Arzash Sadjad, Shivers Jordan L, MacKintosh Fred C
Department of Chemical & Biomolecular Engineering, Rice University, Houston, Texas 77005, USA.
Center for Theoretical Biological Physics, Rice University, Houston, Texas 77030, USA.
Phys Rev E. 2021 Aug;104(2):L022402. doi: 10.1103/PhysRevE.104.L022402.
When subject to applied strain, fiber networks exhibit nonlinear elastic stiffening. Recent theory and experiments have shown that this phenomenon is controlled by an underlying mechanical phase transition that is critical in nature. Growing simulation evidence points to non-mean-field behavior for this transition and a hyperscaling relation has been proposed to relate the corresponding critical exponents. Here, we report simulations on two distinct network structures in three dimensions. By performing a finite-size scaling analysis, we test hyperscaling and identify various critical exponents. From the apparent validity of hyperscaling, as well as the non-mean-field exponents we observe, our results suggest that the upper critical dimension for the strain-controlled phase transition is above three, in contrast to the jamming transition that represents another athermal, mechanical phase transition.
当受到外加应变时，纤维网络会呈现出非线性弹性硬化。最近的理论和实验表明，这种现象受一种本质上为临界的潜在力学相变控制。越来越多的模拟证据表明这种相变具有非平均场行为，并且已经提出了一种超标度关系来关联相应的临界指数。在此，我们报告了对三维空间中两种不同网络结构的模拟。通过进行有限尺寸标度分析，我们检验了超标度并确定了各种临界指数。从超标度的明显有效性以及我们观察到的非平均场指数来看，我们的结果表明，与代表另一种无热力学相变的堵塞相变不同，应变控制相变的上临界维度高于三维。
