Locking and Stability of 3D Woven Composite Reinforcements

2014 ◽  
Vol 611-612 ◽  
pp. 292-299 ◽  
Author(s):  
Sylvain Mathieu ◽  
Philippe Boisse ◽  
Nahiene Hamila ◽  
Florent Bouillon
Keyword(s):  
Finite Element ◽  
Strain Energy ◽  
Constitutive Law ◽  
Element Formulation ◽  
Woven Composite ◽  
Anisotropic Behavior ◽  
Stabilization Procedure ◽  
Bias Extension ◽  
Deformation Modes ◽  
Composite Reinforcements

3D woven composite reinforcements preforming simulations are an unavoidable step of composite part processing. The present paper deals with thick composite fabric behavior modelling and issues arising during the numerical simulation of preforming. After the description of the independent deformation modes of initially orthotropic reinforcements, a physically motivated and invariant based hyperelastic strain energy density is introduced. This constitutive law is used to show the limitations of a classical finite element formulation in 3D fabric simulations. Tension locking is highlighted in bias extension tests and a reduced integration hexahedral finite element with specific physical hourglass stabilization is proposed. Instabilities due to the highly anisotropic behavior law, witnessed in bending dominated situations, are exposed and a stabilization procedure is initiated.

Numerical Implementation and Finite Element Analysis of Anisotropic Hyperelastic Biomaterials - Influence of Fibers Orientation

2013 ◽  
Vol 554-557 ◽  
pp. 2414-2423 ◽  
Author(s):  
Rachid Djeridi ◽  
Mohand Ould Ouali
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Fiber Orientation ◽  
Mechanical Response ◽  
Theoretical Study ◽  
Constitutive Law ◽  
Anisotropic Behavior ◽  
Element Analysis ◽  
Material Parameters ◽  
Fibers Orientation

Modeling anisotropic behavior of fiber reinforced rubberlike materials is actually of a great interest in many industrials sectors. Indeed, accurately description of the mechanical response and damage of such materials allows the increase of the lifecycle of these materials which generally evolve under several environment conditions. In this paper theoretical study and finite element analysis of anisotropic biomaterials is presented. The mechanical model adopted to achieve this study has been implemented into the finite element code Abaqus using an implicit scheme. This constitutive law has been utilized to perform some numerical simulations. The material parameters of the model have been determined by numerical calibration. One fiber family is considered in this work. Effects of the fiber orientation on the mechanical response and stiffness change of biomaterial is studied. Both the compressible and incompressible states have been taken into account. The results show firstly the capability of the model to reproduce the known results and that optimal fiber orientation can be found.

Creep Analysis and Thermal-Fatigue Life Prediction of the Lead-Free Solder Sealing Ring of a Photonic Switch

2002 ◽  
Vol 124 (4) ◽  
pp. 403-410 ◽  
Author(s):  
J. Lau ◽  
Z. Mei ◽  
S. Pang ◽  
C. Amsden ◽  
J. Rayner ◽  
...  
Keyword(s):  
Finite Element ◽  
Fatigue Life ◽  
Energy Density ◽  
Thermal Fatigue ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Constitutive Law ◽  
Isothermal Fatigue ◽  
Thermal Fatigue Life ◽  
Sealing Ring

Thermal reliability of the solder sealing ring of Agilent Technologies’ bubble-actuated photonic cross-connect switches has been investigated in this paper. Emphasis is placed on the determination of the thermal-fatigue life of the solder sealing ring under shipping/storing/handling conditions. The solder ring is assumed to obey the Garofalo-Arrhenius creep constitutive law. The nonlinear responses such as the deflections, stresses, creep strains, and creep strain energy density of the 3-D photonic package have been determined with a commercial finite element code. In addition, isothermal fatigue tests have been performed to obtain the relationship between the number of cycle-to-failure and the strain energy density. Thus, by combining the finite element results and the isothermal fatigue test results, the average thermal-fatigue life of the solder sealing ring is readily determined and is found to be more than adequate for shipping/storing/handling the photonic switches.

Mixed Finite Element Analysis of Elastomeric Butt-Joints

2005 ◽  
Vol 129 (1) ◽  
pp. 11-18 ◽  
Author(s):  
P. A. Kakavas ◽  
G. I. Giannopoulos ◽  
N. K. Anifantis
Keyword(s):  
Finite Element ◽  
Strain Energy ◽  
Poisson Ratio ◽  
Mixed Finite Element ◽  
Three Dimensional ◽  
Butt Joint ◽  
Element Formulation ◽  
Butt Joints ◽  
Element Analysis ◽  
Strain Energy Density Function

This paper presents a mixed finite element formulation approximating large deformations observed in the analysis of elastomeric butt-joints. The rubber has been considered as nearly incompressible continuum obeying the Mooney/Rivlin (M/R) strain energy density function. The parameters of the model were determined by fitting the available from the literature uniaxial tension experimental data with the constitutive equation derived from the M/R model. The optimum value of the Poisson ratio is adjusted by comparing the experimentally observed diametral contraction of the model with that numerically obtained using the finite element method. The solution of the problem has been obtained utilizing the mixed finite element procedure on the basis of displacement/pressure mixed interpolation and enhanced strain energy mixed formulation. For comparison purposes, an axisymmetric with two-parameter M/R model and a three-dimensional (3D) with nine-parameters M/R model of the butt-joint are formulated and numerical results are illustrated concerning axisymmetric or general loading. For small strains the stress and/or strain distribution in the 2D axisymmetric butt-joint problem was compared with derived analytical solutions. Stress distributions along critical paths are evaluated and discussed.

The Cosserat Point Element as an Accurate and Robust Finite Element Formulation for Implicit Dynamic Simulations

2019 ◽  
Vol 17 (01) ◽  
pp. 1844006
Author(s):  
Mahmood Jabareen ◽  
Yehonatan Pestes
Keyword(s):  
Finite Element ◽  
Energy Function ◽  
Strain Energy ◽  
Three Dimensional ◽  
Nonlinear Dynamic Analysis ◽  
Strain Energy Function ◽  
Finite Element Formulation ◽  
Element Formulation ◽  
Dynamic Simulations ◽  
Cosserat Point

The reliability of numerical simulations manifested the need for an accurate and robust finite element formulation. Therefore, in the present study, an eight node brick Cosserat point element ( CPE ) for the nonlinear dynamic analysis of three-dimensional (3D) solids including both thick and thin structures is developed. Within the present finite element formulation, a strain energy function is proposed and additively decoupled into two parts. One part is characterized by any 3D strain energy function, while the other part controls the response to inhomogeneous deformations. Several example problems are presented, which demonstrate the accuracy and the robustness of the developed CPE in modeling the dynamic response of elastic structures.

A Pressure Projection Method for Nearly Incompressible Rubber Hyperelasticity, Part II: Applications

1996 ◽  
Vol 63 (4) ◽  
pp. 869-876 ◽  
Author(s):  
Jiun-Shyan Chen ◽  
Cheng-Tang Wu ◽  
Chunhui Pan
Keyword(s):  
Finite Element ◽  
Energy Density ◽  
Projection Method ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Finite Elasticity ◽  
Element Formulation ◽  
Density Functions ◽  
Hyperelastic Materials ◽  
Pressure Projection

In the first part of this paper a pressure projection method was presented for the nonlinear analysis of structures made of nearly incompressible hyperelastic materials. The main focus of the second part of the paper is to demonstrate the performance of the present method and to address some of the issues related to the analysis of engineering elastomers including the proper selection of strain energy density functions. The numerical procedures and the implementation to nonlinear finite element programs are presented. Mooney-Rivlin, Cubic, and Modified Cubic strain energy density functions are used in the numerical examples. Several classical finite elasticity problems as well as some practical engineering elastomer problems are analyzed. The need to account for the slight compressibility of rubber (finite bulk modulus) in the finite element formulation is demonstrated in the study of apparent Young’s modulus of bonded thin rubber units. The combined shear-bending deformation that commonly exists in rubber mounting systems is also analyzed and discussed.

scholarly journals Thermal Post-Buckling Improvements of Laminated Composite Plates Using the Active Strain Energy Tuning Approach

2011 ◽  
Vol 311-313 ◽  
pp. 2235-2238
Author(s):  
Zainudin A Rasid ◽  
Rizal Zahari ◽  
Ayob Amran ◽  
Dayang Laila Majid ◽  
Ahmad Shakrine M. Rafie
Keyword(s):  
Finite Element ◽  
Shape Memory Alloy ◽  
Shape Memory Alloys ◽  
Shape Memory ◽  
Strain Energy ◽  
Laminated Composite ◽  
Composite Plates ◽  
Element Formulation ◽  
Laminated Composite Plates ◽  
Post Buckling

Shape memory alloy was firstly used commercially as a hydraulic coupling in the Grumman F14A in 1971. It is today used among others to improve structural behaviours such as buckling of composite plates in the aerospace vehicles. In this paper, finite element model and its source code for thermal post-buckling of shape memory alloy laminated composite plates is presented. The shape memory alloy wires induced stress that improved the strain energy, stiffness and thus the buckling behaviour of the composite plates. The finite element formulation catered the combined properties of the composite and shape memory alloys, the addition of the recovery stress and the temperature dependent properties of the shape memory alloys and the composite matrix. This study showed that by embedding shape memory alloy within layers of composite plates, post-buckling behaviours of composite plates can be improved substantially.

scholarly journals Finite Element Formulation of Fractional Constitutive Laws Using the Reformulated Infinite State Representation

2021 ◽  
Vol 5 (3) ◽  
pp. 132
Author(s):  
Matthias Hinze ◽  
André Schmidt ◽  
Remco I. Leine
Keyword(s):  
Finite Element ◽  
Three Dimensional ◽  
Constitutive Law ◽  
Benchmark Problems ◽  
Element Formulation ◽  
Algebraic Equations ◽  
State Representation ◽  
Element Analysis ◽  
Closed Form Solutions ◽  
Infinite State

In this paper, we introduce a formulation of fractional constitutive equations for finite element analysis using the reformulated infinite state representation of fractional derivatives. Thereby, the fractional constitutive law is approximated by a high-dimensional set of ordinary differential and algebraic equations describing the relation of internal and external system states. The method is deduced for a three-dimensional linear viscoelastic continuum, for which the hydrostatic and deviatoric stress-strain relations are represented by a fractional Zener model. One- and two-dimensional finite elements are considered as benchmark problems with known closed form solutions in order to evaluate the performance of the scheme.

Dynamics of Thick Viscoelastic Beams

1997 ◽  
Vol 119 (3) ◽  
pp. 273-278 ◽  
Author(s):  
A. R. Johnson ◽  
A. Tessler ◽  
M. Dambach
Keyword(s):  
Finite Element ◽  
Virtual Work ◽  
Equations Of Motion ◽  
Constitutive Law ◽  
Finite Element Formulation ◽  
Internal Variables ◽  
Element Formulation ◽  
Modal Interactions ◽  
Cantilevered Beam ◽  
Thick Beam

A viscoelastic higher-order thick beam finite element formulation is extended to include elastodynamic deformations. The material constitutive law is a special differential form of the Maxwell solid, which employs viscous strains as internal variables to determine the viscous stresses. The total time-dependent stress is the superposition of its elastic and viscous components. In the constitutive model, the elastic strains and the conjugate viscous strains are coupled through a system of first-order ordinary differential equations. The use of the internal strain variables allows for a convenient finite element formulation. The elastodynamic equations of motion are derived from the virtual work principle. Computational examples are carried out for a thick orthotropic cantilevered beam. Relaxation, creep, relaxation followed by free damped vibrations, and damping related modal interactions are discussed.

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