scholarly journals Rot‐free mixed finite elements for gradient elasticity at finite strains

2020 ◽  
Author(s):  
J. Riesselmann ◽  
J. W. Ketteler ◽  
M. Schedensack ◽  
D. Balzani
Keyword(s):  
Finite Elements ◽  
Gradient Elasticity ◽  
Mixed Finite Elements ◽  
Finite Strains

Mixed Finite Elements for Flexoelectric Solids

2017 ◽  
Vol 84 (8) ◽  
Author(s):  
Feng Deng ◽  
Qian Deng ◽  
Wenshan Yu ◽  
Shengping Shen
Keyword(s):  
Finite Elements ◽  
Mixed Finite Element ◽  
Gradient Elasticity ◽  
Mixed Finite Elements ◽  
Mixed Finite Element Method ◽  
Dielectric Materials ◽  
Concentrated Force ◽  
Lagrangian Multipliers ◽  
Strain Gradients ◽  
Mixed Fem

Flexoelectricity (FE) refers to the two-way coupling between strain gradients and the electric field in dielectric materials, and is universal compared to piezoelectricity, which is restricted to dielectrics with noncentralsymmetric crystalline structure. Involving strain gradients makes the phenomenon of flexoelectricity size dependent and more important for nanoscale applications. However, strain gradients involve higher order spatial derivate of displacements and bring difficulties to the solution of flexoelectric problems. This dilemma impedes the application of such universal phenomenon in multiple fields, such as sensors, actuators, and nanogenerators. In this study, we develop a mixed finite element method (FEM) for the study of problems with both strain gradient elasticity (SGE) and flexoelectricity being taken into account. To use C0 continuous elements in mixed FEM, the kinematic relationship between displacement field and its gradient is enforced by Lagrangian multipliers. Besides, four types of 2D mixed finite elements are developed to study the flexoelectric effect. Verification as well as validation of the present mixed FEM is performed through comparing numerical results with analytical solutions for an infinite tube problem. Finally, mixed FEM is used to simulate the electromechanical behavior of a 2D block subjected to concentrated force or voltage. This study proves that the present mixed FEM is an effective tool to explore the electromechanical behaviors of materials with the consideration of flexoelectricity.

Symmetric coupling of boundary elements and Raviart-Thomas-type mixed finite elements in elastostatics

1996 ◽  
Vol 75 (2) ◽  
pp. 153-174 ◽  
Author(s):  
Ulrich Brink ◽  
Carsten Carstensen ◽  
Erwin Stein
Keyword(s):  
Finite Elements ◽  
Mixed Finite Elements ◽  
Boundary Elements

A Discretization Scheme for a Quasi-Hydrodynamic Semiconductor Model

1997 ◽  
Vol 07 (07) ◽  
pp. 935-955 ◽  
Author(s):  
Ansgar Jüngel ◽  
Paola Pietra
Keyword(s):  
Finite Elements ◽  
Mixed Finite Elements ◽  
Exponential Fitting ◽  
Discretization Scheme ◽  
Drift Diffusion Model ◽  
Drift Diffusion ◽  
Current Conservation ◽  
Numerical Tests ◽  
Finite Elements Methods ◽  
Degenerate Type

A discretization scheme based on exponential fitting mixed finite elements is developed for the quasi-hydrodynamic (or nonlinear drift–diffusion) model for semiconductors. The diffusion terms are nonlinear and of degenerate type. The presented two-dimensional scheme maintains the good features already shown by the mixed finite elements methods in the discretization of the standard isothermal drift–diffusion equations (mainly, current conservation and good approximation of sharp shapes). Moreover, it deals with the possible formation of vacuum sets. Several numerical tests show the robustness of the method and illustrate the most important novelties of the model.

Numerical modeling of two-phase binary fluid mixing using mixed finite elements

2012 ◽  
Vol 16 (4) ◽  
pp. 1101-1124 ◽  
Author(s):  
Shuyu Sun ◽  
Abbas Firoozabadi ◽  
Jisheng Kou
Keyword(s):  
Numerical Modeling ◽  
Finite Elements ◽  
Mixed Finite Elements ◽  
Fluid Mixing ◽  
Two Phase ◽  
Binary Fluid
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