Chen Xin, Li Moxiao, Liu Shaobao, Liu Fusheng, Genin Guy M, Xu Feng, Lu Tian Jian
State Key Laboratory for Strength and Vibration of Mechanical Structures, Xi'an Jiaotong University, Xi'an 710049, China.
State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China.
J Appl Mech. 2019 May;86(5):0510021-5100210. doi: 10.1115/1.4042575. Epub 2019 Mar 5.
The displacement of relatively rigid beads within a relatively compliant, elastic matrix can be used to measure the mechanical properties of the matrix. For example, in mechanobiological studies, magnetic or reflective beads can be displaced with a known external force to estimate the matrix modulus. Although such beads are generally rigid compared to the matrix, the material surrounding the beads typically differs from the matrix in one or two ways. The first case, as is common in mechanobiological experimentation, is the situation in which the bead must be coated with materials such as protein ligands that enable adhesion to the matrix. These layers typically differ in stiffness relative to the matrix material. The second case, common for uncoated beads, is the situation in which the beads disrupt the structure of the hydrogel or polymer, leading to a region of enhanced or reduced stiffness in the neighborhood of the bead. To address both cases, we developed the first analytical solution of the problem of translation of a coated, rigid spherical inclusion displaced within an isotropic elastic matrix by a remotely applied force. The solution is applicable to cases of arbitrary coating stiffness and size of the coating. We conclude by discussing applications of the solution to mechanobiology.
相对刚性的珠子在相对柔顺的弹性基质内的位移可用于测量基质的力学性能。例如，在力学生物学研究中，磁性或反射性珠子可以在已知外力作用下发生位移，以估计基质模量。尽管与基质相比，此类珠子通常是刚性的，但珠子周围的材料通常在一两个方面与基质不同。第一种情况，这在力学生物学实验中很常见，即珠子必须涂覆诸如蛋白质配体等材料，以便与基质粘附。这些涂层相对于基质材料的刚度通常不同。第二种情况，对于未涂覆的珠子很常见，即珠子会破坏水凝胶或聚合物的结构，导致珠子附近区域的刚度增强或降低。为了解决这两种情况，我们开发了第一个解析解，用于解决在各向同性弹性基质中，一个涂覆的刚性球形内含物在远程施加力作用下的平移问题。该解适用于涂层刚度和涂层尺寸任意的情况。我们通过讨论该解在力学生物学中的应用来结束本文。
