Constitutive modeling of porous viscoelastic materials
Constitutive modeling of porous viscoelastic materials
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DOI：
10.1016/j.euromechsol.2007.05.008
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发表时间：
2007-11
影响因子：
4.1
通讯作者：
F. Xu;P. Sofronis;N. Aravas;S. Meyer
中科院分区：
文献类型：
--
作者：
F. Xu;P. Sofronis;N. Aravas;S. Meyer
研究了小应变变形条件下孔隙率对服从标准微分形式本构关系的各向同性线性粘弹性固体本构响应的影响。利用线性粘弹性的对应原理，求解了在轴对称宏观应力作用下含球形孔洞的单胞的粘弹性边值问题。结果被用来设计一个本构势的描述的多孔材料的任何任意组合的流体静力学和偏载荷，并确定相关的3-D本构关系中的拉普拉斯变换域。对时域的反演得到多孔材料的本构律，其为卷积积分的标准形式的孔隙率的函数。孔隙率的存在建立了多孔体的弛豫时间尺度，其不同于纯基质材料的弛豫时间，并为整体流体静力学响应带来粘性特征。在通用有限元代码中的模型的数值实现进行了概述。该模型用于预测多孔固体推进剂材料在室温下的单轴拉伸和循环载荷下的响应。
The effect of porosity on the constitutive response of an isotropic linearly viscoelastic solid that obeys a constitutive law of the standard differential form is investigated under small strain deformation conditions. The correspondence principle of linear viscoelasticity is used to solve the viscoelastic boundary value problem at a unit cell containing a spherical void and loaded axisymmetrically by macroscopic stresses. The results are used to devise a constitutive potential for the description of the porous material for any arbitrary combination of hydrostatic and deviatoric loadings, and the associated 3-D constitutive relationship is determined in the Laplace transform domain. Inversion to the time domain yields the constitutive law of the porous material as a function of porosity in the standard form of convolution integrals. The presence of porosity establishes relaxation time scales for the porous body that differ from the relaxation time of the pure matrix material and brings about a viscous character to the overall hydrostatic response. The numerical implementation of the model in a general purpose finite element code is outlined. The model is used to predict the response of a porous solid propellant material in uniaxial tension and cyclic loading at room temperature.