scholarly journals An exponential constitutive model excluding fibres under compression: Application to extension–inflation of a residually stressed carotid artery

2017 ◽  
Vol 23 (8) ◽  
pp. 1206-1224 ◽  
Author(s):  
Kewei Li ◽  
Ray W Ogden ◽  
Gerhard A Holzapfel
Keyword(s):  
Finite Element ◽  
Carotid Artery ◽  
Constitutive Model ◽  
Dispersion Model ◽  
Three Dimensional ◽  
Uniaxial Extension ◽  
Collagen Fibre ◽  
Strain Energy Function ◽  
Biological Tissues ◽  
Finite Element Program

Detailed information on the three-dimensional dispersion of collagen fibres within layers of healthy and diseased soft biological tissues has been reported recently. Previously we have proposed a constitutive model for soft fibrous solids based on the angular integration approach which allows the exclusion of any compressed collagen fibre within the dispersion. In addition, a computational implementation of that model in a general purpose finite element program has been investigated and verified with the standard fibre-reinforcing model for fibre contributions. In this study, we develop the proposed fibre dispersion model further using an exponential form of the strain-energy function for the fibre contributions. The finite element implementation of this model with a rotationally symmetrical dispersion of fibres is also presented. This includes explicit expressions for the stress and elasticity tensors. The performance and implementation of the new model are demonstrated by means of a uniaxial extension test, a simple shear test, and an extension–inflation simulation of a residually stressed carotid artery segment. In each example we have obtained good agreement between the finite element solution and the analytical or experimental results.

Progressive failure analysis of scarf-repaired composite laminate based on damage constitutive model

2016 ◽  
Vol 233 (2) ◽  
pp. 180-188 ◽  
Author(s):  
Qiuyi Shen ◽  
Zhenghao Zhu ◽  
Yi Liu
Keyword(s):  
Finite Element ◽  
Constitutive Model ◽  
Composite Laminate ◽  
Damage Mechanics ◽  
Cohesive Zone Model ◽  
Load Capacity ◽  
Three Dimensional ◽  
Zone Model ◽  
State Variables ◽  
Element Analysis

A three-dimensional finite element model for scarf-repaired composite laminate was established on continuum damage model to predict the load capacity under tensile loading. The mixed-mode cohesive zone model was adopted to the debonding behavior analysis of adhesive. Damage condition and failure of laminates and adhesive were subsequently addressed. A three-dimensional bilinear constitutive model was developed for composite materials based on damage mechanics and applied to damage evolution and loading capacity analyses by quantifying damage level through damage state variables. The numerical analyses were implemented with ABAQUS finite element analysis by coding the constitutive model into material subroutine VUMAT. Good agreement between the numerical and experimental results shows the accuracy and adaptability of the model.

Nonlinear Finite Element Analysis of Super-Long Pile and Soil Interaction in Soft Soil

2011 ◽  
Vol 201-203 ◽  
pp. 1601-1605 ◽  
Author(s):  
Shang Ping Chen ◽  
Wen Juan Yao ◽  
Sheng Qing Zhu
Keyword(s):  
Finite Element ◽  
Constitutive Model ◽  
Soft Soil ◽  
Three Dimensional ◽  
Nonlinear Behavior ◽  
Element Model ◽  
Element Analysis ◽  
Friction Resistance ◽  
Tip Resistance ◽  
Side Friction

In this paper, a nonlinear three-dimensional finite element model for super-long pile and soil interaction is established. In this model, contact elements are applied to simulate the nonlinear behavior of interaction of super-long pile and soil. A nonlinear elastic constitutive model for concrete is employed to analyze stress-strain relation of pile shaft under the axial load and the Duncan-Chang’s nonlinear constitutive model is used to reflect nonlinear and inelastic properties of soil. The side friction resistance, axial force, pile-tip resistance, and developing trend of soil plastic deformation are obtained and compared with measured results from static load tests. It is demonstrated that a super-long pile has the properties of degradation of side friction resistance and asynchronous action between side and pile-tip resistance, which is different from piles with a short to medium length.

Static and Dynamic Analyses of the LSES Hull Structure

1978 ◽  
Vol 22 (02) ◽  
pp. 110-122
Author(s):  
A. S. Hananel ◽  
E. J. Dent ◽  
E. J. Philips ◽  
S. H. Chang
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Surface Effect ◽  
Three Dimensional ◽  
Element Model ◽  
Finite Element Program ◽  
Hull Structure ◽  
Surface Effect Ship ◽  
Hull Design ◽  
Element Program

To avoid the conservativeness in the large surface-effect ship hull design which results from simplifying assumptions in the stress analysis, the hull structure was analyzed as a three-dimensional elastic body. The NASTRAN finite-element program, level 15.0, was selected for use in this analysis as the most suitable program available. A finite-element model representing the true hull stiffness was used in obtaining the internal load and displacement distributions. The inertia effect of the ship masses was included with each set of static loads. This was done by using the Static Analysis with Inertia Relief solution included in NASTRAN. The stress redistribution around cutouts in the hull was treated in a separate study. The interaction between hull and deckhouse was investigated by attaching a model of the deckhouse onto the hull model, and then solving for the appropriate load conditions. The natural frequencies were obtained using a reduced finite-element model of both the hull and hull/deckhouse combination. A new technique was developed for determining the dynamic stresses and their proper superposition on the static stresses.

A large deformation framework for shape memory polymers: Constitutive modeling and finite element implementation

2012 ◽  
Vol 24 (1) ◽  
pp. 21-32 ◽  
Author(s):  
Mostafa Baghani ◽  
Reza Naghdabadi ◽  
Jamal Arghavani
Keyword(s):  
Finite Element ◽  
Constitutive Model ◽  
Shape Memory ◽  
Finite Deformation ◽  
Deformation Gradient ◽  
Strain Tensor ◽  
Three Dimensional ◽  
Shape Memory Polymers ◽  
Small Strain ◽  
Internal Variables

Shape memory polymers commonly experience both finite deformations and arbitrary thermomechanical loading conditions in engineering applications. This motivates the development of three-dimensional constitutive models within the finite deformation regime. In the present study, based on the principles of continuum thermodynamics with internal variables, a three-dimensional finite deformation phenomenological constitutive model is proposed taking its basis from the recent model in the small strain regime proposed by Baghani et al. (2012). In the constitutive model derivation, a multiplicative decomposition of the deformation gradient into elastic and inelastic stored parts (in each phase) is adopted. Moreover, employing the mixture rule, the Green–Lagrange strain tensor is related to the rubbery and glassy parts. In the constitutive model, the evolution laws for internal variables are derived during both cooling and heating thermomechanical loadings. Furthermore, we present the time-discrete form of the proposed constitutive model in the implicit form. Using the finite element method, we solve several boundary value problems, that is, tension and compression of bars and a three-dimensional beam made of shape memory polymers, and investigate the model capabilities as well as its numerical counterpart. The model is validated by comparing the predicted results with experimental data reported in the literature that shows a good agreement.

scholarly journals A discrete fibre dispersion method for excluding fibres under compression in the modelling of fibrous tissues

2018 ◽  
Vol 15 (138) ◽  
pp. 20170766 ◽  
Author(s):  
Kewei Li ◽  
Ray W. Ogden ◽  
Gerhard A. Holzapfel
Keyword(s):  
Strain Energy ◽  
Dispersion Model ◽  
Substantial Reduction ◽  
Uniaxial Extension ◽  
Biological Tissues ◽  
Fibre Direction ◽  
Fibre Density ◽  
Integration Schemes ◽  
Simple Tension ◽  
Elementary Area

Recently, micro-sphere-based methods derived from the angular integration approach have been used for excluding fibres under compression in the modelling of soft biological tissues. However, recent studies have revealed that many of the widely used numerical integration schemes over the unit sphere are inaccurate for large deformation problems even without excluding fibres under compression. Thus, in this study, we propose a discrete fibre dispersion model based on a systematic method for discretizing a unit hemisphere into a finite number of elementary areas, such as spherical triangles. Over each elementary area, we define a representative fibre direction and a discrete fibre density. Then, the strain energy of all the fibres distributed over each elementary area is approximated based on the deformation of the representative fibre direction weighted by the corresponding discrete fibre density. A summation of fibre contributions over all elementary areas then yields the resultant fibre strain energy. This treatment allows us to exclude fibres under compression in a discrete manner by evaluating the tension–compression status of the representative fibre directions only. We have implemented this model in a finite-element programme and illustrate it with three representative examples, including simple tension and simple shear of a unit cube, and non-homogeneous uniaxial extension of a rectangular strip. The results of all three examples are consistent and accurate compared with the previously developed continuous fibre dispersion model, and that is achieved with a substantial reduction of computational cost.

Muscle and Tendon Tissues: Constitutive Modeling and Computational Issues

2011 ◽  
Vol 78 (4) ◽  
Author(s):  
L. A. Spyrou ◽  
N. Aravas
Keyword(s):  
Constitutive Model ◽  
Three Dimensional ◽  
General Purpose ◽  
Connective Tissues ◽  
Semitendinosus Muscle ◽  
Finite Element Program ◽  
Passive Behavior ◽  
Rate Dependent ◽  
Activation Level ◽  
Element Program

A three-dimensional constitutive model for muscle and tendon tissues is developed. Muscle and tendon are considered as composite materials that consist of fibers and the connective tissues and biofluids surrounding the fibers. The model is nonlinear, rate dependent, and anisotropic due to the presence of the fibers. Both the active and passive behaviors of the muscle are considered. The muscle fiber stress depends on the strain (length), strain-rate (velocity), and the activation level of the muscle, whereas the tendon fiber exhibits only passive behavior and the stress depends only on the strain. Multiple fiber directions are modeled via superposition. A methodology for the numerical implementation of the constitutive model in a general-purpose finite element program is developed. The current scheme is used for either static or dynamic analyses. The model is validated by studying the extension of a squid tentacle during a strike to catch prey. The behavior of parallel-fibered and pennate muscles, as well as the human semitendinosus muscle, is studied.

Numerical Simulation of Polymer Flows in Coat-Hanger Die Using Wagner Constitutive Model

2011 ◽  
Vol 189-193 ◽  
pp. 1941-1945
Author(s):  
Yong Li ◽  
Jian Rong Zheng
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Constitutive Model ◽  
Numerical Solutions ◽  
Flow Behavior ◽  
Computing Time ◽  
Three Dimensional ◽  
Die Design ◽  
Dimensional Simulation ◽  
Element Method

An understanding of flow behavior of polymer melts through a slit die is extremely important for optimizing die design. In this paper numerical simulations have been undertaken for the flow of linear low-density polyethylene through Coat-hanger sheet dies. A new finite element method is proposed to simulate the flow in slit channel using Wagner constitutive model. This is one kind of finite element semi-analytical method by which the velocity distributions in thickness direction is approach by Fourier series. Numerical results of volumetric flow and pressure in coat-hanger dies are given to compare to the three-dimensional simulation using the finite element method. It appears that numerical solutions are as accurate as the complete 3D calculations and the computing time can be saved.

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