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3.3 物理方程
各向同性体的应变分量与应力分量之间的关系已在平面问题的物理方程中给出,即
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以上表达形式,是用应力分量表示应变分量。现在,给出用应变分量表示应力分量,即
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另外,如果已经知道三个主应力,可以利用主应力得出主应变。将坐标轴放在应力主向,并利用式(3-15)、式(3-16)和式(3-17),得出
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另外,还可以通过式(3-15)、式(3-16)和式(3-17),得出体积应变和体积应力之间的关系,即
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即
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式中,Θ=σx+σy+σz为体积应力, 为体积模量。
引入拉梅(Lame)常数和
,则
σx=λθ+2Gεx (3-31)
σy=λθ+2Gεy (3-32)
σz=λθ+2Gεz (3-33)
τyz=Gγyz (3-34)
τzx=Gγzx (3-35)
τxy=Gγxy (3-36)