Stress-strain Definition Research Articles

Optimisation of FE parameters used in fine numerical modelling of steel T-stub elements

In steel frame buildings the role of the beam-to-column connection is crucial for assuring structural integrity, and due to their complexity and non-linear behaviour, the bolted configurations of this type of connection are usually the most vulnerable elements of a building. In order to assess the behaviour of a bolted steel connection, the simplified model of the equivalent T-stub is used. Based on previous experimental studies on a parametric set of T-stubs, the aim of this study is to optimise a numerical model in order to validate the experimental data and produce a fully calibrated finite element model,created with Abaqus/Explicit FE software package. To model properly the nonlinear behaviour of the component, an analysis of the properties of the model was conducted regarding the finite elements properties, analysis properties and discretization. The solid finite element properties considered were such as the number of nodes, integration, contact and true stress-strain material definition, including damage criteria. In this context, the assembly was subjected to a transient quasi-static explicit FE analysis using mass-scaling features. The results are expressed by comparison of Force-displacement curves obtain via numerical analysis and experimental testing.

Numerical modeling of technological stresses in crystallizing viscoelastic polymer

Mathematical model of mechanical behavior of viscoelastic bodies in complex stress state with regard to phase (crystallization) transitions, which describes technological stress field formation regularities in manufacturing polymer articles, is considered. Constitutive relationships describing stress and strain tensors correlation in a wide temperature range, including crystallization temperatures, are suggested. The thermal mechanics boundary-value problem that includes the obtained relationships is formulated. Algorithms of numerical realization of the temperature-conversion problem and the crystallizing system stress-strain state definition problem for an axisymmetric case are examined. Numerical realization features of the mechanical problem solution are discussed. The problem of technological stresses formation during steel and polyethylene tubes permanent connection manufacturing has been solved as the mathematical model application.

The mechanical behaviour of SentryGlas $$^{\circledR }$$ ® ionomer and TSSA silicon bulk materials at different temperatures and strain rates under uniaxial tensile stress state

An innovative type of connections for glass components, called laminated connections, has been developed in the last years. Two materials have been used for laminated connections: the transparent ionomer SentryGlas® (SG) from Kuraray (former Dupont) and the Transparent Structural Silicon Adhesive (TSSA) from Dow Corning. In this paper, the mechanical behaviour of SG and TSSA bulk materials is studied under uniaxial tensile stress condition. The effects of strain rate and temperature variations are investigated. Particular attention is paid (i) to the study of these polymers in cured condition and (ii) to the computation of true stress and strain field during the tests. Firstly, it is observed that the mechanical behaviour of both SG and TSSA are temperature and strain rate dependent. These effects are quantitatively determined in the paper. Secondly, two additional phenomena are observed. For TSSA, it is observed that the material goes from fully transparent to white colour, exhibiting the so-called whitening phenomenon. For SG, instead, it is observed that the strain field distribution is dependent on the temperature. More specifically, the material exhibits a non-uniform strain field distribution due to the occurring of the necking phenomenon. Measurements along the specimens, using Digital Image Correlation techniques, showed that the localized strain propagates over the full specimen length, resulting in a cold-drawing phenomenon. Finally, it is also shown that engineering and true stress–strain definition exhibits large deviation indicating that the finite deformation theory should be used for the computation of the stress–strain curves to be implemented in numerical modelling.

Interaction of internal forces of interior beam-column joints of reinforced concrete frames under seismic action

This paper presents detailed analysis of the internal forces of interior beam-column joints of reinforced concrete (RC) frames under seismic action, identifies critical joint sections, proposes consistent definitions of average joint shear stress and average joint shear strain, derives formulas for calculating average joint shear and joint torque, and reports simplified analysis of the effects of joint shear and torque on the flexural strengths of critical joint sections. Numerical results of internal joint forces and flexural strengths of critical joint sections are presented for a pair of concentric and eccentric interior connections extracted from a seismically designed RC frame. The results indicate that effects of joint shear and torque may reduce the column-to-beam flexural strength ratios to below unity and lead to "joint-yielding mechanism" for seismically designed interior connections. The information presented in this paper aims to provide some new insight into the seismic behavior of interior beam-column joints and form a preliminary basis for analyzing the complicated interaction of internal joint forces.

A comparative study on the uniaxial mechanical properties of the umbilical vein and umbilical artery using different stress–strain definitions

The umbilical cord is part of the fetus and generally includes one umbilical vein (UV) and two umbilical arteries (UAs). As the saphenous vein and UV are the most commonly used veins for the coronary artery disease treatment as a coronary artery bypass graft (CABG), understating the mechanical properties of UV has a key asset in its performance for CABG. However, there is not only a lack of knowledge on the mechanical properties of UV and UA but there is no agreement as to which stress-strain definition should be implemented to measure their mechanical properties. In this study, the UV and UA samples were removed after caesarean from eight individuals and subjected to a series of tensile testing. Three stress definitions (second Piola-Kichhoff stress, engineering stress, and true stress) and four strain definitions (Almansi-Hamel strain, Green-St. Venant strain, engineering strain, and true strain) were employed to determine the linear mechanical properties of UVs and UAs. The nonlinear mechanical behavior of UV/UA was computationally investigated using hyperelastic material models, such as Ogden and Mooney-Rivlin. The results showed that the effect of varying the stress definition on the maximum stress measurements of the UV/UA is significant but not when calculating the elastic modulus. In the true stress-strain diagram, the maximum strain of UV was 92% higher, while the elastic modulus and maximum stress were 162 and 42% lower than that of UA. The Mooney-Rivlin material model was designated to represent the nonlinear mechanical behavior of the UV and UA under uniaxial loading.

Retraction notice

The following article has been included in a multiple retraction: Karimi A, Navidbakhsh M, Yousefi H et al. An experimental study on the elastic modulus of gelatin hydrogels using different stress–strain definitions . J Thermoplast Compos Mater, first published on 29 April 2014, DOI: 10.1177/0892705714533377. In 2015 SAGE became aware of author misconduct concerning the suspected fabrication of identities, as well as the impersonation of legitimate individuals, to manipulate the peer review process across three separate journal publications. SAGE and the journal Editors immediately launched an investigation and have decided to retract the following articles for reasons of author misconduct. Alireza Karimi was the submitting author on 12 of the articles. SAGE regrets the academic record was compromised by manipulation of the peer review process and apologises to readers.

An experimental study on the mechanical properties of rat brain tissue using different stress–strain definitions

There are different stress-strain definitions to measure the mechanical properties of the brain tissue. However, there is no agreement as to which stress-strain definition should be employed to measure the mechanical properties of the brain tissue at both the longitudinal and circumferential directions. It is worth knowing that an optimize stress-strain definition of the brain tissue at different loading directions may have implications for neuronavigation and surgery simulation through haptic devices. This study is aimed to conduct a comparative study on different results are given by the various definitions of stress-strain and to recommend a specific definition when testing brain tissues. Prepared cylindrical samples are excised from the parietal lobes of rats' brains and experimentally tested by applying load on both the longitudinal and circumferential directions. Three stress definitions (second Piola-Kichhoff stress, engineering stress, and true stress) and four strain definitions (Almansi-Hamel strain, Green-St. Venant strain, engineering strain, and true strain) are used to determine the elastic modulus, maximum stress and strain. The highest non-linear stress-strain relation is observed for the Almansi-Hamel strain definition and it may overestimate the elastic modulus at different stress definitions at both the longitudinal and circumferential directions. The Green-St. Venant strain definition fails to address the non-linear stress-strain relation using different definitions of stress and triggers an underestimation of the elastic modulus. The results suggest the application of the true stress-true strain definition for characterization of the brain tissues mechanics since it gives more accurate measurements of the tissue's response using the instantaneous values.

RETRACTED: Experimental and numerical study on the mechanical behavior of rat brain tissue

Brain tissue is a very soft tissue in which the mechanical properties depend on the loading direction. While few studies have characterized these biomechanical properties, it is worth knowing that accurate characterization of the mechanical properties of brain tissue at different loading directions is a key asset for neuronavigation and surgery simulation through haptic devices. In this study, the hyperelastic mechanical properties of rat brain tissue were measured experimentally and computationally. Prepared cylindrical samples were excised from the parietal lobes of rats' brains and experimentally tested by a tensile testing machine. The effects of loading direction on the mechanical properties of brain tissue were measured by applying load on both longitudinal and circumferential directions. The general prediction ability of the proposed hyperelastic model was verified using finite element (FE) simulations of brain tissue tension experiments. The uniaxial experimental results compared well with those predicted by the FE models. The results revealed the influence of loading direction on the mechanical properties of brain tissue. The Ogden hyperelastic material model was suitably represented by the non-linear behavior of the brain tissue, which can be used in future biomechanical simulations. The hyperelastic properties of brain tissue provided here have interest to the medical research community as there are several applications where accurate characterization of these properties are crucial for an accurate outcome, such as neurosurgery, robotic surgery, haptic device design or car manufacturing to evaluate possible trauma due to an impact.

A comparative study on the elastic modulus of polyvinyl alcohol sponge using different stress-strain definitions

There have been different stress-strain definitions to measure the elastic modulus of spongy materials, especially polyvinyl alcohol (PVA) sponge. However, there is no agreement as to which stress-strain definition should be implemented. This study was aimed to show how different results are given by the various definitions of stress-strain used, and to recommend a specific definition when testing spongy materials. A fabricated PVA sponge was subjected to a series of tensile tests in order to measure its mechanical properties. Three stress definitions (second Piola-Kichhoff stress, engineering stress, and true stress) and four strain definitions (Almansi-Hamel strain, Green-St. Venant strain, engineering strain, and true strain) were used to determine the elastic modulus. The results revealed that the Almansi-Hamel strain definition exhibited the highest non-linear stress-strain relation and, as a result, may overestimate the elastic modulus at different stress definitions (second Piola-Kichhoff stress, engineering stress, and true stress). The Green-St. Venant strain definition failed to address the non-linear stress-strain relation using different definitions of stress and invoked an underestimation of the elastic modulus values. Engineering stress and strain definitions were only valid for small strains and displacements, which make them impractical when analyzing spongy materials. The results showed that the effect of varying the stress definition on the maximum stress measurements was significant but not when calculating the elastic modulus. It is important to consider which stress-strain definition is employed when characterizing the mechanical properties of spongy materials. Although the true stress-true strain definition exhibits a non-linear relation, we favor it in spongy materials mechanics as it gives more accurate measurements of the material's response using the instantaneous values.

RETRACTED: Hyperelastic mechanical behavior of rat brain infected by Plasmodium berghei ANKA – Experimental testing and constitutive modeling

The following article has been included in a multiple retraction: Karimi A, Navidbakhsh M, Beigzadeh B, et al. Hyperelastic mechanical behavior of rat brain infected by Plasmodium berghei ANKA – experimental testing and constitutive modelling. Int J Damage Mech 2014;23:857–871, DOI: 10.1177/1056789513514072. In 2015 SAGE became aware of author misconduct concerning the suspected fabrication of identities, as well as the impersonation of legitimate individuals, to manipulate the peer review process across three separate journal publications. SAGE and the journal Editors immediately launched an investigation and have decided to retract the following articles for reasons of author misconduct. Alireza Karimi was the submitting author on 12 of the articles. SAGE regrets the academic record was compromised by manipulation of the peer review process and apologises to readers. OnlineFirst articles (these articles will not be published in an issue) International Journal of Damage Mechanics Karimi A, Navidbakhsh M and Razaghi R. Dynamic finite element simulation of the human head damage mechanics protected by polyvinyl alcohol sponge. Int J Damage Mech, first published on 15 May 2014, DOI: 10.1177/1056789514535945. Journal of Thermoplastic Composite Materials Karimi A, Navidbakhsh M and Haghpanahi M. Constitutive model for numerical analysis of polyvinyl alcohol sponge under different strain rates. J Thermoplast Compos Mater, first published on 15 January 2014, DOI: 10.1177/0892705713520176. Karimi A, Navidbakhsh M, Yousefi H et al. An experimental study on the elastic modulus of gelatin hydrogels using different stress–strain definitions. J Thermoplast Compos Mater, first published on 29 April 2014, DOI: 10.1177/0892705714533377. Elhamian MM, Alizadeh M, Shokrieh MM, et al. An innovative three-dimensional biphasic-laminated composite model for articular cartilage tissue. J Thermoplast Compos Mater, first published on 1 February 2015, DOI: 10.1177/0892705715569821. Perfusion Karimi A, Navidbakhsh M, Yamada H, et al. A comparative study on the quasilinear viscoelastic mechanical properties of the umbilical artery and the umbilical vein. Perfusion, first published on 22 May 2014, DOI: 10.1177/0267659114536761. Tehrani P, Rahmani S, Karimi A, et al. A novel cardiac assist device (AVICENA): a numerical study to compute the generated power. Perfusion, first published on 19 August 2014, DOI: 10.1177/ 0267659114547943. Elhamian SMM, Alizadeh M, Shokrieh MM, et al. The effect of collagen fiber volume fraction on the mechanical properties of articular cartilage by micromechanics models. Perfusion, first published on 20 August 2014, DOI: 10.1177/0267659114547942. Razaghi R, Karimi A, Navidbakhsh M, et al. Determination of the vulnerable plaque in a stenotic human coronary artery – finite element modelling. Perfusion, first published on 28 October 2014, DOI: 10.1177/0267659114557720. Articles published in an issue International Journal of Damage Mechanics Karimi A, Navidbakhsh M, Beigzadeh B, et al. Hyperelastic mechanical behavior of rat brain infected by Plasmodium berghei ANKA – experimental testing and constitutive modelling. Int J Damage Mech 2014;23:857–871, DOI: 10.1177/1056789513514072. Perfusion Karimi A, Navidbakhsh M and Faghihi S. A comparative study on plaque vulnerability using constitutive equations. Perfusion, 2014;29:178–183, DOI: 10.1177/0267659113502835. Abdi M, Karimi A, Navidbakhsh M, et al. Modeling of cerebral aneurysm using equivalent electrical circuit (Lumped Model). Perfusion 2014;29:142–152, DOI: 10.1177/0267659113498617. Karimi A, Navidbakhsh M and Faghihi S. Fabrication and mechanical characterization of a polyvinyl alcohol sponge for tissue engineering applications. Perfusion 2014;29:231–237, DOI: 10.1177/ 0267659113513823. Karimi A, Navidbakhsh M, Yousefi H, et al. Experimental and numerical study on the mechanical behavior of rat brain tissue. Perfusion 2014;29:307–314, DOI: 10.1177/0267659114522088.

RETRACTED: Fabrication and mechanical characterization of a polyvinyl alcohol sponge for tissue engineering applications

Polyvinyl alcohol (PVA) sponges are widely used for clinical applications, including ophthalmic surgical treatments, wound healing and tissue engineering. There is, however, a lack of sufficient data on the mechanical properties of PVA sponges. In this study, a biomechanical method is used to characterize the elastic modulus, maximum stress and strain as well as the swelling ratio of a fabricated PVA sponge (P-sponge) and it is compared with two commercially available PVA sponges (CENEFOM and EYETEC). The results indicate that the elastic modulus of the P-sponge is 5.32% and 13.45% lower than that of the CENEFOM and EYETEC sponges, while it bears 4.11% more and 10.37% less stress compared to the CENEFOM and EYETEC sponges, respectively. The P-sponge shows a maximum strain of 32% more than the EYETEC sponge as well as a 26.78% higher swelling ratio, which is a significantly higher absorbency compared to the CENEFOM. It is believed that the results of this study would help for a better understanding of the extension, rupture and swelling mechanism of PVA sponges, which could lead to crucial improvement in the design and application of PVA-based materials in ophthalmic and plastic surgeries as well as wound healing and tissue engineering.

RETRACTED: Modeling of cerebral aneurysm using equivalent electrical circuit (Lumped Model)

The circle of Willis (CoW) is a key asset in brain performance as it supports adequate blood supply to the brain. The lumped method (electrical equivalent circuits) is a useful model to simulate the process of the human cardiovascular system. In this study, the whole cardiovascular system is modeled, using an equivalent electrical circuit to investigate an aneurysm in an artery. The cerebrovascular system consists of 29 compartments, which includes the CoW. Each vessel is modeled by a resistor, a capacitor and an inductor. Using MATLAB Simulink, the left and right ventricles are modeled by controlled voltage sources and diodes. The effects of the left internal carotid artery aneurysm (Fusiform) on the pressure of the efferent arteries in the circle of Willis are studied. The modeling results are entirely in agreement with the available clinical observations. The results of the present study may have clinical implications for modeling different cardiovascular diseases, such as arterial stiffness and atherosclerosis.

How Should We Measure and Report Elasticity in Aortic Tissue?

Different stress-strain definitions are used in the literature to measure the elastic modulus in aortic tissue. There is no agreement as to which stress-strain definition should be implemented. The purpose of this study is to show how different results are given by the various definitions of stress-strain used and to recommend a specific definition when testing aortic tissues. Circumferential specimens from three patients with ascending thoracic aortic aneurysm (ATAA) were obtained from the greater curvature and their tensile properties were tested uniaxially. Three stress definitions (second Piola-Kirchhoff stress, engineering stress and true stress) and four strain definitions (Almansi-Hamel strain, Green-St. Venant strain, engineering strain and true strain) were used to determine the elastic modulus. We found that the Almansi-Hamel strain definition exhibited the highest non-linear stress-strain relation and consequently may overestimate the elastic modulus when using different stress definitions (second Piola-Kirchhoff stress, engineering stress and true stress). The Green-St. Venant strain definition yielded the lowest non-linear stress-strain relation using different definitions of stress, which may underestimate the values of elastic modulus. Engineering stress and strain definitions are only valid for small strains and displacements, which make them impractical when analysing soft tissues. We show that the effect of varying the stress definition on the elastic modulus measurements is significant for maximum elastic modulus but not when calculating the hypertensive elastic modulus. It is important to consider which stress-strain definition is employed when analysing soft tissues. Although the true stress-true strain definition exhibits a non-linear relation, we favour it in tissue mechanics because it gives more accurate measurements of the material's response using the instantaneous values.

Effects of strain rate, mixing ratio, and stress–strain definition on the mechanical behavior of the polydimethylsiloxane (PDMS) material as related to its biological applications

Tensile tests on Polydimethylsiloxane (PDMS) materials were conducted to illustrate the effects of mixing ratio, definition of the stress-strain curve, and the strain rate on the elastic modulus and stress-strain curve. PDMS specimens were prepared according to the ASTM standards for elastic materials. Our results indicate that the physiological elastic modulus depends strongly on the definition of the stress-strain curve, mixing ratio, and the strain rate. For various mixing ratios and strain rates, true stress-strain definition results in higher stress and elastic modulus compared with engineering stress-strain and true stress-engineering strain definitions. The elastic modulus increases as the mixing ratio increases up-to 9:1 ratio after which the elastic modulus begins to decrease even as the mixing ratio continues to increase. The results presented in this study will be helpful to assist the design of in vitro experiments to mimic blood flow in arteries and to understand the complex interaction between blood flow and the walls of arteries using PDMS elastomer.

Implementation of an Associative Flow Rule Including Hydrostatic Stress Effects into the High Strain Rate Deformation Analysis of Polymer Matrix Composites

A previously developed analytical formulation has been modified in order to more accurately account for the effects of hydrostatic stresses on the nonlinear, strain rate dependent deformation of polymer matrix composites. State variable constitutive equations originally developed for metals have been modified in order to model the nonlinear, strain rate dependent deformation of polymeric materials. To account for the effects of hydrostatic stresses, which are significant in polymers, the classical J2 plasticity theory definitions of effective stress and effective inelastic strain, along with the equations used to compute the components of the inelastic strain rate tensor, are appropriately modified. To verify the revised formulation, the shear and tensile deformation of two representative polymers are computed across a wide range of strain rates. Results computed using the developed constitutive equations correlate well with experimental data. The polymer constitutive equations are implemented within a strength of materials based micromechanics method to predict the nonlinear, strain rate dependent deformation of polymer matrix composites. The composite mechanics are verified by analyzing the deformation of a representative polymer matrix composite for several fiber orientation angles across a variety of strain rates. The computed values compare well to experimentally obtained results.

The strain path dependence of multiaxial cyclic hardening behaviour

The small-strain, isotropic deformation theory is used in incremental form to model an additional cyclic hardening for any arbitrary loading path. The theory is of the unified type and does not employ yield or loading/ unloading criteria. The scalar-valued functions involved in the tensorial constitutive equations as well a growth law for these functions are identified based on idea of the equivalent state. Definitions of equivalent stress and equivalent strain have been developed to correlate step by step loading programmes taking the history of deformation into account. Use is made of the total work increment together with an interpolation method for tensor functions to generalize the simple state to a multiaxial behaviour in the strain space for a given strain increment. For the demonstration of model capability, the numerical simulation is undertaken on cyclic nonproportional paths in two-dimensional axial-shear strain space. The results are verified for stainless steel and brass by comparison with the material response experimentally obtained in the stress space.

Left ventricular myocardial stiffness

Left ventricular (LV) myocardial stiffness (kS) is an index of muscle properties independent of chamber geometry and is important in understanding normal and abnormal physiology, but is difficult to measure in vivo. Defining the LV as a thick-walled prolate sphere with minor radius R, accepted definitions of stress (σ) and natural strain were used to show the σ- R relation is a power function, and kS relates to the curvature by σ = C1 + C2 RkS. Importantly, this derivation avoids constraints on the σ- R relation and the need for LV dimensions at σ = 0. This model was then applied in humans and in dogs with intact pericardium. LV pressure and volume are lowered by nifedipine; in 32 patients kS was unchanged and thus peripheral effects implicated. Ejection fraction (EF) decreases with coronary occlusion and improves with early reperfusion. This could represent salvage of muscle or further damage with increased kS and resultant decrease of muscle bulging. In 20 dogs it was shown that kS increases with coronary occlusion and that early reperfusion causes kS to improve at the same time as EF. This implies salvage with major clinical implications.