress is defined as mixture tensors with the lower index related with current configuration and the upper index related with initial configuration. In this research, after a simply review about the mixture stress tensor, the corresponding motion equations are introduced. Then, the S+R decomposition is used to simplify the non-linear motion equations. To compare the general motion equations obtained in this research with the well-known non-linear motion equations, the motion equations in curvature coordinator systems are derived from general equations, respectively. Finally, the strategy to solve the general motion equations for large deformation is discussed. |
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| Keywords:rational mechanics; large deformation; local rotation; additive decomposition; non-linear motion equation; mixture stress tensor |
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