On constitutive modelling of porous neo-Hookean composites
On constitutive modelling of porous neo-Hookean composites
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DOI：
10.1016/j.jmps.2007.12.007
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发表时间：
2008-06
影响因子：
5.3
通讯作者：
Zaoyang Guo;F. Caner;Xiongqi Peng;B. Moran
中科院分区：
文献类型：
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作者：
Zaoyang Guo;F. Caner;Xiongqi Peng;B. Moran
本文提出了一种适用于有限弹性状态下含连续圆柱孔的neo-Hookean复合材料的超弹性本构模型。虽然基体是不可压缩的，但由于空隙的存在，复合材料本身是可压缩的。对于这种可压缩横观各向同性材料，变形梯度可以乘法分解为三部分：沿着材料择优方向的等容单轴变形（与这里的圆柱形孔的方向相同）;横向平面上的等轴变形（垂直于优选方向的平面）;以及随后的剪切变形（其包括“沿纤维”剪切和横向剪切）。与我们以前的不可压缩纤维增强复合材料模型中使用的乘法分解相比[Guo，Z.，彭，X.Q.，Moran，B.，2006年，一种基于复合材料的超弹性软组织本构模型，应用于人类纤维环。J. Mech. Phys. Solids 54（9），1952-1971]，引入等双轴变形以实现所需的体积变化。为了估计这种复合材料的应变能函数，圆柱形复合材料单元模型。在复合材料单元模型中，推导出了沿着优选方向的等容单轴变形、横截面上的等双轴变形以及“沿纤维”剪切变形的精确应变分布。将基于无限小应变线弹性的传统复合材料理论中的有效剪切模量推广到有限变形状态，以估计与横向剪切变形相关的应变能，从而得到一般有限变形状态下复合材料应变能函数的显式表达式。
In this paper a hyperelastic constitutive model is developed for neo-Hookean composites with aligned continuous cylindrical pores in the finite elasticity regime. Although the matrix is incompressible, the composite itself is compressible because of the existence of voids. For this compressible transversely isotropic material, the deformation gradient can be decomposed multiplicatively into three parts: an isochoric uniaxial deformation along the preferred direction of the material (which is identical to the direction of the cylindrical pores here); an equi-biaxial deformation on the transverse plane (the plane perpendicular to the preferred direction); and subsequent shear deformation (which includes “along-fibre” shear and transverse shear). Compared to the multiplicative decomposition used in our previous model for incompressible fibre reinforced composites [Guo, Z., Peng, X.Q., Moran, B., 2006, A composites-based hyperelastic constitutive model for soft tissue with application to the human annulus fibrosus. J. Mech. Phys. Solids 54(9), 1952–1971], the equi-biaxial deformation is introduced to achieve the desired volume change. To estimate the strain energy function for this composite, a cylindrical composite element model is developed. Analytically exact strain distributions in the composite element model are derived for the isochoric uniaxial deformation along the preferred direction, the equi-biaxial deformation on the transverse plane, as well as the “along-fibre” shear deformation. The effective shear modulus from conventional composites theory based on the infinitesimal strain linear elasticity is extended to the present finite deformation regime to estimate the strain energy related to the transverse shear deformation, which leads to an explicit formula for the strain energy function of the composite under a general finite deformation state.