Compressive modulus and deformation mechanisms of 3DG foams: experimental investigation and multiscale modeling

Due to the wide applications of three-dimensional graphene (3DG) foam in bio-sensors, stretchable electronics, and conductive polymer composites, predicting its mechanical behavior is of paramount importance. In this paper, a novel multiscale finite element model is proposed to predict the compressive modulus of 3DG foams with various densities. It considers the effects of pore size and structure and the thickness of graphene walls on 3DG foams' overall behavior. According to the scanning electron microscope images, a unit cell is selected in the microscale step to represent the incidental arrangement of graphene sheets in 3DG foams. After derivation of equivalent elastic constants of the unit cell by six individual load cases, the whole unit cell is considered an equivalent element. The macroscale model is prepared by defining a representative volume element (RVE), containing a sufficient number of the equivalent elements. Assigning a stochastic local coordinate system for each equivalent element in the macro RVE provides a model that could be utilized for elastic modulus estimation of 3DG foams in macroscale. To investigate the correspondence between the theoretical results and experimental data, 3DG foams were synthesized with four densities, and their compressive behavior were evaluated. The mass densities of the prepared foams were 5.36, 8.50, 9.37, and 11.5 mg cm^-3, and the corresponding measured elastic modulus for each were 6.4, 10.7, 16.9, and 29.1 kPa, respectively. The predicted modulus by the proposed model for the synthesized foams were 6.1, 13.1, 15.6 and 21.7 kPa, respectively. The results show that the maximum divergence between estimated values and experimental data is less than 25%, confirming the high capability of the model in the estimation of 3DG foams' properties.