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硫化橡胶的大变形行为经常在超弹性范围内进行研究。以往的文献提出过各种超弹性模型理论,主要分成两类,一种采用连续介质力学原则,另一种以橡胶分子链网络结构作研究对象。唯象学的连续介质力学模型有两个明确的参数,已经证明Gent模型能完美地模拟橡胶大变形。Gent模型将左Cauchy-Green变形张量的第一个不变量限制为极限最大值,并把著名的neo-Hookean模型作为辅助形式。尽管Gent模型是唯象学的,但它解释了分子链网络的极限或有限延伸性。在过去十年里,研究者用Gent模型分析了各种均化和非均化变形模式。所有这些工作主要研究了分子链极限伸长后引起的硬化效应。本文分析了不可压缩各向同性均匀空心橡胶管的螺旋剪切变形,旨在识别Gent模型模拟的其他潜在定性的特征。这一基础性分析表明,分子链极限伸长使橡胶硬化、应力增加,同时导致了应变场均匀化及各种应变分量的偶合。
The large deformation behavior of vulcanized rubber is often studied in the hyperelastic range. Previous literatures have proposed various hyperelastic model theories, which are mainly divided into two types, one using the principle of continuum mechanics and the other taking the network structure of rubber molecular chains as the research object. The phenomenological continuum mechanics model has two explicit parameters that have proved that the Gent model can perfectly simulate large deformation of rubber. The Gent model limits the first invariant of the Cauchy-Green deformation tensor to the limit maximum and uses the well-known neo-Hookean model as an antecedent. Although the Gent model is phenomenological, it explains the limits or limited extensibility of molecular chain networks. In the past decade, researchers have analyzed various types of homogenization and non-uniform deformation modes using the Gent model. All of these work focuses on the hardening effect caused by the ultimate elongation of the molecular chain. In this paper, spiral shear deformation of an incompressible isotropic homogeneous hollow rubber tube is analyzed to identify other potentially qualitative features of the Gent model simulation. This fundamental analysis shows that the ultimate elongation of the molecular chain hardens the rubber and increases the stress, leading to the homogenization of the strain field and the coupling of various strain components.