Angled Elliptic Notch Problem Under Biaxial Loading

1980 ◽  
Vol 47 (1) ◽  
pp. 57-63 ◽  
Author(s):  
K. J. Chang ◽  
H.-C. Wu
Keyword(s):  
Experimental Data ◽  
Uniaxial Tension ◽  
Uniaxial Compression ◽  
Failure Criterion ◽  
Fracture Behavior ◽  
Biaxial Loading ◽  
Pure Shear ◽  
Present Theory ◽  
Material Parameters ◽  
Special Cases

The strain failure criterion proposed by the second author is applied to obtain general solutions for the angled elliptic notch problem subject to uniform biaxial loading. The solutions can be reduced to those for uniaxial tension, uniaxial compression, or pure shear as special cases. The solution for the case of pure shear is compared with experimental data found in literature. It is remarked that the present theory involves material parameters and predicts that fracture behavior is dependent on materials being investigated.

Numerical Mechanical Analysis of Filled Rubber under Different Deformation States Based on a New Hyperelastic Constitutive Model

2021 ◽  
Vol 1032 ◽  
pp. 15-22
Author(s):  
Xin Tao Fu ◽  
Ze Peng Wang ◽  
Lian Xiang Ma
Keyword(s):  
Experimental Data ◽  
Finite Element ◽  
Constitutive Model ◽  
Pure Shear ◽  
Mechanical Analysis ◽  
Uniaxial Tensile ◽  
Material Parameters ◽  
Finite Element Software ◽  
Filled Rubber ◽  
Deformation State

The accuracy of the rubber constitutive model characterizing experiment data has a crucial influence on the mechanical analysis of rubber structures. In this paper, a new improved hyperelastic constitutive model is proposed, and the model is derived into the stress-strain forms of uniaxial tension, equibiaxial tension and pure shear. Based on the experimental data of filled rubber, the material parameters of each deformation state are obtained by using the newly proposed rubber hyperelastic constitutive model, and the uniaxial tensile (UT), Equibiaxial tension (ET) and Pure shear (PS) specimens are simulated and calculated in the finite element software. the stress state of each finite element specimen is analyzed and the obtained simulation data are compared with the experimental data. It is found that the new model can accurately characterize the hyperelastic mechanical properties of the experimental specimens in different deformation states. At the same time, the reasons for the deviation from the experimental data in the process of plane tensile simulation are analyzed and explained comprehensively. The reliability and accuracy of the classical rubber constitutive relations of polynomial models and eight-chain model are studied. the results show that different hyperelastic models have different ability to describe the hyperelastic behavior in different deformation states. the hyperelastic constitutive model proposed in this paper can be easily embedded into finite element software and has the advantages of accurate results, few material parameters and simple testing.

A new static failure criterion for ductile materials

1997 ◽  
Vol 32 (5) ◽  
pp. 345-350 ◽  
Author(s):  
S-J Wang ◽  
M W Dixon
Keyword(s):  
Experimental Data ◽  
Failure Criterion ◽  
Material Properties ◽  
Maximum Shear Stress ◽  
Stress Theory ◽  
Ductile Materials ◽  
Special Cases ◽  
Von Mises ◽  
New Criterion ◽  
Static Failure

A new static failure criterion is proposed with a function of the stress state as well as the material properties (the ratio of ty /Sy), which is based on the experimentally determined ratio of Ty to Sy and includes the maximum shear stress theory and the von Mises-Hencky theory as special cases. The new criterion has a great potential to fit the experimental data and appears to fit better the very limited experimental data found in the open literature.

The Continuous Damage Theory of Brittle Materials, Part 2: Uniaxial and Plane Response Modes

1981 ◽  
Vol 48 (4) ◽  
pp. 816-824 ◽  
Author(s):  
G. U. Fonseka ◽  
D. Krajcinovic
Keyword(s):  
Uniaxial Tension ◽  
Uniaxial Compression ◽  
Analytical Model ◽  
Brittle Materials ◽  
Strain Fields ◽  
Material Parameters ◽  
Damage Theory ◽  
Response Modes

This part of the paper focuses on the application of the analytical model developed in Part 1 on the uniaxial tension, uniaxial compression, and plane problems (including rotating strain fields and unproportional loading). Identification of the material parameters is discussed in view of the derived results.

Light-Induced Metastable Defects in a-Si:H: Towards an Understanding

1985 ◽  
Vol 49 ◽  
Author(s):  
Martin Stutzmann ◽  
Warren B. Jackson ◽  
Chuang Chuang Tsai
Keyword(s):  
Amorphous Silicon ◽  
Mechanical Stress ◽  
Hydrogenated Amorphous Silicon ◽  
Material Parameters ◽  
Kinetic Behaviour ◽  
Proposed Model ◽  
Special Cases ◽  
The Stability ◽  
Hydrogenated Amorphous

AbstractThe dependence of the creation and the annealing of metastable dangling bonds in hydrogenated amorphous silicon on various material parameters will be discussed in the context of a recently proposed model. After a brief review of the kinetic behaviour governing defect creation and annealing in undoped a- Si:H, a number of special cases will be analyzed: the influence of alloying with O, N, C, and Ge, changes introduced by doping and compensation, and the role of mechanical stress. Finally, possibilities to increase the stability of a-Si:H based devices will be examined.

A Cyclic Plasticity Modeling for Uniaxial and Multiaxial Ratcheting Simulation of Austenitic Steel

2012 ◽  
Author(s):  
Salim Meziani ◽  
Lynda Djimli
Keyword(s):  
Experimental Data ◽  
Stainless Steel ◽  
Constitutive Model ◽  
Data Base ◽  
Good Choice ◽  
Cyclic Plasticity ◽  
Strain History ◽  
Material Parameters ◽  
Plastic Shakedown

The first objective of this paper investigates the influence of the previous strain history on ratcheting of the 304 L stainless steel on ambient temperature. The identification is done using the Chaboche constitutive model. New tests were performed where different strain-controlled histories have been applied prior to ratcheting tests. It is demonstrated that under the same conditions, one can observe ratcheting, plastic shakedown or elasticity according to the prior strain-controlled history. The second objective points out the correlation between the experimental data base devoted to the identification of the material parameters and the quality of the predictions in cyclic plasticity. The results suggest that the choice of the tests should be closely linked to the capabilities of the model. In particular, the presence of non proportional strain-controlled tests in the data base may be not a good choice if the model itself is not able to represent explicitly such a character.

Uncertainty Quantification in Predicting Behaviour of Rubber-Like Materials in Uni-Axial Loading

2020 ◽  
Author(s):  
Aref Ghaderi ◽  
Vahid Morovati ◽  
Pouyan Nasiri ◽  
Roozbeh Dargazany
Keyword(s):  
Uncertainty Quantification ◽  
Mechanical Response ◽  
Pure Shear ◽  
Constitutive Models ◽  
Material Behavior ◽  
Elastic Behavior ◽  
Deterministic Models ◽  
Data Set ◽  
Material Parameters ◽  
Axial Extension

Abstract Material parameters related to deterministic models can have different values due to variation of experiments outcome. From a mathematical point of view, probabilistic modeling can improve this problem. It means that material parameters of constitutive models can be characterized as random variables with a probability distribution. To this end, we propose a constitutive models of rubber-like materials based on uncertainty quantification (UQ) approach. UQ reduces uncertainties in both computational and real-world applications. Constitutive models in elastomers play a crucial role in both science and industry due to their unique hyper-elastic behavior under different loading conditions (uni-axial extension, biaxial, or pure shear). Here our goal is to model the uncertainty in constitutive models of elastomers, and accordingly, identify sensitive parameters that we highly contribute to model uncertainty and error. Modern UQ models can be implemented to use the physics of the problem compared to black-box machine learning approaches that uses data only. In this research, we propagate uncertainty through the model, characterize sensitivity of material behavior to show the importance of each parameter for uncertainty reduction. To this end, we utilized Bayesian rules to develop a model considering uncertainty in the mechanical response of elastomers. As an important assumption, we believe that our measurements are around the model prediction, but it is contaminated by Gaussian noise. We can make the noise by maximizing the posterior. The uni-axial extension experimental data set is used to calibrate the model and propagate uncertainty in this research.

scholarly journals LAGRANGIAN BREAKER CHARACTERISTICS FOR NONLINEAR WATER WAVES PROPAGATING ON SLOPING BOTTOMS

2011 ◽  
Vol 1 (32) ◽  
pp. 15
Author(s):  
Yang-Yih Chen ◽  
Meng-Syue Li ◽  
Hung-Chu Hsu ◽  
Ying-Pin Lin
Keyword(s):  
Experimental Data ◽  
Wave Propagation ◽  
Empirical Formula ◽  
Wave Breaking ◽  
Present Theory ◽  
Empirical Formulas ◽  
Third Order ◽  
Wave Shoaling ◽  
Theoretical Results ◽  
Sloping Bottom

In this paper, a new third-order Lagrangian asymptotic solution describing nonlinear water wave propagation on the surface of a uniform sloping bottom is presented. The model is formulated in the Lagrangian variables and we use a two-parameter perturbation method to develop a new mathematical derivation. The particle trajectories, wave pressure and Lagrangian velocity potential are obtained as a function of the nonlinear wave steepness  and the bottom slope  perturbed to third order. The analytical solution in Lagrangian form satisfies state of the normal pressure at the free surface. The condition of the conservation of mass flux is examined in detail for the first time. The two important properties in Lagrangian coordinates, Lagrangian wave frequency and Lagrangian mean level, are included in the third-order solution. The solution can also be used to estimate the mean return current for waves progressing over the sloping bottom. The Lagrangian solution untangle the description of the features of wave shoaling in the direction of wave propagation from deep to shallow water, as well as the process of successive deformation of a wave profile and water particle trajectories leading to wave breaking. The proposed model has proved to be capable of a better description of non-linear wave effects than the corresponding approximation of the same order derived by using the Eulerian description. The proposed solution has also been used to determine the wave shoaling process, and the comparisons between the experimental and theoretical results are presented in Fig.1a~1b. In addition, the basic wave-breaking criterion, namely the kinematical Stokes stability condition, has been investigated. The comparisons between the present theory, empirical formula of Goda (2004) and the experiments made by Iwagali et al.(1974), Deo et al.(2003) and Tsai et al.(2005) for the breaking index(Hb/L0) versus the relative water depth(d0/L0) under two different bottom slopes are depicted in Figs 2a~2b. It is found that the theoretical breaking index is well agreement with the experimental results for three bottom slopes. However,for steep slope of 1/3 shown in Fig 2b, the result of Goda‘s empirical formula gives a larger value in comparison with the experimental data and the present theory. Some of empirical formulas presented the breaking wave height in terms of deepwater wave condition, such as in Sunamura (1983) and in Rattanapitikon and Shibayama(2000). Base on the results depicted in Fig. 3a~3b, it showed that the theoretical results are in good agreement with the experimental data (Iwagali et al. 1974, Deo et al.2003 and Tsai et al. 2005) than the empirical formulas. The empirical formula of Sunamura (1983) always predicts an overestimation value.

scholarly journals Quantitative Assessment of the Influence of Tensile Softening of Concrete in Beams under Bending by Numerical Simulations with XFEM and Cohesive Cracks

Materials ◽  
2022 ◽  
Vol 15 (2) ◽  
pp. 626
Author(s):  
Ireneusz Marzec ◽  
Jerzy Bobiński
Keyword(s):  
Experimental Data ◽  
Numerical Simulations ◽  
Extended Finite Element ◽  
Three Point Bending ◽  
Material Parameters ◽  
Error Measures ◽  
Rational Bézier Curve ◽  
Initial Fracture ◽  
Experimental Values ◽  
Tensile Softening

Results of the numerical simulations of the size effect phenomenon for concrete in comparison with experimental data are presented. In-plane geometrically similar notched and unnotched beams under three-point bending are analyzed. EXtended Finite Element Method (XFEM) with a cohesive softening law is used. Comprehensive parametric study with the respect to the tensile strength and the initial fracture energy is performed. Sensitivity of the results with respect to the material parameters and the specimen geometry is investigated. Three different softening laws are examined. First, a bilinear softening definition is utilized. Then, an exponential curve is taken. Finally, a rational Bezier curve is tested. An ambiguity in choosing material parameters and softening curve definitions is discussed. Numerical results are compared with experimental outcomes recently reported in the literature. Two error measures are defined and used to quantitatively assess calculated maximum forces (nominal strengths) in comparison with experimental values as a primary criterion. In addition, the force—displacement curves are also analyzed. It is shown that all softening curves produce results consistent with the experimental data. Moreover, with different softening laws assumed, different initial fracture energies should be taken to obtain proper results.

scholarly journals Multilayer method for solving a problem of metals rupture under creep conditions

2019 ◽  
Vol 23 (Suppl. 2) ◽  
pp. 575-582 ◽  
Author(s):  
Evgenii Kuznetsov ◽  
Sergey Leonov ◽  
Dmitry Tarkhov ◽  
Alexander Vasilyev
Keyword(s):  
Neural Network ◽  
Experimental Data ◽  
Parameter Identification ◽  
Uniaxial Tension ◽  
Network Modeling ◽  
Identification Problem ◽  
Neural Network Modeling ◽  
Creep Theory ◽  
Parameter Identification Problem ◽  
Kinetic Creep

The paper deals with a parameter identification problem for creep and fracture model. The system of ordinary differential equations of kinetic creep theory is applied for describing this model. As for solving the parameter identification problem, we proposed to use the technique of neural network modeling, as well as the multilayer approach. The procedures of neural network modeling and multilayer approximation constructing application is demonstrated by the example of finding parameters for uniaxial tension model for isotropic steel 45 specimens at creep conditions. The solution corresponding to the obtained parameters agrees well with theoretical strain-damage characteristics, experimental data, and results of other authors.

Direct Comparison of Some Recent Rubber Elasticity Models

2000 ◽  
Vol 73 (2) ◽  
pp. 366-384 ◽  
Author(s):  
D. J. Seibert ◽  
N. Schöche
Keyword(s):  
Experimental Data ◽  
Finite Element Analysis ◽  
Element Analysis ◽  
Material Parameters ◽  
Complex Membrane ◽  
The Finite Element Analysis ◽  
Generic Class ◽  
Cubic Model ◽  
Polynomial Models ◽  
Special Case

Abstract The paper compares the Arruda—Boyce model, the van der Waals model and the Reduced Polynomial model—a generic class of polynomial models of which Yeoh's cubic model is a special case—in their ability to predict multiaxial deformation states on the basis of uniaxial measurements. These models are reviewed in the light of novel experimental data, giving ample space to the derivation of the equations needed for optimization of the material parameters. The technological relevance of these findings is exemplified in the finite element analysis (FEA) of a complex membrane.

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