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| Referring to the central line of rod to establish local dragging coordinator system, the S+R decomposition of deformation tensor is used to obtain the two sets of non-linear motion equations of rod with large deformation. One set is about the central line, another set is out-central line regions. For simple bending and simple torsion, simplifed non-linear motion equations are obtained. The research shows that: 1) for sharp bending, the exact motion equations for elastic line is obtained; 2) for simple torsion, the intrinsic stretching along the rotation direction is indispensable. This is the main distinction between rigid rotation and the local whole rotation in continuum; 3) when the local rotation angle is big enough, the deformation will jump to the another kind of formation form; 4) the S+R decomposition can be viewed as decomposing the general deformation into one torsion-free local stretching S and one deformation with torsion R. |
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| Keywords:large deformation; local rotation; additive decomposition; non-linear motion equation; mixture stress tensor. |
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