A thermodynamic consistent material model for hysteresis effects in ferroelectric ceramics and its finite element implementation

2007 ◽  
Author(s):  
Sven Klinkel ◽  
Werner Wagner
Keyword(s):  
Finite Element ◽  
Material Model ◽  
Ferroelectric Ceramics ◽  
Finite Element Implementation

scholarly journals A Variational Approach and Finite Element Implementation for Swelling of Polymeric Hydrogels Under Geometric Constraints

2010 ◽  
Vol 77 (6) ◽  
Author(s):  
Min Kyoo Kang ◽  
Rui Huang
Keyword(s):  
Finite Element ◽  
Aspect Ratio ◽  
Numerical Simulations ◽  
Variational Approach ◽  
Chemical Potential ◽  
Polymer Network ◽  
Material Model ◽  
Geometric Constraints ◽  
Free Energy Function ◽  
Finite Element Implementation

A hydrogel consists of a cross-linked polymer network and solvent molecules. Depending on its chemical and mechanical environment, the polymer network may undergo enormous volume change. The present work develops a general formulation based on a variational approach, which leads to a set of governing equations coupling mechanical and chemical equilibrium conditions along with proper boundary conditions. A specific material model is employed in a finite element implementation, for which the nonlinear constitutive behavior is derived from a free energy function, with explicit formula for the true stress and tangent modulus at the current state of deformation and chemical potential. Such implementation enables numerical simulations of hydrogels swelling under various constraints. Several examples are presented, with both homogeneous and inhomogeneous swelling deformation. In particular, the effect of geometric constraint is emphasized for the inhomogeneous swelling of surface-attached hydrogel lines of rectangular cross sections, which depends on the width-to-height aspect ratio of the line. The present numerical simulations show that, beyond a critical aspect ratio, creaselike surface instability occurs upon swelling.

Finite Element Implementation of Anisotropic Quasi-Linear Viscoelasticity Using a Discrete Spectrum Approximation

1998 ◽  
Vol 120 (1) ◽  
pp. 62-70 ◽  
Author(s):  
M. A. Puso ◽  
J. A. Weiss
Keyword(s):  
Finite Element ◽  
Discrete Spectrum ◽  
Soft Tissues ◽  
Transversely Isotropic ◽  
Material Model ◽  
Material Behavior ◽  
Elastic Response ◽  
Test Problems ◽  
Finite Element Program ◽  
Finite Element Implementation

The objective of this work was to develop a theoretical and computational framework to apply the finite element method to anisotropic, viscoelastic soft tissues. The quasi-linear viscoelastic (QLV) theory provided the basis for the development. To allow efficient and easy computational implementation, a discrete spectrum approximation was developed for the QLV relaxation function. This approximation provided a graphic means to fit experimental data with an exponential series. A transversely isotropic hyperelastic material model developed for ligaments and tendons was used for the elastic response. The viscoelastic material model was implemented in a general-purpose, nonlinear finite element program. Test problems were analyzed to assess the performance of the discrete spectrum approximation and the accuracy of the finite element implementation. Results indicated that the formulation can reproduce the anisotropy and time-dependent material behavior observed in soft tissues. Application of the formulation to the analysis of the human femur-medial collateral ligament–tibia complex demonstrated the ability of the formulation to analyze large three-dimensional problems in the mechanics of biological joints.

Delamination in the scoring and folding of paperboard

TAPPI Journal ◽  
2012 ◽  
Vol 11 (1) ◽  
pp. 61-66 ◽  
Author(s):  
DOEUNG D. CHOI ◽  
SERGIY A. LAVRYKOV ◽  
BANDARU V. RAMARAO
Keyword(s):  
Finite Element ◽  
Plane Deformation ◽  
Strain Analysis ◽  
Local Strain ◽  
Uniaxial Stress ◽  
Material Model ◽  
Element Model ◽  
Plastic Behavior ◽  
Stress Strain ◽  
Strain Fields

Delamination between layers occurs during the creasing and subsequent folding of paperboard. Delamination is necessary to provide some stiffness properties, but excessive or uncontrolled delamination can weaken the fold, and therefore needs to be controlled. An understanding of the mechanics of delamination is predicated upon the availability of reliable and properly calibrated simulation tools to predict experimental observations. This paper describes a finite element simulation of paper mechanics applied to the scoring and folding of multi-ply carton board. Our goal was to provide an understanding of the mechanics of these operations and the proper models of elastic and plastic behavior of the material that enable us to simulate the deformation and delamination behavior. Our material model accounted for plasticity and sheet anisotropy in the in-plane and z-direction (ZD) dimensions. We used different ZD stress-strain curves during loading and unloading. Material parameters for in-plane deformation were obtained by fitting uniaxial stress-strain data to Ramberg-Osgood plasticity models and the ZD deformation was modeled using a modified power law. Two-dimensional strain fields resulting from loading board typical of a scoring operation were calculated. The strain field was symmetric in the initial stages, but increasing deformation led to asymmetry and heterogeneity. These regions were precursors to delamination and failure. Delamination of the layers occurred in regions of significant shear strain and resulted primarily from the development of large plastic strains. The model predictions were confirmed by experimental observation of the local strain fields using visual microscopy and linear image strain analysis. The finite element model predicted sheet delamination matching the patterns and effects that were observed in experiments.

Lifetime Prediction of Tires with Regard to Oxidative Aging5

2008 ◽  
Vol 36 (1) ◽  
pp. 63-79 ◽  
Author(s):  
L. Nasdala ◽  
Y. Wei ◽  
H. Rothert ◽  
M. Kaliske
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Temperature Distribution ◽  
Superposition Principle ◽  
Accelerated Aging ◽  
Material Model ◽  
Aging Behavior ◽  
Element Analysis ◽  
Material Parameters ◽  
Reaction Processes

Abstract It is a challenging task in the design of automobile tires to predict lifetime and performance on the basis of numerical simulations. Several factors have to be taken into account to correctly estimate the aging behavior. This paper focuses on oxygen reaction processes which, apart from mechanical and thermal aspects, effect the tire durability. The material parameters needed to describe the temperature-dependent oxygen diffusion and reaction processes are derived by means of the time–temperature–superposition principle from modulus profiling tests. These experiments are designed to examine the diffusion-limited oxidation (DLO) effect which occurs when accelerated aging tests are performed. For the cord-reinforced rubber composites, homogenization techniques are adopted to obtain effective material parameters (diffusivities and reaction constants). The selection and arrangement of rubber components influence the temperature distribution and the oxygen penetration depth which impact tire durability. The goal of this paper is to establish a finite element analysis based criterion to predict lifetime with respect to oxidative aging. The finite element analysis is carried out in three stages. First the heat generation rate distribution is calculated using a viscoelastic material model. Then the temperature distribution can be determined. In the third step we evaluate the oxygen distribution or rather the oxygen consumption rate, which is a measure for the tire lifetime. Thus, the aging behavior of different kinds of tires can be compared. Numerical examples show how diffusivities, reaction coefficients, and temperature influence the durability of different tire parts. It is found that due to the DLO effect, some interior parts may age slower even if the temperature is increased.

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.

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