Cross-linked polymers demonstrate nonlinear behavior under large deformations with inelastic features such as the Mullins effect, permanent set, deformation-induced anisotropy, and progressive stress softening. While several constitutive models are developed to take into account each of those features individually, there are only a few models which can consider damage accumulation in cross-linked elastomers that occur due to multiple parallel factors.Here, a new modular platform is presented to integrate different inelastic mechanisms into one generalized constitutive model. The concept of network decomposition is the keystone of the proposed platform. Based on this concept, the polymer network is considered as a combination of parallel networks, each responsible for the specific inelastic response. The energy of each network is calculated through the concept of the unit sphere. Consequently, the polymer matrix total strain energy can be estimated by summation of the free energy of the sub-networks in all directions. Therefore, a three-dimensional (3D) polymer matrix can be decomposed to unidirectional sub-network elements uniformly distributed over a unit micro-sphere, which hosts a simplified 1D inelastic mechanism. The network models can be substituted, upgraded, or removed without influencing the integrity of the framework. In order to improve the accuracy of the proposed framework, the theory of elastomer elasticity has been revisited. Next, different micro-mechanical models are developed to describe the nature of Mullins effect, permanent set, deformation-induced anisotropy, and necking instability in highly cross-linked elastomeric gels based on different concepts.First, the popular assumptions that influence computational accuracy and simplicity of the proposed framework are examined. In modeling polymeric systems, two competing factors determine the type of material model that should be used in the simulation: computational cost and accuracy. Optimizing the trade-off between these two factors determines the minimum requirements of the model. The proposed modular platform enables us to select the networks based on this trade-off. Furthermore, network models are designed to return strain energy; the scale-transition will be based on a micro-sphere concept, and the Non-Gaussian entropic behavior is assumed for polymer chains. The non-gaussian theory is often approximated by the Kuhn-Grun (KG) distribution function, which is derived from the first-order approximation of the complex Rayleigh's exact Fourier integral distribution. The KG function is widely accepted in polymer physics, where the non-Gaussian theory is often used to describe the energy of the chains with various flexibility ratios. However, the KG function is shown to be relevant only for long chains and becomes extremely inaccurate for chains with fewer than 40 segments. In order to overcome this shortcoming, a novel modification of non-Gaussian theory using the inverse Langevin function is developed to provide a family of approximation functions for non-Gaussian theory with different degrees of accuracy. In addition, a set of simple and accurate approximation of the inverse Langevin function is proposed to further improve the accuracy of the energy of a 1D polymer chain.Next, two constitutive models are developed to understand and describe the mechanical behavior of double network hydrogel (DN gel) based on statistical micro-mechanics of interpenetrating polymer networks. In the first model, the nonlinear behavior of the DN gels is attributed to the existence of pre-damage in the first network due to swelling during the polymerization process. In the second model, DN gels behavior is divided into three parts including pre-necking, necking, and hardening. The first network is dominant in the response of the gel in the pre-necking stage. The breakage of the first network to smaller network fractions (clusters) induces the stress softening observed in this stage. The disentanglement of the second network chains from broken first network chains and long chains in the second network are also considered as main contributors to the response of gels in necking and hardening stages, respectively. The contribution of clusters decreases during the necking as the second network starts hardening. The numerical results of the developed models are validated and compared by uni-axial cyclic tensile experimental data of DN gels. Finally, a finite-element implementation of the proposed model is presented to simulate the initiation and propagation of necking instability.
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