Micromechanical modelling of rubbery networks: The role of chain pre-stretch

IF 2.8 3区 工程技术 Q2 MECHANICS International Journal of Non-Linear Mechanics Pub Date : 2024-07-14 DOI:10.1016/j.ijnonlinmec.2024.104834
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Abstract

Discrete Network (DN) models are a useful tool to investigate structure–property relationships in rubbery networks such as elastomers and hydrogels. In a DN model, polymer chains are represented by entropic springs connected at crosslinking points, and the partitioning of stretches among the chains is dictated by the condition of mechanical equilibrium at each crosslink. A key feature of these models is that springs have a zero natural length, and are therefore pre-stretched in the reference configuration. However, the role of chain pre-stretch distribution on the emerging mechanical properties has often been overlooked. In this work we investigate the elastic properties of DNs where the average chain pre-stretch, chain density and chain length distribution can be prescribed independently via a novel network generation algorithm. We show that increasing the average pre-stretch increases the network stiffness and decreases its extensibility limit. We also compare predictions of semi-analytical micromechanical models of rubber elasticity to DN predictions taken as reference. Deviations between analytical model and DN predictions are attributed to the combination of two factors: the loss of affinity at large strain and the initial pre-stretch distribution, which is not taken into account in analytical estimates. DN simulations further show that the assumption of one-to-one mapping between chain stretch and chain orientation on which microsphere models rely is not satisfied.

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橡胶网络的微机械建模:链预拉伸的作用
离散网络(DN)模型是研究弹性体和水凝胶等橡胶网络结构-性能关系的有用工具。在 DN 模型中,聚合物链由在交联点连接的熵弹簧表示,链之间的拉伸分配由每个交联点的机械平衡条件决定。这些模型的一个主要特点是弹簧的自然长度为零,因此在参考构型中是预拉伸的。然而,链的预拉伸分布对新出现的机械特性的作用往往被忽视。在这项研究中,我们通过一种新颖的网络生成算法,研究了平均链预伸、链密度和链长分布可独立规定的 DN 的弹性特性。我们的研究表明,增加平均预拉伸会增加网络刚度,并降低其延伸极限。我们还将橡胶弹性半分析微观力学模型的预测结果与作为参考的 DN 预测结果进行了比较。分析模型与 DN 预测之间的偏差归因于两个因素的综合作用:大应变时亲和力的损失和初始预拉伸分布,分析估计中没有考虑到这一点。DN 模拟进一步表明,微球模型所依赖的链拉伸和链取向之间一一对应的假设并不满足。
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来源期刊
CiteScore
5.50
自引率
9.40%
发文量
192
审稿时长
67 days
期刊介绍: The International Journal of Non-Linear Mechanics provides a specific medium for dissemination of high-quality research results in the various areas of theoretical, applied, and experimental mechanics of solids, fluids, structures, and systems where the phenomena are inherently non-linear. The journal brings together original results in non-linear problems in elasticity, plasticity, dynamics, vibrations, wave-propagation, rheology, fluid-structure interaction systems, stability, biomechanics, micro- and nano-structures, materials, metamaterials, and in other diverse areas. Papers may be analytical, computational or experimental in nature. Treatments of non-linear differential equations wherein solutions and properties of solutions are emphasized but physical aspects are not adequately relevant, will not be considered for possible publication. Both deterministic and stochastic approaches are fostered. Contributions pertaining to both established and emerging fields are encouraged.
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