基于分数阶微积分的黏弹性材料变形研究

The deformation study in viscoelastic materials based on fractional order calculus

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 describe the strain of viscoelastic materials better, a new strain model based on fractional order calculus is presented. The fractional longitudinal-transverse strain relationship and the fractional volume strain model are obtained, and the corresponding equations under a constant longitudinal strain rate loading are derived. The new models enjoy the advantage of having fewer parameters and simple form. The fractional strain model is verified by a series of tests under a constant longitudinal strain rate. It’s found that the new model can describe not only the volume strain phenomenon of polymer but also the phenomenon of negative and positive dilatancy in geomaterials.