三维大变形产生内秉纽结II:多尺度

Once micro-scale intrinsic curvatures are produced within the material by large deformation in 3-space, what physical feature can be used to identify their existence? Based on the traditional continuity concept, the physical features still can be measured by the macro displacement field. The effects produced by micro-scale intrinsic variation can be expressed by the variations of macro physical constant, where its variation is interpreted by micro dynamics or micro substructure variation. Along this theoretic line, multi-scale concept is introduced in mechanics. This concept is well supported by experiments. So, theoretically, formulating a suitable method to express the multi-scale feature by the macro deformation field should be valuable. In this research, the multi-scale features of material under large deformation are studied by the macro deformation field. That is to say, the macro deformation field is used to evaluate the possible micro-variations. In mathematics, it is equivalent with the inverse problem. Its physical foundation is that the same macro deformation field can be produced by several possible micro-scale deformations. As the curvature is an intrinsic local feature, the research shows that the multi-scale feature of materials under large deformation can be well explained by the curvature concept. The mechanical multi-scales can be obtained by the curvature parameter and the initial elastic parameters of macro scale of material. Therefore, the multi-scale features of material under large deformation are formulated by the deformation field itself rather than introducing other artificial assumption.