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.

Elastoplastic Analysis of a Miniature Circular Disk Bending Specimen

2008 ◽  
Vol 130 (4) ◽  
Author(s):  
Vishnu Verma ◽  
A. K. Ghosh ◽  
G. Behera ◽  
Kamal Sharma ◽  
R. K. Singh
Keyword(s):  
Finite Element ◽  
Analytical Solutions ◽  
Material Properties ◽  
Finite Element Solution ◽  
Bending Test ◽  
Experimental Result ◽  
Strain Hardening Exponent ◽  
Plastic Behavior ◽  
Element Solution ◽  
Element Analysis

The miniature disk bending test is used to evaluate the mechanical behavior of irradiated materials and their properties (e.g., yield stress and strain hardening exponent) to determine mainly ductility loss in steel due to irradiation from the load-deflection behavior of the disk specimen. In the miniature disk bending machine the specimen is firmly held between the two horizontal jaws of punch, and an indentor with a spherical ball travels vertically. Analytical solutions for large amplitude plastic deformation become rather unwieldy. Hence, a finite element analysis has been carried out. The finite element model considers contact between the indentor and test specimen, friction between various pairs of surfaces, and elastic plastic behavior. This paper presents the load versus deflection results of a parametric study where the values of various parameters defining the material properties have been varied by ±10% around the base values. Some well-known analytical solutions to this problem have also been considered. It is seen that the deflection obtained by analytical elastic bending theory is significantly lower than that obtained by the elastoplastic finite element solution at relatively small values of load. The finite element solution has been compared with one experimental result and values are in reasonably good agreement. With these results it will be possible to determine the material properties from the experimentally obtained values of load and deflection.

Elasto-Plastic Analysis of a Miniature Circular Disk Bending Specimen

2006 ◽  
Author(s):  
Vishnu Verma ◽  
A. K. Ghosh ◽  
G. Behera ◽  
Kamal Sharma ◽  
R. K. Singh
Keyword(s):  
Plastic Deformation ◽  
Finite Element ◽  
Yield Stress ◽  
Material Properties ◽  
Stable Solution ◽  
Bending Test ◽  
Uniaxial Tensile ◽  
Uniaxial Tensile Test ◽  
Plastic Behavior ◽  
Element Analysis

Miniature disk bending test is used to evaluate the mechanical behavior of irradiated materials and its properties — mainly ductility loss due to irradiation in steel. In Miniature Disk Bending Machine the specimen is firmly held between the two horizontal jaws of punch, and an indentor with spherical ball travels vertically. Researchers have observed reasonable correlations between values of the yield stress, strain hardening and ultimate tensile strength estimated from this test and mechanical properties determined from the uniaxial tensile test. Some methods for the analysis of miniature disk bending, proposed by various authors have been discussed in the paper. It is difficult to distinguish between the regimes of elastic and plastic deformation since local plastic deformation occurs for very small values of load when the magnitude of spatially averaged stress will be well below the yield stress. Also, the analytical solution for large amplitude, plastic deformation becomes rather unwieldy. Hence a finite element analysis has been carried out. The finite element model, considers contact between the indentor and test specimen, friction between various pairs of surfaces and elastic plastic behavior. The load is increased in steps and converged solution has been obtained and analysis terminated at a load beyond which a stable solution cannot be obtained. A sensitivity study has been carried out by varying the various parameters defining the material properties by ±10% around the base values. This study has been carried out to generate a data base for the load-deflection characteristics of similar materials from which the material properties can be evaluated by an inverse calculation. It is seen that the deflection obtained by analytical elastic bending theory is significantly lower than that obtained by the elasto-plastic finite element solution at relatively small values of load. The FE solution and experimental results are in reasonably good agreement.

scholarly journals Identification of Materials Properties Using Displacement Field Measurement

2011 ◽  
Vol 482 ◽  
pp. 57-65 ◽  
Author(s):  
Marina Fazzini ◽  
Olivier Dalverny ◽  
Sébastien Mistou
Keyword(s):  
Finite Element ◽  
Displacement Field ◽  
Model Updating ◽  
Virtual Work ◽  
Field Measurements ◽  
Element Model ◽  
Field Method ◽  
Element Analysis ◽  
Virtual Field ◽  
Constitutive Parameters

The aim of this work is to identify parameters driving constitutive equations of materials with displacement field measurements carried out by image stereo-correlation during an unidirectional tensile test. We evaluate two identification techniques. The first one is the virtual fields method which consists in writing the principle of virtual work with particular virtual fields. It is generally used in the case of linear elasticity and it requires a perfect knowledge of the model in terms of boundary condition since the virtual fields used must be kinematically admissible. This method allows to determine parameters by a direct and fast calculation, without iterations. The second method is the finite element model updating method. It consists in finding constitutive parameters that achieve the best match between finite element analysis quantities and their experimental counterparts. This method is more adaptable than the virtual field method but it needs to spend more calculation time.

Experimental Study on Displacement and Strain Distributions of Bone Model with Dental Implant

2011 ◽  
Vol 83 ◽  
pp. 73-77 ◽  
Author(s):  
Yasuyuki Morita ◽  
Yasuyuki Matsushita ◽  
Mitsugu Todo ◽  
Kiyoshi Koyano
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Dental Implants ◽  
Cancellous Bone ◽  
Material Properties ◽  
Alveolar Bone ◽  
Image Correlation ◽  
Element Analysis ◽  
Deformation Distribution ◽  
Natural Tooth

For normal healthy teeth, the percussive energy generated by mastication is attenuated by the periodontal ligament at the healthy bone/natural tooth interface. However, when a natural tooth must be replaced by an implant because of damage or disease, the ligament is lost and the implant will transmit the percussive forces to the bone directly. Studies have evaluated the deformation distribution of the alveolar bone in the vicinity of implants using finite element analysis and photoelasticity. However, finite element analysis requires clinical verification or a determination of material properties, and photoelastic materials generally have material properties and structure quite different from those of actual bone. Therefore, this study examined the deformation distribution around dental implants in cortical/cancellous bone experimentally using sawbone cortical/cancellous bone models. Dental implants were placed in the bone models and the displacement distribution was measured using the digital image correlation method, and the strain distribution was visualized under a compressive load that simulated the occlusion force.

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.

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