Prony级数形式的形状记忆聚合物有限应变黏弹性本构模型

为考察形状记忆聚合物（SMPs）的有限应变力学特性，将SMPs材料的弹性响应采用Neo-Hookean超弹性本构方程描述，黏性响应采用Prony级数描述，从经典遗传积分形式的黏弹性本构方程出发，推导出有限应变格式的黏弹性本构方程和相应的材料参数拟合公式.采用环氧基形状记忆树脂（ESMP）进行拉伸-松弛试验，利用推导的公式进行非线性拟合得到本构方程的参数.对不同温度下ESMP的黏弹性力学特性进行试验研究，表明在试验温度范围内随温度升高ESMP的初始模量降低，初始模量中黏性部分所占比例降低，但弹性部分模量值基本不变.针对三维的SMPs结构分析问题，基于所推导本构，应用ABAQUS软件建立数值模拟方法.对拉伸-松弛试验进行数值模拟，结果表明所推导的本构方程用于SMPs的大应变分析中具有较高准确性.此外，所推导的有限应变黏弹性本构方程及参数拟合公式也适用于具有黏弹性特点的其他各向同性高聚物.
Abstract: To investigate the finite strain mechanical behavior of SMPs (shape memory polymers), a finite strain viscoelastic model was derived from the classical viscoelastic model in which the elastic and viscous mechanical response were formulated with Neo-Hookean hyperelastic model and Prony series respectively, and parameters fitting equations were derived in particular tensile case. Tension-relaxation tests of ESMP (epoxy shape memory polymer) were carried out to validate the proposed constitutive model, and the constitutive parameters were identified through nonlinear fitting using the derived parameters fitting equations. The experimental research on viscoelastic properties of ESMP at various temperatures was also conducted; the initial instantaneous modulus and the ratio of viscous modulus to the initial instantaneous modulus decrease when the temperature rises, but the elastic part modulus remains unchangeable. The numerical simulation method was developed by the proposed constitutive model and ABAQUS software, which could be used to solve three-dimensional problem of SMPs' structures. The tension-relaxation simulation tests were carried out, and comparisons between numerical simulations and experimental results demonstrates that the proposed constitutive model is reasonable in the finite strain analysis of SMPs structural problem. Meanwhile, the proposed method could be used in other kinds of isotropic viscoelastic polymers.