Prediction of mechanical-hysteresis behavior and complex moduli using the phase field crystal method with modified pressure controlled dynamic equation

Damping materials have been used in numerous engineering applications. The important property that plays a key role in this type of material is a damping capacity which is related to mechanical-hysteresis behavior of viscoelasticity. During the last decade, the phase-field-crystal (PFC) model has emerged as a robust tool to predict various material phenomena. This density-functional-type model has the advantage over a conventional phase-field model in terms of atomistic resolution and molecular dynamics in terms of computational expense. In this work, we propose a method to predict mechanical-hysteresis behavior and its related complex moduli parameters using a modified-pressure-controlled dynamics (MPCD) equation incorporating with the PFC model, denoted as PFC-MPCD method, in a three-dimensional solid structure. We modify the previously proposed pressure-controlled dynamics (PCD) equation by introducing the pressure-time derivative term which allows us to produce the results consistent with the standard linear solid model (SLS) at the broader frequency range. We apply sinusoidal pressure oscillation and compare the results predicted by both models. The results demonstrate that mechanical-hysteresis behavior and complex moduli parameters predicted by PFC-MPCD method are in good agreement with those of SLS model and consistent with numerous experimental observations whereas the results produced by original PCD equation tends to exhibit inaccurate results at the very frequency. We expect that this new PFC-MPCD method can be extended to a more complex system and still be capable to exhibit the accurate mechanical-hysteresis behavior and complex moduli parameters which results in predicting more reliable damping capacity parameter in damping material design.