Finite Element-Based Virtual Fields Method with Pseudo-Real Deformation Fields for Identifying Constitutive Parameters

2021 ◽  
pp. 111204
Author(s):  
Chanyang Kim ◽  
Myoung-Gyu Lee
Keyword(s):  
Finite Element ◽  
Virtual Fields Method ◽  
Constitutive Parameters ◽  
Real Deformation

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.

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 Biaxial estimation of biomechanical constitutive parameters of passive porcine sclera soft tissue

2021 ◽  
Author(s):  
Zwelihle Ndlovu ◽  
Dawood Desai ◽  
Thanyani Pandelani ◽  
Harry Ngwangwa ◽  
Fulufhelo Nemavhola
Keyword(s):  
Finite Element ◽  
Soft Tissue ◽  
Finite Element Model ◽  
Test Data ◽  
Element Model ◽  
Finite Element Models ◽  
Anisotropic Model ◽  
Material Models ◽  
Material Parameters ◽  
Constitutive Parameters

This study assesses the modelling capabilities of four constitutive hyperplastic material models to fit the experimental data of the porcine sclera soft tissue. It further estimates the material parameters and discusses their applicability to a finite element model by examining the statistical dispersion measured through the standard deviation. Fifteen sclera tissues were harvested from porcine’ slaughtered at an abattoir and were subjected to equi-biaxial testing. The results show that all the four material models yielded very good correlations at correlations above 96 %. The polynomial (anisotropic) model gave the best correlation of 98 %. However, the estimated material parameters varied widely from one test to another such that there would be needed to normalise the test data to avoid long optimisation processes after applying the average material parameters to finite element models. However, for application of the estimated material parameters to finite element models, there would be needed to consider normalising the test data to reduce the search region for the optimisation algorithms. Although the polynomial (anisotropic) model yielded the best correlation, it was found that the Choi-Vito had the least variation in the estimated material parameters thereby making it an easier option for application of its material parameters to a finite element model and also requiring minimum effort in the optimisation procedure. For the porcine sclera tissue, it was found that the anisotropy more influenced by the fiber-related properties than the background material matrix related properties.

scholarly journals Optimized Polynomial Virtual Fields Method for Constitutive Parameters Identification of Orthotropic Bimaterials

2020 ◽  
Vol 2020 ◽  
pp. 1-27
Author(s):  
Xueyi Ma ◽  
Yu Wang ◽  
Jian Zhao
Keyword(s):  
Relative Error ◽  
Numerical Experiments ◽  
A Priori ◽  
Heterogeneous Materials ◽  
Image Correlation ◽  
Constitutive Parameter ◽  
Virtual Fields Method ◽  
Bending Load ◽  
Virtual Field ◽  
Constitutive Parameters

Heterogeneous materials are widely applied in many fields. Owing to the spatial variation of its constitutive parameters, the mechanical characterization of heterogeneous materials is very important. The virtual fields method has been used to identify the constitutive parameters of materials. However, there is a limitation: constitutive parameters of one material have to be a priori; then, constitutive parameters of the other one can be identified. Aiming at this limitation, this article presents a method to identify the constitutive parameters of heterogeneous orthotropic bimaterials under the condition that constitutive parameters of both materials are all unknown from a single test. A constitutive parameter identification method of orthotropic bimaterials based on optimized virtual field and digital image correlation is proposed. The feasibility of this method is verified by simulating the deformation fields of a two-layer material under three-point bending load. The results of numerical experiments with FEM simulations show that the weighted relative error of the constitutive parameter is less than 1%. The results suggest that the variation coefficient-to-noise ratio can perform a priori evaluation of a confidence interval on the identified stiffness components. The results of numerical experiments with DIC simulations show that the weighted relative error is 1.44%, which is due to the noise in the strain data calculated by DIC method.

An Elastic/Viscoplastic Finite Element Model for Predicting Polymerization Stresses in Light-Activated Dental Composites

2003 ◽  
Author(s):  
Gayle A. Laughlin ◽  
John L. Williams ◽  
J. David Eick
Keyword(s):  
Finite Element ◽  
Element Model ◽  
Numerical Approach ◽  
Mechanical Analysis ◽  
Dental Composite ◽  
Time Dependent ◽  
Dental Composites ◽  
Cavity Preparation ◽  
Constitutive Parameters ◽  
Perzyna's Theory

The purpose of this paper is to apply a finite deformation, elastic/viscoplastic approach to predict curing stresses in three light-cured dental composites, using Perzyna’s theory. Time-dependent constitutive parameters were obtained from mercury dilatometry, dynamic mechanical analysis and constrained shrinkage strerss testing. The numerical approach was verified by using the results of an experiment on a simple aluminum tooth model of a cavity preparation that was bulk-filled with light-cured dental composite restorative materials. The numerically predicted strain patterns were similar to those seen experimentally for the three different dental composites.

scholarly journals The Virtual Fields Method for Extracting Constitutive Parameters From Full-Field Measurements: a Review

Strain ◽  
2008 ◽  
Vol 42 (4) ◽  
pp. 233-253 ◽  
Author(s):  
M. Grédiac ◽  
F. Pierron ◽  
S. Avril ◽  
E. Toussaint
Keyword(s):  
Field Measurements ◽  
Virtual Fields Method ◽  
Full Field ◽  
Constitutive Parameters

Nonlinear Material Parameter Estimation Using Inverse Finite Element Analysis

2007 ◽  
Author(s):  
Jeffrey E. Bischoff
Keyword(s):  
Finite Element ◽  
Boundary Conditions ◽  
Nonlinear Material ◽  
Material Structure ◽  
In Vitro Tests ◽  
Experimental Conditions ◽  
Element Analysis ◽  
Material Parameters ◽  
Constitutive Parameters

Constitutive parameters for biological materials are ideally regressed against data from well-designed experiments in which the loading and boundary conditions give rise to a homogeneous region of deformation. Such conditions may exist for healthy tissue within the context of in vitro tests, but rarely are met when attempting to measure parameters physiologically or noninvasively, due to complex boundary conditions or heterogeneous material structure and properties. The ability to estimate parameters in these situations is essential in many clinically relevant studies, including determination of tendon/ligament parameters in whole knee studies, non-destructive evaluation of evolving material parameters in laboratory studies, and estimation of heterogeneous parameters due to local normal or pathologic disruptions in tissue microstructure. In such cases, computational algorithms must be used to regress material parameters for a given constitutive model against the available data, in which the experimental conditions are modeled as accurately as possible without significant regard to complexity. The work presented here is focused on development of an iterative, inverse finite element (FE) algorithm for estimation of material parameters from experimental data obtained from tests with nonlinear complexities from contact, large deformations, and constitutive models.

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