9 - Nonlinear elastic finite deformation of flexible composites

Summary

Introduction

Flexible composites, which are described in Chapter 8, behave very differently from conventional rigid polymer composites in the following ways:

1. (1) Flexible composites are highly anisotropic (i.e. longitudinal elastic modulus/transverse elastic modulus » 1). Figure 9.1 compares the normalized effective Young's modulus (E_xx/E₂₂) vs. fiber orientation for two types of unidirectional composites. The upper curve obtained from Kevlar- 49/silicone elastomer shows that the stiffness of the elastomeric composite lamina is very sensitive to the fiber orientation. At a 5δ off-axis fiber orientation, for example, a 1° change in fiber angle causes the effective stiffness to change by 53%. The lower curve obtained from Kevlar- 49/epoxy shows less than 7% change at the same off-axis angle.

2. (2) Flexible composites show low shear modulus and hence large shear distortion, which allows the fibers to change their orientations under loading.

3. (3) Flexible composites have a much larger elastic deformation range than that of conventional rigid polymer composites. Thus, the geometric changes of the configuration (i.e. area, direction, etc.) need to be taken into consideration.

4. (4) The nonlinear elastic behavior with stretching–shear coupling, due to material and geometrical effects, is pronounced in flexible composites under finite deformation.

Therefore, the conventional linear elastic theory, based on the infinitesimal strain assumption for rigid matrix composites, may no longer be applicable to elastomeric composites under finite deformation.

The theories of non-linear and finite elasticity made a major advancement during the Second World War, in response to the development of the rubber industry. M. Mooney, in 1940, advanced his well-known strain–energy function.