Hyperelastic Modeling of Rubber-Like Photopolymers for Additive Manufacturing Processes

This chapter addresses design issues of components realized with rubber-like PhotoPolymers (PP) recently introduced in Rapid Prototyping. In particular, the determination of accurate, hyperelastic, constitutive models which describe the PP behavior is discussed in detail. In fact, Stereolithography and Polyjet processes allow the production of highly flexible objects by using photosensitive resins whose mechanical properties are, in some cases, similar to natural rubber. These parts, being fabricated with an additive approach, eventually represent a final product instead of a mere ‘prototype’. Therefore, the term Additive Manufacturing (AM) might be used in substitution to Rapid Prototyping (Gibson et al., 2010) in order to underline a closer link to the end-use component. From a designer’s point of view, AM technologies offer the possibility, before unknown, to customize and singularly optimize each product for the end user, such that focused design methods are needed. In the case of rubber-like PP, the considered materials usually experience deviatoric (isochoric), fully reversible deformations which can be well described by hyperelastic constitutive theories capable of dealing with large (finite) strains (Holzapfel, 2001). The capability to undergo finite deformations may intrinsically solve several functional design requirements but this requires an accurate representation of the material behavior through proper constitutive models. Unfortunately, the only data which are available (e.g. data from Objet Geometries Ltd., http://www.objet.com/docs/) are limited to basicmaterial properties, namely tensile strength, tensile modulus at few reference stretch ratios, compression set, and hardness. Hence, the correct design and verification of AM rubber-like products become impossible or, at least, very difficult. For example, every shape optimization through nonlinear Finite Element Analysis (FEA) requires a constitutive material law (i.e. a relation between stress and deformation) as a key input of the numerical model. In the same way, the calculation of hardness and friction influence on the product contact behavior requires a detailed description of its deformation state for given applied loads (Shallamach, 1952). If a rough estimate of any stress-strain field based on the aforementioned data may be acceptable for the first-attempt sizing of a prototype, nonetheless the design for direct manufacturing of 6