An Energy Model for Bifurcation Analysis of a Double-Notched Concrete Panel: Continuum Model

2003 ◽  
Vol 6 (1) ◽  
pp. 45-51 ◽  
Author(s):  
G. Chen ◽  
G. Baker
Keyword(s):  
Continuum Model ◽  
Peak Load ◽  
Companion Paper ◽  
Constitutive Law ◽  
Simplified Model ◽  
Plasticity Model ◽  
Notch Depth ◽  
Axial Tension ◽  
Order Energy ◽  
Energy Computation

In this paper, the uni-axial tension of double-notched concrete specimens is analyzed by using a continuum plasticity model. As in a companion paper, the concept of minimization of the second-order energy is used as the criterion for judging a bifurcation. The energy computation is formulated in standard continuum plasticity. The analysis confirms that the unsymmetrical crack propagation (i.e. strains localizing on one side of the specimen) may occur either before or after the peak load. Influences on bifurcation of three factors, the notch depth to panel width, the local constitutive law, and the ratio of the panel width to panel length are investigated. A larger ratio of the notch depth to panel width, a steeper softening constitutive law, and a smaller ratio of the panel width to panel length, leads to an earlier bifurcation. These conclusions are consistent with those obtained from a simplified model.

An Energy Model for Bifurcation Analysis of a Double-Notched Concrete Panel: Simplified Model

2003 ◽  
Vol 6 (1) ◽  
pp. 37-44 ◽  
Author(s):  
G. Chen ◽  
G. Baker
Keyword(s):  
Crack Propagation ◽  
Peak Load ◽  
Shear Stiffness ◽  
Constitutive Law ◽  
Crack Plane ◽  
Elastic Rods ◽  
Bifurcation Problem ◽  
Factors Affecting ◽  
Axial Tension ◽  
Order Energy

The uni-axial tension of a double-notched concrete panel is analyzed. The unsymmetrical crack propagation is treated as a bifurcation problem. The concept of minimization of the second-order energy is used as the criterion for the bifurcation from symmetrical crack propagation to unsymmetrical crack propagation. In order to study the decisive factors affecting bifurcation, a simplified softening model is adopted where the cracked material is represented by softening rods, and un-cracked material by elastic rods. The influences on bifurcation of the crack plane dimension, the material cohesiveness, and the local constitutive law are analyzed. The analysis shows that the unsymmetrical crack propagation (i.e. strains localizing on one side of the specimen) may occur either before or after the peak load. Whether the unsymmetrical crack propagation occurs before the peak load or not depends on the ratio of the cracked length to un-cracked ligament. Shear stiffness does not have a significant influence on crack propagation before the peak load; however, it does determine whether the unsymmetrical crack propagation arises after the peak load.

scholarly journals Fast four-dimensional tensile test monitored via X-ray computed tomography: Elastoplastic identification from radiographs

2019 ◽  
Vol 54 (1) ◽  
pp. 44-53 ◽  
Author(s):  
Clément Jailin ◽  
Ante Buljac ◽  
Amine Bouterf ◽  
François Hild ◽  
Stéphane Roux
Keyword(s):  
Tensile Test ◽  
Correlation Method ◽  
Integrated Approach ◽  
Companion Paper ◽  
Constitutive Law ◽  
Free Form ◽  
Model Parameters ◽  
Displacement Fields ◽  
Integrated Method ◽  
Ductile Behavior

A projection-based digital volume correlation method (presented in a companion paper) is extended to an integrated approach for the calibration of an elastoplastic law based on a single radiograph per loading step. Instead of following a two-step sequential procedure (i.e. first, measurement of the displacement field; second, identification), the integrated method aims at identifying few model parameters directly from the gray-level projections. The analysis of an in situ tensile test composed of 127 loading steps performed in 6 min is presented. An isotropic elastoplastic constitutive law with free-form hardening behavior (i.e. controlled by only eight parameters) is identified and shows a ductile behavior (up to 6.3% strain before failure). A large improvement on the residual quality is shown and validates the proposed model and procedure. The obtained displacement fields are similar to those measured with no mechanical integration. A different parameterization of the constitutive law provides a very close result, thereby assessing the robustness of the procedure.

3D Hyperelastic Constitutive Model for Yarn Behaviour Description

2012 ◽  
Vol 504-506 ◽  
pp. 267-272 ◽  
Author(s):  
Adrien Charmetant ◽  
Emmanuelle Vidal-Sallé ◽  
Philippe Boisse
Keyword(s):  
Longitudinal Shear ◽  
Constitutive Law ◽  
Energy Potential ◽  
Double Curvature ◽  
Axial Tension ◽  
Proposed Model ◽  
Tension And Compression ◽  
Bias Extension ◽  
Definition Of ◽  
Continuous Material

The preforming stage of the LCM composite manufacturing processes lead to fibrous reinforcement deformations which may be very large especially for double curvature shapes. Those deformations have significant influence on the second stage of the process, i.e. the injection of the resin. A way to predict accurately the spatial distribution of the permeability tensor consists in simulating for various configurations, the deformed shape of the reinforcement at the scale of the yarns. Mesoscopic scale analyses of textile reinforcements generally consider the yarns as a continuous material despite their fibrous nature. In order to have an accurate simulation tool, it is necessary to build up a constitutive law which accounts for the physical specificities linked to the microstructure of the yarns. Several models exist with reasonable accuracy. The present paper proposes a new approach in the hyperelasticity framework. The proposed model is based on the definition of mathematical invariants linked to the four main deformation modes of the yarn material: tension, compaction, longitudinal shear and transverse shear. The strain energy potential build up with those invariants is identified using classical fabric material tests: uni- and bi-axial tension and compression. The model has been validated on laboratory tests such as bias extension tests and gives promising results.

Effect of Triaxiality and Lode Angle on the Plasticity Behaviour of a Ti-6Al-4V Titanium Alloy

2013 ◽  
Vol 577-578 ◽  
pp. 413-416
Author(s):  
Andrea Gilioli ◽  
Andrea Manes ◽  
Marco Giglio ◽  
Nima Allahverdizadeh
Keyword(s):  
Titanium Alloy ◽  
Tensile Tests ◽  
Constitutive Law ◽  
Plasticity Model ◽  
Virtual Test ◽  
Test Methodology ◽  
Lode Angle ◽  
Mises Plasticity ◽  
Von Mises ◽  
Von Mises Plasticity

The widespread Von Mises plasticity model fails to take the hydrostatic and the Lode angle effects into account and the assumption of this model is not valid for all types of metallic alloys. Hence in the present work the applicability of the Von Mises plasticity model in applications on a Ti-6Al-4V Titanium alloy have been analysed. A virtual test methodology, combination of experiments and numerical analysis have been developed. For this purpose various tensile tests on different specimen shapes have been carried out experimentally. These tests have been subsequently numerically reproduced to calibrate a constitutive law which fits every single test best, highlighting the possible effect of triaxiality and Lode angle on plasticity (strain hardening behaviour). An analysis of the specimen fracture surfaces have been carried out to evaluate possible effect of triaxiality and Lode angle down to a microscopic level.

scholarly journals Study of Frictional Effects of Granite Subjected to Quasi-Static Contact Loading

Lubricants ◽  
2020 ◽  
Vol 8 (12) ◽  
pp. 106
Author(s):  
Hossein Shariati ◽  
Mahdi Saadati ◽  
Kenneth Weddfelt ◽  
Per-Lennart Larsson ◽  
Francois Hild
Keyword(s):  
Stress State ◽  
Frictional Contact ◽  
Frictional Coefficient ◽  
Constitutive Law ◽  
Spherical Indentation ◽  
Plasticity Model ◽  
Frictionless Contact ◽  
Weibull Parameters ◽  
Static Contact ◽  
Frictional Effects

The rock fragmentation response to drilling, in particular percussive drilling, is important in order to improve the efficiency of such an operation. The resulting problem includes spherical contact between the drill bit and the material and therefore, a numerical analysis of frictional effects in quasi-static spherical indentation of Bohus granite is presented. The frictional coefficient between the indenter and the granite surface is accounted for in numerical simulations. A previously determined constitutive law is used for the purpose of numerical analyses. The latter consists of a Drucker-Prager plasticity model with variable dilation angle coupled with an anisotropic damage model. Since the tensile strength is random, Weibull statistics was considered. Using a frictionless contact model, the stress state of Bohus granite corresponding to the first material failure occurrence, observed in indentation experiments, was numerically determined. However, the frictional effects, which are of interest in this study, may lead to changes in the numerically established stress state and consequently the Weibull parameters should be recalibrated. The so-called Weibull stress decreases from 120 MPa for a frictionless contact to 75 MPa for frictional contact, and the Weibull modulus from 24 to 12. It is numerically observed that the predicted force-penetration response, using the new set of Weibull parameters, is not influenced by friction. Conversely, the predicted fracture pattern, in the case of frictional contact, is similar to the case of frictionless contact, but its size is somewhat larger. Last, a parametric study analyzing the dependence of the friction coefficient is carried out and no significant changes are detected. The novelty of the present findings concerns the fact that both an advanced damage description in combination with an advanced plasticity model, both implemented for finite element analyses, is used to analyze frictional effects at granite indentation.

On Reduction of Stress Concentration around the Pin Hole in Turbine Discs

2013 ◽  
Vol 482 ◽  
pp. 55-58
Author(s):  
Liang Shi ◽  
Yan Rong Wang ◽  
Shan Hu Yuan ◽  
Da Sheng Wei
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Stress Concentration ◽  
Stress Concentration Factor ◽  
Simplified Model ◽  
Arc Length ◽  
Notch Depth ◽  
Characteristic Parameters ◽  
Element Analysis ◽  
Turbine Disc

The stress concentration phenomenon around holes in rotated components is discussed. Firstly, finite element analysis of a simplified model of turbine disc flange is carried out, and then a method is developed by designing an intended-cut notch on the model to reduce the stress around the pin hole. Furthermore, two characteristic parameters which determine the configuration of the notch, namely notch depth and arc length parameter, are investigated by changing the notch dimensions. The results show that this method can reduce the stress around the hole significantly, notch depth and arc length have an important impact on the stress concentration factor (SCF), the SCF decreases with the increase of notch depth, and increasing the arc length within a critical scope results in the decrease of the SCF.

scholarly journals A continuum model of lipid bilayers

2004 ◽  
Vol 15 (4) ◽  
pp. 487-508 ◽  
Author(s):  
J. G. BLOM ◽  
M. A. PELETIER
Keyword(s):  
Simple Model ◽  
Lipid Bilayers ◽  
Continuum Model ◽  
Hydrophobic Interactions ◽  
Model Membrane ◽  
Numerical Calculations ◽  
Simplified Model ◽  
One Dimensional ◽  
Rigid Rod

We study a one-dimensional continuum model for lipid bilayers. The system consists of water and lipid molecules; lipid molecules are represented by two ‘beads’, a head bead and a tail bead, connected by a rigid rod. We derive a simplified model for such a system, in which we only take into account the effects of entropy and hydrophilic/hydrophobic interactions. We show that for this simple model membrane-like structures exist for certain choices of the parameters, and numerical calculations suggest that they are stable.

Evaluation of Rotation Capacity of RHS Aluminium Alloy Beams by FEM Simulation: Temper T6

2016 ◽  
Vol 710 ◽  
pp. 281-287 ◽  
Author(s):  
Paolo Castaldo ◽  
Elide Nastri ◽  
Vincenzo Piluso
Keyword(s):  
Aluminium Alloy ◽  
Slenderness Ratio ◽  
Fem Simulation ◽  
Companion Paper ◽  
Constitutive Law ◽  
Geometrical Parameters ◽  
Rotation Capacity ◽  
Moment Gradient ◽  
The Moment ◽  
Material Constitutive Law

The aim of this work is the numerical assessment of the ultimate behaviour of aluminium alloy beams subjected to non-uniform bending. An extensive numerical analysis has been performed by means of FE code ABAQUS with reference to RHS sections considering different values of the main geometrical and mechanical parameters. In particular, regarding the geometrical parameters the flange slenderness, the flange-to-web slenderness ratio and the moment gradient parameter have been considered. In particular, their influence on the ultimate behaviour of such beams has been investigated by adopting the material constitutive law proposed by Eurocode 9 based on the Ramberg-Osgood model. The investigations concern these parameters considered separately as well as their interaction. The results are herein reported with reference to temper T6 and show the importance of the investigated parameters on the buckling strength and the rotational capacity of aluminium alloy beams. Temper T6 gives rise to a quite low hardening compared to temper T4, which is analysed in a companion paper.

A novel continuum model for the reduction of numerical errors of finite-element analysis

2011 ◽  
Vol 225 (4) ◽  
pp. 817-825 ◽  
Author(s):  
H Mohammadi ◽  
F Bahramian ◽  
W Herzog
Keyword(s):  
Finite Element ◽  
Continuum Model ◽  
Constitutive Models ◽  
Least Square ◽  
Constitutive Law ◽  
Element Analysis ◽  
Element Mesh ◽  
Numerical Errors ◽  
Proposed Model ◽  
Numerical Formulation

The authors developed a novel numerical formulation that reduces the computational expense of solving linear and non-linear constitutive models. A finite-element constitutive law followed by a novel continuum model is discussed. The proposed approach is employed to reduce numerical errors obtained from the standard finite-element method. The continuum model is based on the Lagrange multipliers strategy along with the finite-difference method and a least-square algorithm. It is crucial to this approach that the components of either the strain or the stress tensor are known at the nodes of the finite-element mesh. The proposed model is independent of element topology which can be strongly and arbitrarily distorted.

Effect Of Elevated Temperatures On Complete Concrete Deformation Diagrams

2019 ◽  
pp. 9-14
Keyword(s):  
Experimental Data ◽  
Elastic Modulus ◽  
Elevated Temperatures ◽  
Peak Load ◽  
Relative Deformation ◽  
Deformation Characteristics ◽  
Compression Tests ◽  
Strain Behavior ◽  
Different Temperatures ◽  
Deformation Diagrams

The analysis of the previous results of the study on concrete stress-strain behavior at elevated temperatures has been carried out. Based on the analysis, the main reasons for strength retrogression and elastic modulus reduction of concrete have been identified. Despite a significant amount of research in this area, there is a large spread in experimental data received, both as a result of compression and tension. In addition, the deformation characteristics of concrete are insufficiently studied: the coefficient of transverse deformation, the limiting relative compression deformation corresponding to the peak load and the almost complete absence of studies of complete deformation diagrams at elevated temperatures. The two testing chambers provided creating the necessary temperature conditions for conducting studies under bending compression and tension have been developed. On the basis of the obtained experimental data of physical and mechanical characteristics of concrete at different temperatures under conditions of axial compression and tensile bending, conclusions about the nature of changes in strength and deformation characteristics have been drawn. Compression tests conducted following the method of concrete deformation complete curves provided obtaining diagrams not only at normal temperature, but also at elevated temperature. Based on the experimental results, dependences of changes in prism strength and elastic modulus as well as an equation for determining the relative deformation and stresses at elevated temperatures at all stages of concrete deterioration have been suggested.

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