Numerical analysis of the hyperelastic behavior of polymer materials has drawn significant interest from within the field of mechanical engineering. Currently, hyperelastic models based on the energy density function, such as the Neo-Hookean, Mooney-Rivlin, and Ogden models, are used to investigate the hyperelastic responses of materials. Conventionally, constants relating to materials were determined from experimental data by using global least-squares fitting. However, formulating a constitutive equation to capture the complex behavior of hyperelastic materials was difficult owing to the limitations of the analytical model and experimental data. This study addresses these limitations by using a system of neural networks (NNs) to design a data-driven surrogate model without a specific function formula, and employs molecular dynamics (MD) simulations to calculate the massive amount of combined loading data of hyperelastic materials. Thus, MD simulations were used to propose an NN constitutive model for hyperelasticity to derive the constitutive equation to model the complex hyperelastic response. In addition, the probability distributions of the numerical solutions of hyperelasticity are used to characterize the uncertainty of the MD models. These statistical finite element results not only present numerical results with reliability ranges but also scattered distributions of the solution obtained from the MD-based probability distributions.

Ratcheting behavior of highly–cross‐linked epoxy polymers was investigated considering the effect of molecular structure of curing agents by molecular dynamics simulations. Cyclic loading–unloading simulations at two different frequencies were conducted using atomistic models for epoxies cured by aliphatic and aromatic curing agents, triethylenetetramine (TETA) and diethyltoluenediamine (DETDA), respectively. Different ratcheting strain evolutions, dihedral angle stress accumulations, and stiffness variations were observed during the cyclic deformation simulations depending on the molecular structure of curing agents. The epoxy cured by DETDA exhibited a more rapid increase of ratcheting strain and a decrease of the stiffness toward the loading direction. Structural analyses were carried out by observing the orientation order parameter of the monomers, radius of gyration, and free volume evolution to understand the ratcheting strain behaviors and stiffness variations at atomistic scale. The structural analyses revealed that irreversible dihedral angle transitions near the benzene ring of the curing agent DETDA were responsible for low ratcheting resistance and stiffness degradation during the cyclic deformations. Whereas, the aliphatic curing agent TETA, which does not exhibit any stress possession by the irreversible dihedral angle change, was revealed to be advantageous for the ratcheting resistance and stiffness variation of the epoxy polymers.

Ever since several formations of polymer-based nanocomposites were reported, research on their modeling, characterization, and computerized analysis methodology has been extensively investigated to become a major academic field of advanced material science and technology. This paper mainly summarizes the multiscale computational analysis methodology for polymer nanocomposites. We also introduce various computational modeling approaches to characterizing the physical behavior of polymer nanocomposites, which are the molecular dynamics approach, and the continuum approach. Based on the various computational analyses, we summarize how the material properties and phenomenological behaviors of polymer nanocomposites were analyzed.

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