A Review on the Mullins Effect in Tough Elastomers and Gels

A Review on the Mullins Effect in Tough Elastomers and Gels

26 February 2024 | Lin Zhan, Shaoxing Qu, Rui Xiao
This review provides a comprehensive analysis of the Mullins effect in tough elastomers and gels, focusing on nanocomposite gels, double-network hydrogels, and multi-network elastomers. The Mullins effect refers to stress softening observed during loading and unloading cycles in these materials. The review discusses experimental observations, recent developments in constitutive models, and the role of damage mechanisms and network representations. It emphasizes the challenges in accurately predicting multiaxial data and the need for anisotropic models tailored for tough gels and elastomers. The Mullins effect is characterized by a hysteresis loop during loading-unloading cycles, primarily observed in uniaxial deformation. However, studies also show anisotropic damage behaviors in biaxial deformation. Despite variations in damage mechanisms, similar mechanical responses allow the application of the same theoretical framework across different soft materials. Developing damage models for filled rubbers is of great interest due to its engineering applications. Representative models include the continuum damage model, pseudo-elastic model, two-phase model, network alternation theory, and progressive damage model. The review highlights the importance of understanding damage mechanisms and reliable polymer network models in describing the Mullins effect. Recent developments include models based on new damage mechanisms and network representations, such as the model of Wang et al., which accounts for the pullout effect in the matrix network of double-network hydrogels. The model of Tang et al. explains the stress softening in nanocomposite hydrogels through chain slip on clay surfaces. The model of Lavoie et al. uses progressive damage concepts, while the model of Bacca et al. incorporates chain extensibility constraints. The model of Wang et al. describes the damage and recovery effects in nanocomposite hydrogels through chain detachment and re-attachment. The review also discusses the development of models based on new network representations, such as Zhao's model, which uses an interpenetrating polymer network (IPN) model to describe the large deformation and damage behaviors of double-network hydrogels. The model incorporates the Langevin single-chain model and eight-chain network representation. The damage in the rigid first network is described by the network alternation theory, with increasing chain length and decreasing chain density specified by exponential functions. Overall, the review emphasizes the importance of understanding the underlying mechanisms of the Mullins effect in tough elastomers and gels, and the need for advanced models that can accurately predict the behavior of these materials under various loading conditions.This review provides a comprehensive analysis of the Mullins effect in tough elastomers and gels, focusing on nanocomposite gels, double-network hydrogels, and multi-network elastomers. The Mullins effect refers to stress softening observed during loading and unloading cycles in these materials. The review discusses experimental observations, recent developments in constitutive models, and the role of damage mechanisms and network representations. It emphasizes the challenges in accurately predicting multiaxial data and the need for anisotropic models tailored for tough gels and elastomers. The Mullins effect is characterized by a hysteresis loop during loading-unloading cycles, primarily observed in uniaxial deformation. However, studies also show anisotropic damage behaviors in biaxial deformation. Despite variations in damage mechanisms, similar mechanical responses allow the application of the same theoretical framework across different soft materials. Developing damage models for filled rubbers is of great interest due to its engineering applications. Representative models include the continuum damage model, pseudo-elastic model, two-phase model, network alternation theory, and progressive damage model. The review highlights the importance of understanding damage mechanisms and reliable polymer network models in describing the Mullins effect. Recent developments include models based on new damage mechanisms and network representations, such as the model of Wang et al., which accounts for the pullout effect in the matrix network of double-network hydrogels. The model of Tang et al. explains the stress softening in nanocomposite hydrogels through chain slip on clay surfaces. The model of Lavoie et al. uses progressive damage concepts, while the model of Bacca et al. incorporates chain extensibility constraints. The model of Wang et al. describes the damage and recovery effects in nanocomposite hydrogels through chain detachment and re-attachment. The review also discusses the development of models based on new network representations, such as Zhao's model, which uses an interpenetrating polymer network (IPN) model to describe the large deformation and damage behaviors of double-network hydrogels. The model incorporates the Langevin single-chain model and eight-chain network representation. The damage in the rigid first network is described by the network alternation theory, with increasing chain length and decreasing chain density specified by exponential functions. Overall, the review emphasizes the importance of understanding the underlying mechanisms of the Mullins effect in tough elastomers and gels, and the need for advanced models that can accurately predict the behavior of these materials under various loading conditions.
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