各向异性弹性介质中应变能密度的构成分析

COMPONENT ANALYSIS OF STRAIN ENERGY DENSITY IN ANISOTROPIC ELASTIC MEDIA

  • 摘要: 应变能密度是应变的二次函数,而叠加原理通常只适用于线性运算,那么,将应变分为体应变与偏应变时,应变能密度未必可分解为体积改变能密度与畸变能密度。本文说明,各向同性材料中,球应力不引起偏应变,偏应力也不引起球应变,因此应变能就可分解为体积改变能与畸变能。对于各向异性材料,球应力可引起偏应变,偏应力可引起球应变,当球应力和偏应力都不为零时,球应力与球应变的乘积之半不具有体积改变能密度的意义,应变能无法分解为体积改变能和畸变能。

     

    Abstract: Since the superposition principle applies only to linear operations, dividing strain into volumetric strain and deviatoric strain does not necessarily allow strain energy—a quadratic function of strain—to be decomposed into volumetric energy and distortional energy. This study demonstrates that in linear isotropic materials, spherical stress does not induce deviatoric strain, and deviatoric stress does not induce volumetric strain. Consequently, the strain energy can be decomposed into volumetric energy and distortional energy. However, for anisotropic materials, because part of the volumetric strain is generated by deviatoric stress, half the product of spherical stress and volumetric strain does not represent volumetric energy. Therefore, strain energy in anisotropic materials cannot be decomposed into volumetric energy and distortional energy.

     

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