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黏弹性材料的变形行为更加复杂,为了合理地描述黏弹性材料的横向-纵向应变关系,利用分数阶微积分,建立了分数阶横向-纵向应变关系,并推导了等应变率加载时的相应公式,又根据新关系构建了分数阶体积应变公式,为黏弹性材料横向应变及体积应变的求解提供了一种新方法.通过验证,发现该模型能够描述黏弹性材料的横向-纵向应变关系及体积应变,不仅能够表现高分子聚合物等应变率拉伸初期的体积微缩现象,还能反映岩土材料的剪缩剪胀现象.
In order to reasonably describe the transverse-longitudinal strain relationship of viscoelastic materials, fractional-order calculus is used to establish the fractional transverse-longitudinal strain relationship and to deduce the corresponding formula at constant strain rate loading , And according to the new relationship, a new method of fractional volume strain is established, which provides a new method for solving the transverse strain and volume strain of viscoelastic material. The results show that the model can describe the transverse-longitudinal strain relation and the volume of viscoelastic material Strain can not only reflect the volume shrinkage at the initial stage of strain rate of polymer such as polymers, but also reflect the phenomenon of shear and dilatancy of geomaterials.