Chen Sihan, Markovich Tomer, MacKintosh Fred C
Department of Physics and Astronomy, Rice University, Houston, TX 77005, USA.
Center for Theoretical Biological Physics, Rice University, Houston, TX 77005, USA.
Soft Matter. 2023 Nov 1;19(42):8124-8135. doi: 10.1039/d3sm00810j.
Networks of stiff fibers govern the elasticity of biological structures such as the extracellular matrix of collagen. These networks are known to stiffen nonlinearly under shear or extensional strain. Recently, it has been shown that such stiffening is governed by a strain-controlled athermal but critical phase transition, from a floppy phase below the critical strain to a rigid phase above the critical strain. While this phase transition has been extensively studied numerically and experimentally, a complete analytical theory for this transition remains elusive. Here, we present an effective medium theory (EMT) for this mechanical phase transition of fiber networks. We extend a previous EMT appropriate for linear elasticity to incorporate nonlinear effects an anharmonic Hamiltonian. The mean-field predictions of this theory, including the critical exponents, scaling relations and non-affine fluctuations qualitatively agree with previous experimental and numerical results.
由刚性纤维构成的网络决定着诸如胶原蛋白细胞外基质等生物结构的弹性。已知这些网络在剪切或拉伸应变下会非线性地变硬。最近，研究表明这种变硬过程受应变控制的无热但临界的相变支配，即从低于临界应变的松弛相转变为高于临界应变的刚性相。虽然这一相变已在数值和实验方面得到广泛研究，但关于这一转变的完整解析理论仍未找到。在此，我们针对纤维网络的这种力学相变提出一种有效介质理论（EMT）。我们扩展了先前适用于线性弹性的有效介质理论，以纳入非线性效应——一个非简谐哈密顿量。该理论的平均场预测，包括临界指数、标度关系和非仿射涨落，在定性上与先前的实验和数值结果一致。
