Continuum Based Modeling and Analysis for the Mechanics of Fiber Reinforced Hyperelastic Composite Material: Plane, Out of Plane Response and Pseudo-elasticity
Creators: Islam, Suprabha
Publisher: name: University of Alberta Library
Year: 2023

<p>In recent days, hyperelastic composites (i.e., elastomeric composites reinforced with fibers) have shown promising outcomes in various engineering applications involving tissue engineering, shape-morphing structures, microfluidics, wearable devices, biomechanics, and soft robotics. Typically, elastomeric materials can sustain a large range of strains e.g., Ecoflex can sustain up to 10 times its initial length. When the elastomeric materials are used in conjunction with systematically arranged continuous fibers such as fiber mesh and interpenetrating networks, they display a distinct strain-stiffening phenomenon, known as J-shaped stress-strain behavior. This unique characteristic makes elastomeric composite highly useful in tissue engineering, biomedical, and other engineering applications. Moreover, when elastomeric materials are filled with nanofibers, their mechanical, conductive, and dielectric properties can be improved greatly making them proper candidates for the design of flexible and wearable electronic devices. Due to the great potential of these materials, the modeling of hyperelastic composites has become a subject of intense study during the last few decades. The primary motivation behind this research study is to develop a generalized and complete hyperelastic model for the fiber-reinforced composite material. The presented generalized model may accommodate some unique features including, higher-order gradient continua, precise characterization of fiber reinforcement, pseudoelasticity, damage mechanics, and multi-scale capability that makes the model uniquely versatile in the modeling and design of hyperelastic composites. The existing hyperelastic models fail to attain this level of versatility.<br>
We started by presenting a continuum model for hyperelastic material reinforced with unidirectional fibers resistant to flexure and extension. Which is then refined to accommodate bi-directional fibers having different orientations (i.e., 45 and 90-degree orientations), different types of nonlinear extension potential (i.e., polynomial and exponential), and torsional resistance. The response of elastomeric matrix material is characterized by using the Moony-Rivlin strain energy potential. The kinematics of the embedded fibers are formulated via the first and second gradient of continuum deformations through which the stretch, bending, and torsional responses of fibers are modeled. By means of variational principles and a virtual work statement, the Euler equilibrium equation and the associated boundary conditions are derived. The system is then numerically solved via custom-built numerical procedures. The results from the generalized model demonstrate excellent correspondence to the experimental results in capturing the deformations and mechanical responses under different loading conditions including pure bending, uniaxial tension, and out-of-plane deformations. The model is then further refined by introducing damage parameters and damage functions inspired by Ogden Roxburgh’s model and Weibull’s fiber damage model. The obtained models can successfully predict the Mullins effects in biological soft tissues and damage mechanics due to fiber breakage. Furthermore, we have extended our model to accommodate the size, orientation effects, and volume fraction of the reinforcing fibers by introducing the shear-lag, Krenchel orientation, and energy fraction parameters, respectively. This extension allows the model to predict the responses of nanofiber-reinforced hyperelastic composites having different micromechanical characterizations. We also propose a non-uniform interface stiffness parameter to incorporate the damage mechanics of nanofiber-reinforced elastomeric composites due to interfacial debonding. The resulting model closely assimilates both the gradual and rapid debonding processes of a certain type of soft/stiff matrix-based nanocomposite. The practical utility of the presented generalized model may be expected in the design and analysis of elastomeric composites for different engineering applications.</p>