scholarly journals On the computational modelling of nonlinear electro-elasticity in heterogeneous bodies at finite deformations

2021 ◽  
Vol 3 (1) ◽  
Author(s):  
Anas Kanan ◽  
Michael Kaliske
Keyword(s):  
Mechanical Properties ◽  
Finite Element Method ◽  
Finite Element ◽  
Numerical Solutions ◽  
Volume Fraction ◽  
Material Model ◽  
Electric Response ◽  
Tube Model ◽  
The Finite Element Method ◽  
Element Method

AbstractDielectric elastomer actuators (DEA) have been demonstrated to exhibit a quasi-immediate electro-mechanical actuation response with relatively large deformation capability. The properties of DEA make them suitable to be used in the form of major active components within soft robotics and biomimetic artificial muscles. However, some of the electro-active material properties impose limitations on its applications. Therefore, researchers attempt to modify the structure of the homogeneous DEA material by the incorporation of fillers that possess distinct electro-mechanical properties. This modification of the material’s structure leads to a fabricated inhomogeneous composite. From the point of mathematical material modelling and numerical simulation, we propose a material model and a computational framework using the finite element method, which is capable of emulating nonlinear electro-elastic interactions. We consider a coupled electro-mechanical description with the electric and the electro-mechanical properties of the material assumed to be nonlinearly dependent on the deformation. Furthermore, we demonstrate a coupled ansatz that expresses the electric response as dielectrically quasi-linear with only density-dependent electric permittivity. We couple the electro-mechanical models to the extended tube model, which is a suitable approach for the realistic emulation of the hyperelastic response of rubber-like materials. Thereafter, we demonstrate analytical and numerical solutions of a homogeneous electro-elastic body with the Neo-Hookean material model and the extended tube model to express the hyperelastic response. Finally, we use the finite element method to investigate several heterogeneous configurations consisting of soft DEA matrix filled with spherical stiff inclusions with changing volume fraction and ellipsoidal inclusions with varying aspect ratio.

Application of the Finite Element Method in Screening of Body Turn up Heights for Radial Truck Tires

2001 ◽  
Vol 29 (3) ◽  
pp. 186-196 ◽  
Author(s):  
X. Yan
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Material Model ◽  
The Finite Element Method ◽  
Truck Tires ◽  
Contact Constraint ◽  
Nonlinear Mechanical ◽  
Critical Regions ◽  
Constraint Method ◽  
Element Method

Abstract A method is described to predict relative body turn up endurance of radial truck tires using the finite element method. The elastomers in the tire were simulated by incompressible elements for which the nonlinear mechanical properties were described by the Mooney-Rivlin model. The belt, carcass, and bead were modeled by an equivalent orthotropic material model. The contact constraint of a radial tire structure with a flat foundation and rigid rim was treated using the variable constraint method. Three groups of tires with different body turn up heights under inflation and static footprint loading were analyzed by using the finite element method. Based on the detail analysis for stress analysis parameters in the critical regions in the tires, the relative body turn up edge endurance was predicted.

Linearization of the finite element method for gradient flows by Newton’s method

2020 ◽  
Author(s):  
Georgios Akrivis ◽  
Buyang Li
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Newton’S Method ◽  
Newton's Method ◽  
Numerical Solutions ◽  
Resolvent Estimate ◽  
Optimal Order ◽  
Gradient Flows ◽  
The Finite Element Method ◽  
Element Method

Abstract The implicit Euler scheme for nonlinear partial differential equations of gradient flows is linearized by Newton’s method, discretized in space by the finite element method. With two Newton iterations at each time level, almost optimal order convergence of the numerical solutions is established in both the $L^q(\varOmega )$ and $W^{1,q}(\varOmega )$ norms. The proof is based on techniques utilizing the resolvent estimate of elliptic operators on $L^q(\varOmega )$ and the maximal $L^p$-regularity of fully discrete finite element solutions on $W^{-1,q}(\varOmega )$.

Increasing the Solution Accuracy in the Numerical Modeling of Boundary Value Problems Using Finite Element Method Based on Hankel Shape Functions

2019 ◽  
Vol 11 (07) ◽  
pp. 1950062
Author(s):  
S. Farmani ◽  
M. Ghaeini-Hessaroeyeh ◽  
S. Hamzehei-Javaran
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Boundary Value Problems ◽  
Numerical Solutions ◽  
Boundary Value ◽  
The Finite Element Method ◽  
Shape Functions ◽  
Element Approach ◽  
Solution Accuracy ◽  
Element Method

A new finite element approach is developed here for the modeling of boundary value problems. In the present model, the finite element method (FEM) is reformulated by new shape functions called spherical Hankel shape functions. The mentioned functions are derived from the first and second kind of Bessel functions that have the properties of both of them. These features provide an improvement in the solution accuracy with number of elements which are equal or lower than the ones used by the classic FEM. The efficiency and accuracy of the suggested model in the potential problems are examined by several numerical examples. Then, the obtained results are compared with the analytical and numerical solutions. The comparisons indicate the high accuracy of the present method.

scholarly journals Specific solution of problem of water filtering in the rocks by the finite element method

2019 ◽  
Vol 109 ◽  
pp. 00093 ◽  
Author(s):  
Olena Slashchova ◽  
Ihor Slashchov ◽  
Iryna Sapunova
Keyword(s):  
Mechanical Properties ◽  
Finite Element Method ◽  
Finite Element ◽  
Strain State ◽  
Water Saturation ◽  
Physical And Mechanical Properties ◽  
Critical Parameters ◽  
The Finite Element Method ◽  
Water Saturated ◽  
Element Method

The article is devoted to development of methods for geofiltration calculations with taking into account peculiarities of changes of the rock physical and mechanical properties at water saturation. Methods: mathematical modeling of geomechanical and filtration processes with the help of finite element method and laboratory and underground studies. A mathematical model was formulated for solving a problem of elasticity theory by the finite element method, which took into account peculiarities of water-saturated rocks. Pattern of stress-strain state changing in the fractured water-saturated rocks under the action of critical loads, which occurred around the preparatory roadways during their operation, were established. In order to solve the filtration problems, a bank of collected initial data on physical and mechanical properties of water-saturated rocks was processed with the help of variation coefficients, which were taken into account by the method, which assumed calculation of the model loading with critical parameters.

scholarly journals Some Novel Numerical Applications of Cosserat Continua

2018 ◽  
Vol 15 (06) ◽  
pp. 1850054 ◽  
Author(s):  
Nicholas Fantuzzi ◽  
Lorenzo Leonetti ◽  
Patrizia Trovalusci ◽  
Francesco Tornabene
Keyword(s):  
Mechanical Properties ◽  
Finite Element Method ◽  
Finite Element ◽  
Size Effects ◽  
Heterogeneous Materials ◽  
Numerical Implementation ◽  
The Finite Element Method ◽  
Strong Formulation ◽  
Cosserat Continua ◽  
Element Method

Cosserat continua demonstrated to have peculiar mechanical properties, with respect to classic Cauchy continua, because they are able to more accurately describe heterogeneous materials, as particle composites and masonry-like material, taking into account size effects. Many studies have been devoted to their numerical implementation. In this paper, some reference benchmarks, referred to an isotropic heterogeneous sample, are shown by comparing the solutions provided by strong and weak formulations. The strong formulation finite element method (SFEM), implemented in MATLAB®, is compared to the finite element method (FEM), given by COMSOL® Multiphysics, and the advantages of the two approaches are highlighted and discussed.

scholarly journals Finite element modeling of fluid flow in fractured porous media using unified approach

2020 ◽  
Vol 43 (1) ◽  
pp. 13-22
Author(s):  
Hai-Bang Ly ◽  
Hoang-Long Nguyen ◽  
Minh-Ngoc Do
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Porous Media ◽  
Fluid Flow ◽  
Numerical Solutions ◽  
Fractured Porous Media ◽  
Flow In Porous Media ◽  
Soil Science ◽  
The Finite Element Method ◽  
Element Method

Understanding fluid flow in fractured porous media is of great importance in the fields of civil engineering in general or in soil science particular. This study is devoted to the development and validation of a numerical tool based on the use of the finite element method. To this aim, the problem of fluid flow in fractured porous media is considered as a problem of coupling free fluid and fluid flow in porous media or coupling of the Stokes and Darcy equations. The strong formulation of the problem is constructed, highlighting the condition at the free surface between the Stokes and Darcy regions, following by the variational formulation and numerical integration using the finite element method. Besides, the analytical solutions of the problem are constructed and compared with the numerical solutions given by the finite element approach. Both local properties and macroscopic responses of the two solutions are in excellent agreement, on condition that the porous media are sufficiently discretized by a certain level of finesse. The developed finite element tool of this study could pave the way to investigate many interesting flow problems in the field of soil science.

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