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: from 2021 to 2023
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 492535144

• Final Report Year: 2024

Final Report Abstract

This research project provided comprehensive evaluation of the flexoelectricity effect using numerical simulations. The governing equations for the electromechanical coupling mechanism were derived from the total electrical enthalpy. The numerical solution was solved by NURBS-based IGA formulations. The research investigated flexoelectric composites constituted by flexo and elastic phases. A robust optimization has been developed to design cantilever nano-structure under uncertainty. The objective of the optimization was to find the geometries with the largest coupling effect, which requires finding the optimal distribution of the materials blocks. Alternative to the classical methods, multi-level monte Carlo was used in this study based on multilevel hierarchy of computational meshes obtained by a uniform refinement in a geometric sequence. Accordingly, the research calculated the growth rate of the simulation cost, in addition to the rates of decay in the expectation and the variance of the differences between the approximations over the hierarchy. The proposed method has been implemented in considerably lower computation time without loss of the accuracy. Moreover, this work applied computational homogenization to calculate the effective pizo- and flexoelectricity coefficients. A 3D RVE model of longitudinally oriented flexoelectric inclusion was generated for this purpose. The RVE was subjected to uniform and inhomogeneous strains to approximate the piezoelectric and flexoelectric coefficients, respectively. The numerical simulations indicated that while the effective tensor of piezoelectricity is isotropic, the flexoelectricity tensor is transversely anisotropic concerning the geometry of the composite’s phases. The elastic behaviour of liquid-solid composites was modeld by employing a stochastic multiscale approach and considering the elasto-capillary coupling. The mesostructure consists of randomly distributed droplets in percolated network and uniform dispersions to account for agglomeration. The elastocapillary length scale in comparison to the droplet size has provided a scale to determine the elastic response in term of softening and stiffening. The influence of selecting material model at the mesoscale on the uncertainty as an additional source of uncertainty was taken into account in global sensitivity analysis . Due to their high main effects indices, the surface tension and the radius of the droplets need to be better measured. Greatest reduction is expected in uncertainty when fixed to their true value. Furthermore, the results suggests that more attention should be drawn to select the right material model at mesoscale when considering uncertainties from the joint effects.

Publications

• Effects of functional group type and coverage on the interfacial strength and load transfer of graphene-polyethylene nanocomposites: a molecular dynamics simulation. Applied Physics A, 128(4).
  Karimi, M. R.; Abrinia, K.; Hamdia, Khader M.; Hashemianzadeh, Seyed Majid & Baniassadi, Majid
  
• Multilevel Monte Carlo method for topology optimization of flexoelectric composites with uncertain material properties. Engineering Analysis with Boundary Elements, 134, 412-418.
  Hamdia, Khader M.; Ghasemi, Hamid; Zhuang, Xiaoying & Rabczuk, Timon
  
• Quantifying the uncertainties in modeling soft composites via a multiscale approach. International Journal of Solids and Structures, 256, 111959.
  Hamdia, Khader M. & Ghasemi, Hamid
  
• A Numerical Study of Crack Mixed Mode Model in Concrete Material Subjected to Cyclic Loading. Materials, 16(5), 1916.
  Alrayes, Omar; Könke, Carsten & Hamdia, Khader M.
  
• Modeling Cyclic Crack Propagation in Concrete Using the Scaled Boundary Finite Element Method Coupled with the Cumulative Damage-Plasticity Constitutive Law. Materials, 16(2), 863.
  Alrayes, Omar; Könke, Carsten; Ooi, Ean Tat & Hamdia, Khader M.
  
• Reliability analysis of the stress intensity factor using multilevel Monte Carlo methods. Probabilistic Engineering Mechanics, 74, 103497.
  Hamdia, Khader M. & Ghasemi, Hamid
  
• The J-Integral Method Compared to the API 579-1/ASME FFS-1 Standard to Calculate Stress Intensity Factor (SIF): Leak-Before-Break (LBB) Application with Uncertainty Quantification. Arabian Journal for Science and Engineering, 49(4), 4643-4654.
  Ghasemi, Hamid & Hamdia, Khader M.
  
• A representative volume element model to evaluate the effective properties of flexoelectric nanocomposite. European Journal of Mechanics - A/Solids, 103, 105149.
  Hamdia, Khader M.