scholarly journals General Finite-Element Framework of the Virtual Fields Method in Nonlinear Elasticity

2021 ◽  
Author(s):  
Yue Mei ◽  
Jiahao Liu ◽  
Xu Guo ◽  
Brandon Zimmerman ◽  
Thao D. Nguyen ◽  
...  
Keyword(s):  
Finite Element ◽  
Nonlinear Elasticity ◽  
Soft Tissues ◽  
Model Parameters ◽  
Virtual Fields Method ◽  
Identification Problems ◽  
Unknown Parameters ◽  
Volume Of Interest ◽  
Constitutive Parameters ◽  
Scalar Equations

AbstractThis paper presents a method to derive the virtual fields for identifying constitutive model parameters using the Virtual Fields Method (VFM). The VFM is an approach to identify unknown constitutive parameters using deformation fields measured across a given volume of interest. The general principle for solving identification problems with the VFM is first to derive parametric stress field, where the stress components at any point depend on the unknown constitutive parameters, across the volume of interest from the measured deformation fields. Applying the principle of virtual work to the parametric stress fields, one can write scalar equations of the unknown parameters and solve the obtained system of equations to deduce the values of unknown parameters. However, no rules have been proposed to select the virtual fields in identification problems related to nonlinear elasticity and there are multiple strategies possible that can yield different results. In this work, we propose a systematic, robust and automatic approach to reconstruct the systems of scalar equations with the VFM. This approach is well suited to finite-element implementation and can be applied to any problem provided that full-field deformation data are available across a volume of interest. We also successfully demonstrate the feasibility of the novel approach by multiple numerical examples. Potential applications of the proposed approach are numerous in biomedical engineering where imaging techniques are commonly used to observe soft tissues and where alterations of material properties are markers of diseased states.

scholarly journals General Finite-Element Framework of the Virtual Fields Method in Nonlinear Elasticity

2021 ◽  
Author(s):  
Yue Mei ◽  
Jiahao Liu ◽  
Xu Guo ◽  
Brandon Zimmerman ◽  
Thao D Nguyen ◽  
...  
Keyword(s):  
Finite Element ◽  
Nonlinear Elasticity ◽  
Soft Tissues ◽  
Model Parameters ◽  
Virtual Fields Method ◽  
Identification Problems ◽  
Unknown Parameters ◽  
Volume Of Interest ◽  
Constitutive Parameters ◽  
Scalar Equations

This paper presents a method to derive the virtual fields for identifying constitutive model parameters using the Virtual Fields Method (VFM). The VFM is an approach to identify unknown constitutive parameters using deformation fields measured across a given volume of interest. The general principle for solving identification problems with the VFM is first to derive parametric stress field, where the stress components at any point depend on the unknown constitutive parameters, across the volume of interest from the measured deformation fields. Applying the principle of virtual work to the parametric stress fields, one can write scalar equations of the unknown parameters and solve the obtained system of equations to deduce the values of unknown parameters. However, no rules have been proposed to select the virtual fields in identification problems related to nonlinear elasticity and there are multiple strategies possible that can yield different results. In this work, we propose a systematic, robust and automatic approach to reconstruct the systems of scalar equations with the VFM. This approach is well suited to finite-element implementation and can be applied to any problem provided that full-field deformation data are available across a volume of interest. We also successfully demonstrate the feasibility of the novel approach by multiple numerical examples. Potential applications of the proposed approach are numerous in biomedical engineering where imaging techniques are commonly used to observe soft tissues and where alterations of material properties are markers of diseased states.

scholarly journals The Finite Element Simulation of the Upper Airway of Patients with Moderate and Severe Obstructive Sleep Apnea Hypopnea Syndrome

2017 ◽  
Vol 2017 ◽  
pp. 1-5 ◽  
Author(s):  
Huiping Luo ◽  
Austin Scholp ◽  
Jack J. Jiang
Keyword(s):  
Finite Element ◽  
Obstructive Sleep Apnea ◽  
Sleep Apnea ◽  
Soft Tissue ◽  
Soft Tissues ◽  
Upper Airway ◽  
Model Parameters ◽  
Obstructive Sleep ◽  
Hypopnea Syndrome ◽  
Fluid Solid Interaction

Objectives. To investigate the snoring modes of patients with Obstructive Sleep Apnea Hypopnea Syndrome and to discover the main sources of snoring in soft tissue vibrations. Methods. A three-dimensional finite element model was developed with SolidEdge to simulate the human upper airway. The inherent modal simulation was conducted to obtain the frequencies and the corresponding shapes of the soft tissue vibrations. The respiration process was simulated with the fluid-solid interaction method through ANSYS. Results. The first 6 orders of modal vibration were 12 Hz, 18 Hz, 21 Hz, 22 Hz, 36 Hz, and 39 Hz. Frequencies of modes 1, 2, 4, and 5 were from tongue vibrations. Frequencies of modes 3 and 6 were from soft palate vibrations. Steady pressure distribution and air distribution lines in the upper airway were shown clearly in the fluid-solid interaction simulation results. Conclusions. We were able to observe the vibrations of soft tissue and the modeled airflow by applying the finite element methods. Future studies could focus on improving the soft tissues vibration compliances by adjusting the model parameters. Additionally, more attention should be paid to vibrational components below 20 Hz when performing an acoustic analysis of human snore sounds due to the presence of these frequencies in this model.

scholarly journals Extracting elastic constitutive parameters using the VFM within peridynamics

2019 ◽  
Author(s):  
Rolland Delorme ◽  
Patrick Diehl ◽  
Ilyass Tabiai ◽  
Louis Laberge Lebel ◽  
Martin Levesque
Keyword(s):  
Finite Element ◽  
Displacement Field ◽  
Material Properties ◽  
Noise Analysis ◽  
Image Correlation ◽  
Bending Test ◽  
Virtual Fields Method ◽  
Element Analysis ◽  
Constitutive Parameters

This paper implements the Virtual Fields Method within the ordinary state based peridynamic framework to identify material properties. The key equations derived in this approach are based on the principle of virtual works written under the ordinary state based peridynamic formalism for two-dimensional isotropic linear elasticity. In-house codes including a minimization process have also been developed to implement the method. A three-point bending test and two independent virtual fields arbitrarily chosen are used as a case study throughout the paper. The numerical validation of the virtual fields method has been performed on the case study by simulating the displacement field by finite element analysis. This field has been used to extract the elastic material properties and compared them to those used as input in the finite element model, showing the robustness of the approach. Noise analysis and the effect of the missing displacement fields on the specimen’s edges to simulate digital image correlation limitations have also been studied in the numerical part. This work focuses on pre-damage properties to demonstrate the feasibility of the method and provides a new tool for using full-field measurements within peridynamics with a reduced calculation time as there is no need to compute the displacement field. Future works will deal with damage properties which is the main strength of peridynamics.

Finite element modelling for soft tissues surgery based on nonlinear elasticity behaviour

2004 ◽  
Vol 1268 ◽  
pp. 384-389 ◽  
Author(s):  
Y. Tillier ◽  
A. Paccini ◽  
J. Delotte ◽  
M. Durand-Réville ◽  
J.-L. Chenot
Keyword(s):  
Finite Element ◽  
Nonlinear Elasticity ◽  
Finite Element Modelling ◽  
Soft Tissues ◽  
Element Modelling

scholarly journals Combining Freehand Ultrasound-Based Indentation and Inverse Finite Element Modeling for the Identification of Hyperelastic Material Properties of Thigh Soft Tissues

2020 ◽  
Vol 142 (9) ◽  
Author(s):  
Nolwenn Fougeron ◽  
Pierre-Yves Rohan ◽  
Diane Haering ◽  
Jean-Loïc Rose ◽  
Xavier Bonnet ◽  
...  
Keyword(s):  
Finite Element ◽  
Finite Element Modeling ◽  
Material Properties ◽  
Soft Tissues ◽  
Force Sensor ◽  
Element Analysis ◽  
Element Modeling ◽  
The Mean ◽  
Constitutive Parameters

Abstract Finite element analysis (FEA) is a numerical modeling tool vastly employed in research facilities to analyze and predict load transmission between the human body and a medical device, such as a prosthesis or an exoskeleton. Yet, the use of finite element modeling (FEM) in a framework compatible with clinical constraints is hindered by, among others, heavy and time-consuming assessments of material properties. Ultrasound (U.S.) imaging opens new and unique opportunities for the assessment of in vivo material properties of soft tissues. Confident of these advances, a method combining a freehand U.S. probe and a force sensor was developed in order to compute the hyperelastic constitutive parameters of the soft tissues of the thigh in both relaxed (R) and contracted (C) muscles' configurations. Seven asymptomatic subjects were included for the experiment. Two operators in each configuration performed the acquisitions. Inverse FEM allowed for the optimization of an Ogden's hyperelastic constitutive model of soft tissues of the thigh in large displacement. The mean shear modulus identified for configurations R and C was, respectively, 3.2 ± 1.3 kPa and 13.7 ± 6.5 kPa. The mean alpha parameter identified for configurations R and C was, respectively, 10 ± 1 and 9 ± 4. An analysis of variance showed that the configuration had an effect on constitutive parameters but not on the operator.

On the Development and Computational Implementation of Complex Constitutive Models and Parameters’ Identification Procedures

2013 ◽  
Vol 554-557 ◽  
pp. 936-948 ◽  
Author(s):  
Tiago Jordão Grilo ◽  
Nelson Souto ◽  
Robertt Angelo Fontes Valente ◽  
António Andrade-Campos ◽  
Sandrine Thuillier ◽  
...  
Keyword(s):  
Finite Element ◽  
Aluminum Alloys ◽  
Constitutive Model ◽  
Constitutive Models ◽  
High Strength ◽  
Model Parameters ◽  
Finite Element Code ◽  
Mapping Procedure ◽  
Computational Implementation ◽  
Constitutive Parameters

Nowadays, the automotive industry has focused its attention to weight reduction of the vehicles to overcome environmental restrictions. For this purpose, new materials, namely, advanced high strength steels and aluminum alloys have emerged. These materials combine good formability and ductility, with a high tensile strength due to a multi-phase structure (for the steel alloys) and reduced weight (for the aluminum alloys). As a consequence of their advanced performances, complex constitutive models are required in order to describe the various mechanical features involved. In this work, the anisotropic plastic behavior of dual-phase steels and high strength aluminum alloys is described by the non-quadratic Yld2004-18p yield criterion, combined with a mixed isotropic-nonlinear kinematic hardening law. This phenomenological model allows for an accurate description of complex anisotropy and Bauschinger effects of the materials, which are essential for a reliable prediction of deep drawing and springback results using numerical simulations. To this end, an efficient computational implementation is needed, altogether with an inverse methodology to properly identify the constitutive parameters to be used as numerical simulation input. The constitutive model is implemented in the commercial finite element code ABAQUS as a user-defined material subroutine (UMAT). A multi-stage return mapping procedure, which utilizes the control of the potential residual, is implemented to integrate the constitutive equations at any instant of time (pseudo-time), during a deformation process. Additionally, an inverse methodology is developed to identify the constitutive model parameters of the studied alloys. The identification framework is based on an interface program that links an optimization software and the commercial finite element code. This methodology compares experimental data with the respective results numerically obtained. The implemented optimization process aims to minimize an objective function, which defines the difference between experimental and numerical results using the Levenberg-Marquardt gradient-based optimization method. The proposed integrated approach is validated in a number of benchmarks in sheet metal forming, including monotonic and cyclic loading, with the goal to infer about the modelling of anisotropic effects.

Representation of bolted joints in a structure using finite element modelling and model updating

2020 ◽  
Vol 14 (3) ◽  
pp. 7141-7151 ◽  
Author(s):  
R. Omar ◽  
M. N. Abdul Rani ◽  
M. A. Yunus
Keyword(s):  
Finite Element ◽  
Dynamic Behaviour ◽  
Model Updating ◽  
Complex Structure ◽  
Bolted Joints ◽  
Model Parameters ◽  
Fe Model ◽  
Bolted Joint ◽  
Fe Modelling ◽  
Joint Structure

Efficient and accurate finite element (FE) modelling of bolted joints is essential for increasing confidence in the investigation of structural vibrations. However, modelling of bolted joints for the investigation is often found to be very challenging. This paper proposes an appropriate FE representation of bolted joints for the prediction of the dynamic behaviour of a bolted joint structure. Two different FE models of the bolted joint structure with two different FE element connectors, which are CBEAM and CBUSH, representing the bolted joints are developed. Modal updating is used to correlate the two FE models with the experimental model. The dynamic behaviour of the two FE models is compared with experimental modal analysis to evaluate and determine the most appropriate FE model of the bolted joint structure. The comparison reveals that the CBUSH element connectors based FE model has a greater capability in representing the bolted joints with 86 percent accuracy and greater efficiency in updating the model parameters. The proposed modelling technique will be useful in the modelling of a complex structure with a large number of bolted joints.

scholarly journals Simulation of thermal cycle aging process on fiber-reinforced polymers by extended finite element method

2017 ◽  
Vol 52 (14) ◽  
pp. 1947-1958 ◽  
Author(s):  
Sergio González ◽  
Gianluca Laera ◽  
Sotiris Koussios ◽  
Jaime Domínguez ◽  
Fernando A Lasagni
Keyword(s):  
Finite Element ◽  
Degradation Process ◽  
Damage Mechanism ◽  
Fiber Reinforced Polymers ◽  
Model Parameters ◽  
Suitable Model ◽  
Fiber Reinforced ◽  
Aging Effects ◽  
Extended Finite Element ◽  
Element Analysis

The simulation of long life behavior and environmental aging effects on composite materials are subjects of investigation for future aerospace applications (i.e. supersonic commercial aircrafts). Temperature variation in addition to matrix oxidation involves material degradation and loss of mechanical properties. Crack initiation and growth is the main damage mechanism. In this paper, an extended finite element analysis is proposed to simulate damage on carbon fiber reinforced polymer as a consequence of thermal fatigue between −50℃ and 150℃ under atmospheres with different oxygen content. The interphase effect on the degradation process is analyzed at a microscale level. Finally, results are correlated with the experimental data in terms of material stiffness and, hence, the most suitable model parameters are selected.

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