A Constitutive Representation of Inhomogeneous Polymeric Systems
Highly crosslinked network polymers appear to be inhomogeneous in both crosslink density and local orientations in their microstructure. To obtain some understanding of these systems a constitutive representation of such inhomogeneous polymeric systems is presented. The state of stress is calculated in terms of the contributions resulted in from deformations of microstructural systems. The approach is kept fairly general to maintain its validity for a wide variety of somewhat similar systems. The mathematical model used is composed of a large number of star-shaped basic units which are simple enough to reduce the complexity of the problem. However, attempts are made particularly to bring out the inhomogeneous nature of the crosslink density as well as the local orientations in the individual microstructural units. In order to assure a proper distribution for all the units in the network system,the strain energy is optimized through the use of variational principles with respect to basic quantities in any deformational processes. A simple constrained condition is introduced in the variational process to guide the mode of deformation of the network system. In the case that the network system deforms elastically, all quantities introduced in the analysis are properly interpreted.
KeywordsNatural Rubber Crosslink Density Local Orientation Constitutive Representation Crosslinked Network Polymer
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