An efficient method for modelling flexoelectricity in soft material toward uncertainty quantification and reliability analysis

• Applicant: Dr.-Ing. Khader Hamdia
• Subject Area: Computer-Aided Design of Materials and Simulation of Materials Behaviour from Atomic to Microscopic Scale ; Mechanics
• Term: since 2021
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 492535144

The main objective of this project is to develop and implement a robust computational uncertainty quantification method to study the effect of flexoelectricity in soft materials. Soft materials can be found in a wide range of the modern technology. Among others, they can be used as: structural materials, foams and adhesives, colloids and granular materials, lubricants and fuel additives, and rubber in tires. In addition, a number of biological materials (e.g. blood, muscle, milk) are also classifiable as soft matter. Flexoelectricity is generated in soft dielectrics as a result of the coupling between electric polarization and strain gradient. It can be explained by the non-uniform displacement of ions under a strain gradient. The energy conversion due to the coupling is expected to largely enhanced since the soft material at nanoscale can sustain larger deformation. In this regards, numerical modeling of the electromechanical coupling due to flexoelectricity is subjected inherently to various source of uncertainty which leads to significant fluctuations from the desired performance. In the numerical approximation, the uncertainties can be generally related to the numerical method and its input parameters. The former is the bias error resulting from the assumptions and the simplifications of the physical behavior. Meanwhile, the latter concerns to the stochastic variance of the input parameters. The higher the uncertainties in the inputs, the more uncertain the predictions will be. We will provide an effective tool to support the characterization, analysis, and design optimization of flexoelectricity in soft materials with large deformation. The proposed method will capture the full statistical properties of the related electromechanical coupling effect. It will allow also the preselection of optimal materials and design geometries within the probability space. Reliable performance will be evaluated by calculating the probability that the functional quantity of interest in the intended application is (or is not) met. To solve the governing equations of flexoelectricity we will devise a NURBS-based IGA formulation using a hierarchy of multilevel discretizations. With the isogeometric formulations, complex geometries can be modeled more easily, while the multilevel hierarchy scheme will enable reducing the computation cost in the numerical experiments without loss of the accuracy. Doing so, we will virtually test the performance under various loading conditions in a set of benchmark examples.

• DFG Programme: Research Grants