【摘要】 研究非线性超弹性体应力与应变能函数之间的关系,等比例加载方法不再适用,因为剪应变要产生正应力,正应变也要产生剪应力。为此,构建了应力应变张量与应变能函数之间的微分、积分关系。从表示定理出发,围绕共轭应力、应变变量,研究了各向同性、横观各向同性、正交各向异性非线性超弹性体的本构方程、应变能函数,推导了应力应变张量与应变能函数之间的微分、积分关系。应用微分积分关系,对应力张量函数直接积分,即可得到应变能函数。这种方法具有普适性,简洁性,能进一步拓宽解决非线性超弹性体问题的途径。更多还原

【Abstract】 When the relations between stress-strain tensor and strain energy function of nonlinear elastic solids are studied,geometric proportion loading method can not be applied,because shear strain may produce normal stress and normal strain may produce shear stress too.This paper constitutes the differential/integral relationship between stress-strain tensor and strain energy function.From the expression principles,the conjugate variable of stress-strain,the constitutive equations and strain energy function of isotopic,transversely isotopic and orthotropic non-linear hyperelastic solid are studied.The differential/integral relations between stress-strain tensor and strain energy function are derived.These relations are expressed with the invariant.Using the differential/integral relationship stress-strain tensor function is directly integrated to obtain strain energy function.This approach is concise and widely appliable.更多还原