论文标题
在网络定向亲和力上的聚合物和通过链条拉伸的微麦克罗连接中
On the network orientational affinity assumption in polymers and the micro-macro connection through the chain stretch
论文作者
论文摘要
我们质疑聚合物变形下建模链方向的网络亲和力假设，以及从正确的cauchy-green变形张量（或从该度量得出的非氨基微裂缝）投射的拉伸度量的使用作为微麦克罗过渡的基本状态变量。这些成分是标准配置，取自聚合物的统计理论，并用于大多数微机械聚合物网络和软组织模型中。 亲和力假设在网络中施加了约束，从而导致链条方向的各向异性分布，因此，在应包括的附加配置熵中。这种额外的熵会导致额外的应力张量。但是，可以说是一种更自然的替代方案，与链行为本身的典型假设相一致，并且鉴于对这些力的无视，它是要考虑到网络可能会波动不受限制以适应宏观变形。这样，在变形过程中，保持链方向的各向同性统计分布将不受限制，并且没有施加额外的压力。然后，我们表明，这个自由透失的网络假设等效于考虑从拉伸张量（而不是右cauchy绿色变形量张量）作为网络链变形的状态变量。 我们使用两种假定的行为显示了预测的非常重要的差异，并证明，通过自由泄漏网络假设，我们可以仅使用一个测试曲线来校准模型的聚合物中所有测试的准确预测。通过采用网络亲和力假设的相同宏观微晶状体方法，我们只能准确捕获用于校准模型的测试，而不是整体聚合物行为。
We question the network affinity assumption in modeling chain orientations under polymer deformations, and the use of the stretch measure projected from the right Cauchy-Green deformation tensor (or non-affine micro-stretches derived from that measure) as a basic state variable for the micro-macro transition. These ingredients are standard, taken from the statistical theory of polymers, and used in most micromechanical polymer network and soft tissue models. The affinity assumption imposes a constraint in the network which results in an anisotropic distribution of the orientation of the chains and, hence, in an additional configurational entropy that should be included. This additional entropy would result in an additional stress tensor. But an arguably more natural alternative, in line with the typical assumption for the chain behavior itself and with the disregard of these forces, is to consider that the network may fluctuate unconstrained to adapt to macroscopic deformations. This way, the isotropic statistical distribution of the orientation of the chains is maintained unconstrained during deformation and no additional stress is imposed. Then, we show that this free-fluctuating network assumption is equivalent to consider the stretch projected from the stretch tensor (instead of the right Cauchy-Green deformation tensor) as the state variable for the deformation of the network chains. We show very important differences in predictions using both assumed behaviors, and demonstrate that with the free-fluctuating network assumption, we can obtain accurate predictions for all tests in polymers using just one test curve to calibrate the model. With the same macro-micro-macro approach employing the network affinity assumption, we are capable of capturing accurately only the test used for calibration of the model, but not the overall polymer behavior.
