CAJ | 학술논문

研究了非线性Green弹性材料弹性张量独立分量,归纳推导出横观各向同性Green弹性材料、各向同性非线性弹性材料独立的弹性常数个数.从张量函数出发,用含有高阶弹性张量的张量多项式,推导出四阶非线性横观各向同性,各向同性材料Green弹性材料本构方程及其势函数.并将本构方程及其势甬数用张量不变量,标量不变量表示.证明了方程是完备的,不可约的,满足张量函数表示定理.
연구료비선성Green탄성재료탄성장량독립분량,귀납추도출횡관각향동성Green탄성재료、각향동성비선성탄성재료독립적탄성상수개수.종장량함수출발,용함유고계탄성장량적장량다항식,추도출사계비선성횡관각향동성,각향동성재료Green탄성재료본구방정급기세함수.병장본구방정급기세용수용장량불변량,표량불변량표시.증명료방정시완비적,불가약적,만족장량함수표시정리.
The independent components of elastic tensor in nonlinear Green elastic materials were studied. The numbers of independent elastic constants were derived for transversely isotropy and isotropy Green e-lastic materials. From tensor function, the constitutive equations and Potential Function of 4th order transversely isotropy nonlinear Green elastic materials and isotropy Green elastic materials were derived by tensor polynomial with high order elasticity tensor. The constitutive equations and potential functions can be expressed as tensor invariant and scalar invariant. The equations are proved complete and irreduci-ble, and satisfy the law of tensor function expressions.