Mixed FEM for flexoelectric effect analyses in a viscoelastic material

2021 ◽  
pp. 111269
Author(s):  
Jan Sladek ◽  
Vladimir Sladek ◽  
Xinpeng Tian ◽  
Qian Deng
Keyword(s):  
Viscoelastic Material ◽  
Flexoelectric Effect ◽  
Mixed Fem

A Consistent Implementation of Inelastic Material Models into Steady State Rolling

2016 ◽  
Vol 44 (3) ◽  
pp. 174-190 ◽  
Author(s):  
Mario A. Garcia ◽  
Michael Kaliske ◽  
Jin Wang ◽  
Grama Bhashyam
Keyword(s):  
Steady State ◽  
Numerical Simulations ◽  
Viscoelastic Material ◽  
Rolling Contact ◽  
Arbitrary Lagrangian Eulerian ◽  
Ale Formulation ◽  
Inelastic Material ◽  
Material Formulation ◽  
Steady State Rolling ◽  
Efficient Alternative

ABSTRACT Rolling contact is an important aspect in tire design, and reliable numerical simulations are required in order to improve the tire layout, performance, and safety. This includes the consideration of as many significant characteristics of the materials as possible. An example is found in the nonlinear and inelastic properties of the rubber compounds. For numerical simulations of tires, steady state rolling is an efficient alternative to standard transient analyses, and this work makes use of an Arbitrary Lagrangian Eulerian (ALE) formulation for the computation of the inertia contribution. Since the reference configuration is neither attached to the material nor fixed in space, handling history variables of inelastic materials becomes a complex task. A standard viscoelastic material approach is implemented. In the inelastic steady state rolling case, one location in the cross-section depends on all material locations on its circumferential ring. A consistent linearization is formulated taking into account the contribution of all finite elements connected in the hoop direction. As an outcome of this approach, the number of nonzero values in the general stiffness matrix increases, producing a more populated matrix that has to be solved. This implementation is done in the commercial finite element code ANSYS. Numerical results confirm the reliability and capabilities of the linearization for the steady state viscoelastic material formulation. A discussion on the results obtained, important remarks, and an outlook on further research conclude this work.

A non-classical theory of elastic dielectrics incorporating couple stress and quadrupole effects: part I – reconsideration of curvature-based flexoelectricity theory

2021 ◽  
pp. 108128652110015
Author(s):  
YL Qu ◽  
GY Zhang ◽  
YM Fan ◽  
F Jin
Keyword(s):  
Classical Theory ◽  
Couple Stress ◽  
Couple Stress Theory ◽  
Constitutive Relations ◽  
Stress Theory ◽  
Isotropic Materials ◽  
Flexoelectric Effect ◽  
Beam Bending ◽  
Gradient Theories ◽  
Anisotropic And Isotropic Materials

A new non-classical theory of elastic dielectrics is developed using the couple stress and electric field gradient theories that incorporates the couple stress, quadrupole and curvature-based flexoelectric effects. The couple stress theory and an extended Gauss’s law for elastic dielectrics with quadrupole polarization are applied to derive the constitutive relations of this new theory through energy conservation. The governing equations and the complete boundary conditions are simultaneously obtained through a variational formulation based on the Gibbs-type variational principle. The constitutive relations of general anisotropic and isotropic materials with the corresponding independent material constants are also provided, respectively. To illustrate the newly proposed theory and to show the flexoelectric effect in isotropic materials, one pure bending problem of a simply supported beam is analytically solved by directly applying the formulas derived. The analytical results reveal that the flexoelectric effect is present in isotropic materials. In addition, the incorporation of both the couple stress and flexoelectric effects always leads to increased values of the beam bending stiffness.

Flexoelectric effect in boron nitride–graphene heterostructures

2021 ◽  
Author(s):  
S. I. Kundalwal ◽  
V. K. Choyal ◽  
Vijay Choyal
Keyword(s):  
Boron Nitride ◽  
Flexoelectric Effect

scholarly journals Modeling the flexoelectric effect of an anisotropic dielectric nanoplate

2021 ◽  
Vol 60 (3) ◽  
pp. 3099-3106
Author(s):  
A.R. El Dhaba ◽  
M.E. Gabr
Keyword(s):  
Anisotropic Dielectric ◽  
Flexoelectric Effect
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