A Study on a Grade-One Type of Hypo-Elastic Models

2014 ◽  
Author(s):  
S. Alireza Momeni ◽  
Mohsen Asghari
Keyword(s):  
Constitutive Models ◽  
Specific Model ◽  
Elasticity Tensor ◽  
Elastic Model ◽  
Cauchy Stress ◽  
Spin Tensor ◽  
Positive Real ◽  
Corotational Rate ◽  
Deformation Rate Tensor ◽  
Grade One

In Hypo-elastic constitutive models an objective rate of the Cauchy stress tensor is expressed in terms of the current state of the stress and the deformation rate tensor D in a way that the dependency on the latter is a homogeneously linear one. In this work, a type of grade-one hypo-elastic models (i.e. models with linear dependency of the hypo-elasticity tensor on the stress) is considered for isotropic materials based on the objective corotational rates of stress. A positive real parameter denoted by n is involved in the considered type. Different values can be selected for this parameter, each selection leads to a specific model within the class of grade-one hypo-elasticity. The spin of the associated corotational rate is also dependent on the parameter n. In the special case of n=0, the corresponding hypo-elastic model reduces to a grade-zero one with the logarithmic rate of stress; noting that this rate is a corotational rate associated with the logarithmic spin tensor. Moreover, by choosing n=2, the model reduces to a grade-one hypo-elastic model with the Jaumann rate, i.e. the corotational rate associated with the vorticity spin tensor. As case studies, the simple shear problem is investigated with utilizing the considered type of hypo-elastic models with various values for parameter n, and the curves for the stress-shear response are depicted.

scholarly journals Finite element modelling of an energy-geomembrane underground pumped hydroelectric energy storage system

2020 ◽  
Vol 205 ◽  
pp. 07001
Author(s):  
Hans Henning Stutz ◽  
Peter Norlyk ◽  
Kenneth Sørensen ◽  
Lars Vabbersgaard Andersen ◽  
Kenny Kataoka Sørensen ◽  
...  
Keyword(s):  
Finite Element ◽  
Energy Storage ◽  
Storage System ◽  
Constitutive Models ◽  
Energy System ◽  
Energy Storage System ◽  
Elastic Model ◽  
Hydroelectric Energy ◽  
Linear Elastic ◽  
Soil Behaviour

The increasing need for energy storage technology has led to a massive interest in novel energy storage methods. The energy geomembrane system is such a novel energy storage method. The concept of the system is briefly introduced, and a holistic numerical model of the system is presented. The model uses advanced finite-element techniques to model the energy storage system using fluid cavity elements. The developed geomembrane energy system is modelled with different constitutive models to represent the soil behaviour: a linear elastic model, a nonlinear Mohr-Coulomb model, and a hypoplastic constitutive model. The consequences of these different models on the results are studied. Hereby, the focus is the first inflation and deflation cycle of the system.

scholarly journals Comparison between Duncan and Chang’s EB Model and the Generalized Plasticity Model in the Analysis of a High Earth-Rockfill Dam

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Weixin Dong ◽  
Liming Hu ◽  
Yu Zhen Yu ◽  
He Lv
Keyword(s):  
Constitutive Models ◽  
Elastic Model ◽  
Plasticity Model ◽  
Rockfill Dam ◽  
Generalized Plasticity ◽  
Rockfill Materials ◽  
Confining Pressures ◽  
Mechanical Behaviours ◽  
Nonlinear Elastic ◽  
Relationship Of

Nonlinear elastic model and elastoplastic model are two main kinds of constitutive models of soil, which are widely used in the numerical analyses of soil structure. In this study, Duncan and Chang's EB model and the generalized plasticity model proposed by Pastor, Zienkiewicz, and Chan was discussed and applied to describe the stress-strain relationship of rockfill materials. The two models were validated using the results of triaxial shear tests under different confining pressures. The comparisons between the fittings of models and test data showed that the modified generalized plasticity model is capable of simulating the mechanical behaviours of rockfill materials. The modified generalized plasticity model was implemented into a finite element code to carry out static analyses of a high earth-rockfill dam in China. Nonlinear elastic analyses were also performed with Duncan and Chang's EB model in the same program framework. The comparisons of FEM results andin situmonitoring data showed that the modified PZ-III model can give a better description of deformation of the earth-rockfill dam than Duncan and Chang’s EB model.

Fractional Derivative Constitutive Models for Finite Deformation of Viscoelastic Materials

2015 ◽  
Vol 10 (6) ◽  
Author(s):  
Masataka Fukunaga ◽  
Nobuyuki Shimizu
Keyword(s):  
Fractional Derivative ◽  
Stress Tensor ◽  
Finite Deformation ◽  
Dynamical Behavior ◽  
Strain Tensor ◽  
Constitutive Models ◽  
Cauchy Stress ◽  
Viscoelastic Materials ◽  
Kirchhoff Stress Tensor ◽  
Biot Stress

A methodology to derive fractional derivative constitutive models for finite deformation of viscoelastic materials is proposed in a continuum mechanics treatment. Fractional derivative models are generalizations of the models given by the objective rates. The method of generalization is applied to the case in which the objective rate of the Cauchy stress is given by the Truesdell rate. Then, a fractional derivative model is obtained in terms of the second Piola–Kirchhoff stress tensor and the right Cauchy-Green strain tensor. Under the assumption that the dynamical behavior of the viscoelastic materials comes from a complex combination of elastic and viscous elements, it is shown that the strain energy of the elastic elements plays a fundamental role in determining the fractional derivative constitutive equation. As another example of the methodology, a fractional constitutive model is derived in terms of the Biot stress tensor. The constitutive models derived in this paper are compared and discussed with already existing models. From the above studies, it has been proved that the methodology proposed in this paper is fully applicable and effective.

Constitutive Properties Determination of Human Cranium by an Experimental–Computational Modal Analysis

2019 ◽  
Vol 142 (1) ◽  
Author(s):  
Ashkan Eslaminejad ◽  
Mohamad Hosseini-Farid ◽  
Mariusz Ziejewski ◽  
Ghodrat Karami
Keyword(s):  
Tensile Test ◽  
Modal Analysis ◽  
Constitutive Models ◽  
Elastic Model ◽  
Fe Model ◽  
Strain Rates ◽  
Test Results ◽  
Human Skull ◽  
Linear Elastic ◽  
Constitutive Parameters

Abstract In this paper, we identified the material constitutive parameters of the human skull from reported tensile test results. Initially, we applied both linear-elastic and Mooney–Rivlin nonlinear hyperelastic constitutive models to the available tensile test data at different strain rates of 0.005, 0.10, 10, and 150 1/sec. It was shown that the suggested hyperelastic model fitted the test results with higher accuracy in comparison with the linear-elastic model. In the next step, the experimental modal analysis was carried out through roving hammer-impact tests on a dried human skull. The first four natural frequencies of the skull were measured to be 496, 543, 1250, and 1287 Hz, and these values were verified by the modal assurance criterion. Then, a 3D finite element (FE) model of that human skull was created by a 3D scanner and discretized to carry out a computational modal analysis. The performance of the determined material properties for the human skull from both linear and hyperelastic material models was evaluated using FE modal analysis. The calculated modal frequencies were then compared to the experimentally measured frequencies. It was shown that the material parameters from both the linear and hyperelastic constitutive models obtained at a strain rate of 0.10 1/sec, provided the best performance in computational modal analysis with minimum deviations relative to the experimental results. These results confer a better understanding of the human skull behavior among different strain rates, which could increase the accuracy of nonlinearity dynamic simulations on the skull.

A Large Strain Hyperelastic Constitutive Model for Intraluminal Thrombus From Abdominal Aortic Aneurysm

1999 ◽  
Author(s):  
David H. J. Wang ◽  
Michel S. Makaroun ◽  
Marshall W. Webster ◽  
David A. Vorp
Keyword(s):  
Abdominal Aortic Aneurysm ◽  
Aortic Aneurysm ◽  
Constitutive Model ◽  
Large Strain ◽  
Constitutive Models ◽  
Wall Stress ◽  
Accurate Estimation ◽  
Elastic Model ◽  
Intraluminal Thrombus ◽  
Abdominal Aortic

Abstract Rupture of abdominal aortic aneurysm (AAA) occurs when the wall stress acting on the dilated aortic wall exceeds the strength of the tissue. Therefore, accurate estimation of the wall stress distribution in AAA may be a clinically useful tool to predict their rupture. A majority of AAA contains a laminated, stationary, intraluminal thrombus (ILT) (Harter et al., 1982). Previous investigations have shown that ILT may significantly alter the wall stress acting on AAA (Inzoli et al., 1993; Mower et al., 1997; Stringfellow et al., 1987; Vorp et al., 1998; Di Martino et al., 1998). However, all of those studies used a simplified linear elastic model for ILT. This is inappropriate and can lead to inaccuracies since both AAA wall and contained ILT undergo large deformation during the cardiac cycle (Vorp et al., 1996). Therefore, to accomplish accurate stress analysis of AAA, appropriate constitutive models for both the wall and ILT are necessary. Our group has previously proposed a finite strain constitutive model for the AAA wall (Raghavan et al., in press). The purpose of this work was to derive a more suitable constitutive model and the associated mechanical properties for the ILT within AAA.

A Finite Element Implementation of Knowles Stored-Energy Function: Theory, Coding and Applications

2011 ◽  
Vol 58 (3) ◽  
pp. 319-346 ◽  
Author(s):  
Cyprian Suchocki
Keyword(s):  
Finite Element ◽  
Energy Function ◽  
Function Theory ◽  
Constitutive Models ◽  
Elasticity Tensor ◽  
Stored Energy ◽  
Energy Potential ◽  
Hyperelastic Materials ◽  
Finite Element Implementation ◽  
Living Tissues

A Finite Element Implementation of Knowles Stored-Energy Function: Theory, Coding and Applications This paper contains the full way of implementing a user-defined hyperelastic constitutive model into the finite element method (FEM) through defining an appropriate elasticity tensor. The Knowles stored-energy potential has been chosen to illustrate the implementation, as this particular potential function proved to be very effective in modeling nonlinear elasticity within moderate deformations. Thus, the Knowles stored-energy potential allows for appropriate modeling of thermoplastics, resins, polymeric composites and living tissues, such as bone for example. The decoupling of volumetric and isochoric behavior within a hyperelastic constitutive equation has been extensively discussed. An analytical elasticity tensor, corresponding to the Knowles stored-energy potential, has been derived. To the best of author's knowledge, this tensor has not been presented in the literature yet. The way of deriving analytical elasticity tensors for hyperelastic materials has been discussed in detail. The analytical elasticity tensor may be further used to develop visco-hyperelastic, nonlinear viscoelastic or viscoplastic constitutive models. A FORTRAN 77 code has been written in order to implement the Knowles hyperelastic model into a FEM system. The performance of the developed code is examined using an exemplary problem.

The Role of Flow-Independent Viscoelasticity in the Biphasic Tensile and Compressive Responses of Articular Cartilage

2001 ◽  
Vol 123 (5) ◽  
pp. 410-417 ◽  
Author(s):  
Chun-Yuh Huang ◽  
Van C. Mow ◽  
Gerard A. Ateshian
Keyword(s):  
Articular Cartilage ◽  
Viscoelastic Model ◽  
Constitutive Models ◽  
Constitutive Law ◽  
Molecular Organization ◽  
Solid Matrix ◽  
Uniaxial Tensile ◽  
Elastic Model ◽  
Compressive Properties ◽  
Stress Strain

A long-standing challenge in the biomechanics of connective tissues (e.g., articular cartilage, ligament, tendon) has been the reported disparities between their tensile and compressive properties. In general, the intrinsic tensile properties of the solid matrices of these tissues are dictated by the collagen content and microstructural architecture, and the intrinsic compressive properties are dictated by their proteoglycan content and molecular organization as well as water content. These distinct materials give rise to a pronounced and experimentally well-documented nonlinear tension–compression stress–strain responses, as well as biphasic or intrinsic extracellular matrix viscoelastic responses. While many constitutive models of articular cartilage have captured one or more of these experimental responses, no single constitutive law has successfully described the uniaxial tensile and compressive responses of cartilage within the same framework. The objective of this study was to combine two previously proposed extensions of the biphasic theory of Mow et al. [1980, ASME J. Biomech. Eng., 102, pp. 73–84] to incorporate tension–compression nonlinearity as well as intrinsic viscoelasticity of the solid matrix of cartilage. The biphasic-conewise linear elastic model proposed by Soltz and Ateshian [2000, ASME J. Biomech. Eng., 122, pp. 576–586] and based on the bimodular stress-strain constitutive law introduced by Curnier et al. [1995, J. Elasticity, 37, pp. 1–38], as well as the biphasic poroviscoelastic model of Mak [1986, ASME J. Biomech. Eng., 108, pp. 123–130], which employs the quasi-linear viscoelastic model of Fung [1981, Biomechanics: Mechanical Properties of Living Tissues, Springer-Verlag, New York], were combined in a single model to analyze the response of cartilage to standard testing configurations. Results were compared to experimental data from the literature and it was found that a simultaneous prediction of compression and tension experiments of articular cartilage, under stress-relaxation and dynamic loading, can be achieved when properly taking into account both flow-dependent and flow-independent viscoelasticity effects, as well as tension–compression nonlinearity.

Elastic-Plastic Modeling of Hardening Materials Using a Corotational Rate Based on the Plastic Spin Tensor

2007 ◽  
Author(s):  
Kamyar Ghavam ◽  
Reza Naghdabadi
Keyword(s):  
Kinematic Hardening ◽  
Deformation Gradient ◽  
Isotropic Hardening ◽  
Strain Rate Tensor ◽  
Spin Tensor ◽  
Plastic Spin ◽  
Elastic Plastic ◽  
Proposed Model ◽  
Corotational Rate ◽  
Shear Problem

In this paper based on the multiplicative decomposition of the deformation gradient, the plastic spin tensor and the plastic spin corotational rate are introduced. Using this rate (and also log-rate), an elastic-plastic constitutive model for hardening materials are proposed. In this model, the Armstrong-Frederick kinematic hardening and the isotropic hardening equations are used. The proposed model is solved for the simple shear problem with the material properties of the stainless steel SUS 304. The results are compared with those obtained experimentally by Ishikawa [1]. This comparison shows a good agreement between the results of proposed theoretical model and the experimental data. As another example, the Prager kinematic hardening equation is used. In this case, the stress results are compared with those obtained by Bruhns et al. [2], in which they used the additive decomposition of the strain rate tensor.

scholarly journals Rheology-Informed Neural Networks (RhINNs) for forward and inverse metamodelling of complex fluids

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Mohammadamin Mahmoudabadbozchelou ◽  
Safa Jamali
Keyword(s):  
Neural Networks ◽  
Constitutive Equations ◽  
Automatic Differentiation ◽  
Complex Fluids ◽  
Shear Banding ◽  
Constitutive Models ◽  
Soft Materials ◽  
Specific Model ◽  
Model Parameters ◽  
Rate Dependent

AbstractReliable and accurate prediction of complex fluids’ response under flow is of great interest across many disciplines, from biological systems to virtually all soft materials. The challenge is to solve non-trivial time and rate dependent constitutive equations to describe these structured fluids under various flow protocols. We present Rheology-Informed Neural Networks (RhINNs) for solving systems of Ordinary Differential Equations (ODEs) adopted for complex fluids. The proposed RhINNs are employed to solve the constitutive models with multiple ODEs by benefiting from Automatic Differentiation in neural networks. In a direct solution, the RhINNs platform accurately predicts the fully resolved solution of constitutive equations for a Thixotropic-Elasto-Visco-Plastic (TEVP) complex fluid for a series of flow protocols. From a practical perspective, an exhaustive list of experiments are required to identify model parameters for a multi-variant constitutive TEVP model. RhINNs are found to learn these non-trivial model parameters for a complex material using a single flow protocol, enabling accurate modeling with limited number of experiments and at an unprecedented rate. We also show the RhINNs are not limited to a specific model and can be extended to include various models and recover complex manifestations of kinematic heterogeneities and transient shear banding of thixotropic fluids.

Applicability of Duncan-Chang Model and its Modified Versions to Methane Hydrate-Bearing Sands

2011 ◽  
Vol 347-353 ◽  
pp. 3384-3387 ◽  
Author(s):  
Ju Hua Xiong ◽  
Xiao Yong Kou ◽  
Fang Liu ◽  
Ming Jing Jiang
Keyword(s):  
Methane Hydrate ◽  
Constitutive Models ◽  
Constitutive Law ◽  
Triaxial Tests ◽  
Elastic Model ◽  
Clathrate Compound ◽  
Constitutive Response ◽  
Nonlinear Elastic ◽  
Hydrate Bearing Sediments ◽  
Chang Model

Methane hydrate is ice-like clathrate compound that attracts global attention due to its huge potential as a future energy source. The constitutive law of methane hydrate-bearing sediments remains unknown and becomes a barrier in sustainable exploitation of methane hydrate from marine sediments. The Duncan-Change model is a nonlinear elastic model which was widely accepted by the geotechnical community in approximating the constitutive response of geo-materials. This model and its evolved versions were employed in this study to model the stress-strain response observed in triaxial tests on methane hydrate-bearing sands. Duncan-Chang type models capture well the strain hardening behaviors. However, they fall short of incorporating the dependency of temperature and saturation degree of methane hydrate, which have to be taken into account in future constitutive models of methane hydrate-bearing deposits.

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