In this chapter, we learn how to model rubber elasticity that allows a large deformation. Before looking at a model for the rubber elasticity, we first learn how elastic a polymer chain is. The simplest model is a polymer chain in one dimension (Section 8.2). We apply the canonical‐ensemble statistical mechanics to consider the 1D polymer chain and find the relationship of the chain's extension to the force applied. Then, we skip two dimensions, and proceed to consider a polymer chain in three dimensions in Section 8.3. We then briefly look at a model for the rubber elasticity.
8.1 Rubber
Rubber is a special class of an elastic material. All solids and glasses are elastic materials, but rubbers stand out, since they allow large deformations while still returning to the original dimension when the pulling force is released. Figure 8.1 shows a typical relationship between stress σ and strain ε for steel and rubber within the elasticity limit, i.e. in the absence of plastic deformation. There are different types of steel and different types of rubber (soft and hard). The figure shows a typical curve for steel and rubber, respectively.
Figure 8.1 Typical relationship between stress σ and strain ε for steel and rubber within the elasticity limit.
The strain of rubber at its elasticity limit is large, often several hundred percent, but it can be reached with a ...
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