Pence Thomas J, Monroe Ryan J, Wright Neil T
Department of Mechanical Engineering, Michigan State University, East Lansing, MI 48824, USA.
J Biomech Eng. 2008 Aug;130(4):041009. doi: 10.1115/1.2917432.
Some recent analyses modeled the response of collagenous tissues, such as epicardium, using a hypothetical network consisting of interconnected springlike fibers. The fibers in the network were organized such that internal nodes served as the connection point between three such collagen springs. The results for assumed affine and nonaffine deformations are contrasted after a homogeneous deformation at the boundary. Affine deformation provides a stiffer mechanical response than nonaffine deformation. In contrast to nonaffine deformation, affine deformation determines the displacement of internal nodes without imposing detailed force balance, thereby complicating the simplest intuitive notion of stress, one based on free body cuts, at the single node scale. The standard notion of stress may then be recovered via average field theory computations based on large micromesh realizations. An alternative and by all indications complementary viewpoint for the determination of stress in these collagen fiber networks is discussed here, one in which stress is defined using elastic energy storage, a notion which is intuitive at the single node scale. It replaces the average field theory computations by an averaging technique over randomly oriented isolated simple elements. The analytical operations do not require large micromesh realizations, but the tedious nature of the mathematical manipulation is clearly aided by symbolic algebra calculation. For the example case of linear elastic deformation, this results in material stiffnesses that relate the infinitesimal strain and stress. The result that the affine case is stiffer than the nonaffine case is recovered, as would be expected. The energy framework also lends itself to the natural inclusion of changes in mechanical response due to the chemical, electrical, or thermal environment.
最近的一些分析使用由相互连接的弹簧状纤维组成的假设网络，对诸如心外膜等胶原组织的响应进行了建模。网络中的纤维组织方式使得内部节点成为三个这样的胶原弹簧之间的连接点。在边界处进行均匀变形后，对比了假设的仿射和非仿射变形的结果。仿射变形比非仿射变形提供更硬的力学响应。与非仿射变形不同，仿射变形在不施加详细力平衡的情况下确定内部节点的位移，从而在单节点尺度上使基于自由体切割的最简单直观的应力概念变得复杂。然后可以通过基于大型微观网格实现的平均场理论计算来恢复标准的应力概念。这里讨论了一种用于确定这些胶原纤维网络中应力的替代且从各方面迹象来看是互补的观点，即在单节点尺度上使用弹性能量存储来定义应力，这一概念很直观。它通过对随机取向的孤立简单元素进行平均技术来取代平均场理论计算。解析运算不需要大型微观网格实现，但符号代数计算显然有助于简化数学操作的繁琐性质。对于线性弹性变形的示例情况，这会得出将无穷小应变和应力联系起来的材料刚度。正如预期的那样，恢复了仿射情况比非仿射情况更硬的结果。能量框架也自然地适用于纳入由于化学、电或热环境引起的力学响应变化。
