ABSTRACT

Collagen networks are usually modeled as an inelastic material that accentuates the role of bond dynamics in their viscoelastic response. However, permanent cross-links can be used to fix these fibers to a large degree. Here, we model a network in which the fibers are assumed to maintain their viscoelasticity nature while the cross-linking bonds between them are fixed. Our models show that the interplay between fiber orientation and energy dissipation due to the viscoelasticity of fibers gives rise to a rich mechanical response. The network can stiffen, soften, or have an approximately constant stiffness as a function of strain when different loading rates are imposed. Using the order parameters of Q-tensor, we verify that the stiffening is due to the orientation of fibers, which is a well-established behavior in fibrous networks. In contrast to inelastic networks where there is always a linear initial response, the present network exhibits a constant stiffness only for a small range of loading rates. Also, it is shown that this duality is independent of the fiber concentration and only depends on the loading rate. Consequently, the existence of both strain-softening and strain-stiffening responses is a general behavior that is in common in fibrous networks with viscoelastic components and permanent cross-links.

摘要

通常将胶原蛋白网络建模为一种非弹性材料，该材料强调了键动力学在其粘弹性响应中的作用。但是，可以使用永久性交联剂在很大程度上固定这些纤维。在这里，我们对网络进行建模，在该网络中，假定纤维在保持它们之间的交联键不变的情况下保持其粘弹性。我们的模型表明，由于纤维的粘弹性，纤维取向和能量耗散之间的相互作用产生了丰富的机械响应。当施加不同的加载速率时，网络可以根据应变变硬，变软或具有近似恒定的刚度。使用Q张量的阶次参数，我们验证了硬化是由于纤维的取向而引起的，这是纤维网络中公认的行为。与始终存在线性初始响应的非弹性网络相反，本网络仅在较小的加载速率范围内显示出恒定的刚度。而且，表明该对偶性与纤维浓度无关，并且仅取决于负载率。因此，应变软化和应变刚度响应的存在是在具有粘弹性成分和永久性交联的纤维网络中常见的一般行为。