Semi-inverse method for predicting stress–strain relationship from cone indentations

2003 ◽  
Vol 18 (9) ◽  
pp. 2068-2078 ◽  
Author(s):  
A. DiCarlo ◽  
H. T. Y. Yang ◽  
S. Chandrasekar
Keyword(s):  
A Priori ◽  
Model Material ◽  
Material Behavior ◽  
The Finite Element Method ◽  
Stress Strain ◽  
Indentation Tests ◽  
Strain Relationship ◽  
Initial Force ◽  
Relationship Of ◽  
Force Displacement

A method for determining the stress–strain relationship of a material from hardness values H obtained from cone indentation tests with various apical angles is presented. The materials studied were assumed to exhibit power-law hardening. As a result, the properties of importance are the Young's modulus E, yield strength Y, and the work-hardening exponent n. Previous work [W.C. Oliver and G.M. Pharr, J. Mater. Res. 7, 1564 (1992)] showed that E can be determined from initial force–displacement data collected while unloading the indenter from the material. Consequently, the properties that need to be determined are Y and n. Dimensional analysis was used to generalize H/E so that it was a function of Y/E and n [Y-T. Cheng and C-M. Cheng, J. Appl. Phys. 84, 1284 (1999); Philos. Mag. Lett. 77, 39 (1998)]. A parametric study of Y/E and n was conducted using the finite element method to model material behavior. Regression analysis was used to correlate the H/E findings from the simulations to Y/E and n. With the a priori knowledge of E, this correlation was used to estimate Y and n.

scholarly journals The Uniaxial Stress–Strain Relationship of Hyperelastic Material Models of Rubber Cracks in the Platens of Papermaking Machines Based on Nonlinear Strain and Stress Measurements with the Finite Element Method

Materials ◽  
2021 ◽  
Vol 14 (24) ◽  
pp. 7534
Author(s):  
Huu-Dien Nguyen ◽  
Shyh-Chour Huang
Keyword(s):  
Finite Element ◽  
Working Conditions ◽  
Uniaxial Stress ◽  
Hyperelastic Material ◽  
The Finite Element Method ◽  
Stress Strain ◽  
Material Models ◽  
Strain Relationship ◽  
Relationship Of ◽  
Better Than

Finite element analysis is extensively used in the design of rubber products. Rubber products can suffer from large amounts of distortion under working conditions as they are nonlinearly elastic, isotropic, and incompressible materials. Working conditions can vary over a large distortion range, and relate directly to different distortion modes. Hyperelastic material models can describe the observed material behaviour. The goal of this investigation was to understand the stress and relegation fields around the tips of cracks in nearly incompressible, isotropic, hyperelastic accouterments, to directly reveal the uniaxial stress–strain relationship of hyperelastic soft accouterments. Numerical and factual trials showed that measurements of the stress–strain relationship could duly estimate values of nonlinear strain and stress for the neo-Hookean, Yeoh, and Arruda–Boyce hyperelastic material models. Numerical models were constructed using the finite element method. It was found that results concerning strains of 0–20% yielded curvatures that were nearly identical for both the neo-Hookean, and Arruda–Boyce models. We could also see that from the beginning of the test (0–5% strain), the curves produced from our experimental results, alongside those of the neo-Hookean and Arruda–Boyce models were identical. However, the experiment’s curves, alongside those of the Yeoh model, converged at a certain point (30% strain for Pieces No. 1 and 2, and 32% for Piece No. 3). The results showed that these finite element simulations were qualitatively in agreement with the actual experiments. We could also see that the Yeoh models performed better than the neo-Hookean model, and that the neo-Hookean model performed better than the Arruda–Boyce model.

Surface Strain Variation in Human Patellar Tendon and Knee Cruciate Ligaments

1990 ◽  
Vol 112 (1) ◽  
pp. 38-45 ◽  
Author(s):  
D. L. Butler ◽  
M. Y. Sheh ◽  
D. C. Stouffer ◽  
V. A. Samaranayake ◽  
M. S. Levy
Keyword(s):  
Patellar Tendon ◽  
Local Strain ◽  
Surface Strain ◽  
Material Behavior ◽  
Cruciate Ligaments ◽  
Stress Strain ◽  
Strain Relationship ◽  
Strain Stress ◽  
Relationship Of ◽  
Simple Stress

Local surface strains in bone-fascicle-bone subunits from human patellar tendon and anterior and posterior cruciate ligaments were measured between markers using low-speed photography during low rate subfailure testing. A simple stress-strain relationship of the power form was found to describe the bone-to-bone responses up to four percent strain for all three tissue types examined. The regional material behavior were best fit using an inverted strain-stress relationship, however. The power model, fitted to the experimental data, conformed to the expected stress-strain relationship better than either the quadratic or cubic models. With few exceptions, for a given stress, the strains near the proximal and distal bone ends were not significantly different from each other, but were significantly higher than the strains in the tissue midregions. Local strain patterns generally varied among subunits from the same tissue.

scholarly journals An Investigation of Nanomechanical Properties of Materials using Nanoindentation and Artificial Neural Network

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
Hyuk Lee ◽  
Wai Yeong Huen ◽  
Vanissorn Vimonsatit ◽  
Priyan Mendis
Keyword(s):  
Work Hardening ◽  
Stress Strain ◽  
Indentation Force ◽  
Wide Range ◽  
Indentation Tests ◽  
Strain Relationship ◽  
Properties Of Materials ◽  
Artificial Neural ◽  
Hardening Power ◽  
Force Displacement

Abstract Mechanical properties of materials can be derived from the force-displacement relationship through instrumented indentation tests. Complications arise when establishing the full elastic-plastic stress-strain relationship as the accuracy depends on how the material’s and indenter’s parameters are incorporated. For instance, the effect of the material work-hardening phenomenon such as the pile-up and sink-in effect cannot be accounted for with simplified analytical indentation solutions. Due to this limitation, this paper proposes a new inverse analysis approach based on dimensional functions analysis and artificial neural networks (ANNs). A database of the dimensional functions relating stress and strain parameters of materials has been developed. The database covers a wide range of engineering materials that have the yield strength-to-modulus ratio (σy/E) between 0.001 to 0.5, the work-hardening power (n) between 0–0.5, Poisson’s ratio (v) between 0.15–0.45, and the indentation angle (θ) between 65–80 degrees. The proposed algorithm enables determining the nanomechanical stress-strain parameters using the indentation force-displacement relationship, and is applicable to any materials that the properties are within the database range. The obtained results are validated with the conventional test results of steel and aluminum samples. To further demonstrate the application of the proposed algorithm, the nanomechanical stress-strain parameters of ordinary Portland cement phases were determined.

Study on Stress-Strain Relationship of Loess

2004 ◽  
Vol 274-276 ◽  
pp. 241-246 ◽  
Author(s):  
Bo Han ◽  
Hong Jian Liao ◽  
Wuchuan Pu ◽  
Zheng Hua Xiao
Keyword(s):  
Stress Strain ◽  
Strain Relationship ◽  
Relationship Of

scholarly journals Simulating the Stress-Strain Relationship of Geomaterials by Support Vector Machine

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Hongbo Zhao ◽  
Zenghui Huang ◽  
Zhengsheng Zou
Keyword(s):  
Support Vector Machine ◽  
Constitutive Relationship ◽  
Support Vector ◽  
Nonlinear Relationship ◽  
Ann Model ◽  
Stress Strain ◽  
Svm Model ◽  
Strain Relationship ◽  
Artificial Neural Network Ann ◽  
Relationship Of

Stress-strain relationship of geomaterials is important to numerical analysis in geotechnical engineering. It is difficult to be represented by conventional constitutive model accurately. Artificial neural network (ANN) has been proposed as a more effective approach to represent this complex and nonlinear relationship, but ANN itself still has some limitations that restrict the applicability of the method. In this paper, an alternative method, support vector machine (SVM), is proposed to simulate this type of complex constitutive relationship. The SVM model can overcome the limitations of ANN model while still processing the advantages over the traditional model. The application examples show that it is an effective and accurate modeling approach for stress-strain relationship representation for geomaterials.

scholarly journals Stress-strain model for grade 275 reinforcing steel with cyclic loading

1978 ◽  
Vol 11 (2) ◽  
pp. 101-109 ◽  
Author(s):  
K. J. Thompson ◽  
R. Park
Keyword(s):  
Axial Loading ◽  
Strain Curve ◽  
Cyclic Stress ◽  
Stress Strain ◽  
Reinforcing Bar ◽  
Strain Behaviour ◽  
Strain Relationship ◽  
Reversed Loading ◽  
Relationship Of ◽  
Strain Model

The stress-strain relationship of Grade 275 steel reinforcing bar under cyclic (reversed) loading is examined using experimental results obtained previously from eleven test specimens to which a variety of axial loading cycles has been applied. A Ramberg-Osgood function is fitted to the experimental stress-strain curves to follow the cyclic stress-strain behaviour after the first load run in the plastic range. The empirical constants in the function are determined by regression analysis and are found to depend mainly on the plastic strain imposed
in the previous loading run. The monotonic stress-strain curve for the steel, with origin of strains suitably adjusted, is assumed to be the envelope curve giving the upper limit of stress. The resulting Ramberg-Osgood expression and envelope is found to give good agreement with the experimentally measured cyclic stress-strain curves.

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