TY - JOUR

T1 - Hodge duality and continuum theory of defects

AU - Yamasaki, Kazuhito

AU - Nagahama, Hiroyuki

PY - 1999/11/5

Y1 - 1999/11/5

N2 - Dual material space-time with defect field is presented in the language of differential forms: one is the strain space-time whose basic equation is the continuity equation for the dislocation 2-form; the other is the stress space-time whose basic equation is the continuity equation for the couple-stress and angular momentum 2-form. Continuity and kinematic equations in each space can be derived by the transformation from p-form to (p + 1)-form. Moreover, several constitutive equations can be recognized as the transformation between the p-form of the strain space-time and the (4 - p)-form of the stress space-time. These kinematic, continuity and constitutive equations can be interpreted geometrically as Cartan structure equations, Bianchi identities and Hodge duality transformations, respectively.

AB - Dual material space-time with defect field is presented in the language of differential forms: one is the strain space-time whose basic equation is the continuity equation for the dislocation 2-form; the other is the stress space-time whose basic equation is the continuity equation for the couple-stress and angular momentum 2-form. Continuity and kinematic equations in each space can be derived by the transformation from p-form to (p + 1)-form. Moreover, several constitutive equations can be recognized as the transformation between the p-form of the strain space-time and the (4 - p)-form of the stress space-time. These kinematic, continuity and constitutive equations can be interpreted geometrically as Cartan structure equations, Bianchi identities and Hodge duality transformations, respectively.

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U2 - 10.1088/0305-4470/32/44/103

DO - 10.1088/0305-4470/32/44/103

M3 - Article

AN - SCOPUS:0033527508

SN - 0305-4470

VL - 32

SP - L475-L481

JO - Journal of Physics A: Mathematical and General

JF - Journal of Physics A: Mathematical and General

IS - 44

ER -