@article{oai:jaxa.repo.nii.ac.jp:00034590,
 author = {YOSHIMURA, Yoshimaru},
 issue = {3},
 journal = {東京大學航空研究所報告, Report/Aeronautical Research Institute, University of Tokyo},
 month = {Mar},
 note = {The present investigation provides a basic theory concerning the concepts of strain, strain increment and stress, which underlie mechanics of continua for small and finite deformations. All the deformations of all the matters form fluids to solids, viewed from their mechanism, are classfied into the two types, one is the elastic deformation due to the change in the distances among constituent particles and the other the plastic deformation due to the change in the mode of interconnection among particles. In order to construct a self-consistent theory for the two kinds of deformation over the whole range of small and finite deformations, the notion of strain and stress is needed to be introduced as being specific to each of the two types, and the conclusions are as follows : 1. The elastic strain is specifid by the change in the geometrical configuration from the uniquely determinable undeformed state, and is defined by ^eE=1/2(g_<ij>-g^^゜_<ij>)e^^゜^ie^^゜^j, and the elastic strain increment by D^eE=1/2Dg_<ij>e^^゜^ie^^゜^j. Where g^^゜_<ij> and g_<ij> represent the fundamental metric tensors before and after deformation respectively, and e^^゜^i the vectors reciprocal to the basis e^^゜_i in the undeformed state, referring to the Lagrangian coordinate system. The strain ^eE of a elastically deformed state does not depend on the deformation path up to the state, i.e. &conint;D^eE=0. 2. The quantity introduced primarily concerning the plastic deformation is the strain increment, which is specified by the change in the metric during the current infinitesimal deformation, as D^pE=(D^pε)_<ij>e^ie^j=1/2Dg_<ij>e^ie^j, where e^i are the vectors reciprocal to the basis e_i in the deformed current state. The plastic strain ^pE=^pε^<ij>e^ie^j is obtainable by integrating the plastic strain increment D^pE, hence the simultaneous differential equations D^pε_<ij>-g^<rs>[^pε_<rj>&ultri;_i(Du)_s+^pε_<jr>&ultri;_j(Du)_s]=(D^pε)_<ij> along a given path of deformation, where (Du)_i are the components of the incremental displacement with regard to e^i. The plastic strain depends on the deformation path, but not no the change in the geometrical configuration, and therefore, it is regarded as a mechanical quantity nominated "strain history". This means that &conint;D^pE&nedot;0. 3. Between D^eE and D^pE it holds the relation D^eE=J・D^pE・J^^-, J=e^^゜^ie_i. 4. The stress tensor T=σ^<ij>e_ie_j which describes equilibrium condition is common to the both deformations, and is so defined as to give the actual force per unit of sectional area in the deformed state. This stress T is also the stress ^pT for describing, together with ^pE and D^pE, the plastic deformation. 5.The stress ^eT for describing the elastic deformation is defined by ^eT=J^^-^<-1>・^pT・J^<-1> By means of these dualistic definitions of strain and stress for the two types of deformation, the theories of elasticity and plasticity are emancipated from essential self-inconsistencies ever lurked, and reorganized from beginning under harmonious contrast, over the whole range of small and finite deformations., 資料番号: SA2404803000},
 pages = {43--65},
 title = {Meta-theory of Mechanics of Continua Subject to Deformations of Arbitrary Magnitudes : Duality of Definitions of Strain, Strain Increment and Stress for Elastic and Plastic Finite Deformations},
 volume = {25},
 year = {1959}
}