Kao Philip H, Lammers Steven R, Hunter Kendall, Stenmark Kurt R, Shandas Robin, Qi H Jerry
Department of Mechanical Engineering, University of Colorado, Boulder, CO 80309.
Int J Struct Changes Sol. 2010 Apr;2(1):19-29.
Many biological materials are composites composed of a soft matrix reinforced with stiffer fibers. These stiffer fibers may have a tortuous shape and wind through the soft matrix. At small material deformation, these fibers deform in a bending mode and contribute little to the material stiffness; at large material deformation, these fibers deform in a stretching mode and induce a stiffening effect in the material behavior. The transition from bending mode deformation to stretching mode deformation yields a characteristic J-shape stress-strain curve. In addition, the spatial distribution of these fibers may render the composite an anisotropic behavior. In this paper, we present an anisotropic finite-deformation hyperelastic constitutive model for such materials. Here, the matrix is modeled as an isotropic neo-Hookean material. "The behaviors of single tortuous fiber are represented by a crimped fiber model". The anisotropic behavior is introduced by a structure tensor representing the effective orientation distribution of crimped fibers. Parametric studies show the effect of fiber tortuosity and fiber orientation distribution on the overall stress-strain behaviors of the materials.
许多生物材料是由较硬的纤维增强的软质基体组成的复合材料。这些较硬的纤维可能具有曲折的形状，并蜿蜒穿过软质基体。在材料发生小变形时，这些纤维以弯曲模式变形，对材料刚度的贡献很小；在材料发生大变形时，这些纤维以拉伸模式变形，并在材料行为中产生硬化效应。从弯曲模式变形到拉伸模式变形的转变产生了特征性的J形应力-应变曲线。此外，这些纤维的空间分布可能使复合材料呈现各向异性行为。在本文中，我们提出了一种针对此类材料的各向异性有限变形超弹性本构模型。在此，基体被建模为各向同性的新胡克材料。“单根曲折纤维的行为由卷曲纤维模型表示”。通过表示卷曲纤维有效取向分布的结构张量引入各向异性行为。参数研究表明了纤维曲折度和纤维取向分布对材料整体应力-应变行为的影响。
