Thermomechanical Fracture on a Pressurized Cylindrical Vessel Induced by a Localized Energy Source

1999 ◽  
Vol 121 (2) ◽  
pp. 160-169
Author(s):  
J. Beraun ◽  
J. K. Chen ◽  
D. Y. Tzou
Keyword(s):  
Energy Source ◽  
Strain Energy ◽  
Integral Transform ◽  
Axial Stress ◽  
Cylindrical Vessel ◽  
Physical Parameters ◽  
Stress And Strain ◽  
Thermally Induced ◽  
Thermally Driven ◽  
Elastic Fracture

Thermally induced elastic fracture around a localized energy source on a pressurized cylindrical vessel is studied in this work. Analytical solutions are obtained via the method of dual integral transform, with emphasis on the identification of the dominating parameters in thermal cracking. Directions for crack extension from the heat source are examined by the stress and strain-energy-based criteria, including the effects of internal pressure and axial stress. Special features include the intrinsic transition between the thermally driven and the mechanically driven fracture patterns. The physical parameters governing such transition are determined.

A REVIEW OF THE MECHANICAL STRESSES PREDISPOSING ABDOMINAL AORTIC ANEURYSMAL RUPTURE: UNIAXIAL EXPERIMENTAL APPROACH

2020 ◽  
Vol 20 (08) ◽  
pp. 2030001
Author(s):  
MARIYA ANTONOVA ◽  
SOFIA ANTONOVA ◽  
LYUDMILA SHIKOVA ◽  
MARIA KANEVA ◽  
VALENTIN GOVEDARSKI ◽  
...  
Keyword(s):  
Strain Energy ◽  
Experimental Approach ◽  
Strain Energy Function ◽  
Ultimate Stress ◽  
Physical Parameters ◽  
Stress And Strain ◽  
Cauchy Stress ◽  
Biomechanical Behavior ◽  
Abdominal Aortic ◽  
Experimental Protocols

In this paper, problems concerning the uniaxial experimental investigation of the human abdominal aortic aneurysm (AAA) biomechanical characteristics, concomitant values of the associated Cauchy stress, failure (ultimate) stress in AAA, and the constitutive modeling of AAA are considered. The aim of this paper is to review and compare the disposable experimental data, to reveal the reasons for the high dissipation of the results between studies, and to propound some unification criteria. We examined 22 literature sources published between 1994 and 2017 and compared their results, including our own results. The experiments in the reviewed literature have been designed to obtain the stress–strain characteristics and the failure (ultimate) stress and strain of the aneurysmal tissue. A variety of forms of the strain–energy function (SEF) have been applied in the considered studies to model the biomechanical behavior of the aneurysmal wall. The specimen condition and physical parameters, the experimental protocols, the failure stress and strain, and SEFs differ between studies, contributing to the differences between the final results. We propound some criteria and suggestions for the unification of the experiments leading to the comparable results.

Storing Energy in the Mechanical Domain

2014 ◽  
Vol 1679 ◽  
Author(s):  
O.G. Súchil ◽  
G. Abadal ◽  
F. Torres
Keyword(s):  
Energy Source ◽  
Energy Density ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Critical Strain ◽  
Substrate Surface ◽  
Maximum Load ◽  
Linear Buckling ◽  
Initial Ph ◽  
Self Powered

ABSTRACTSelf-powered microsystems as an alternative to standard systems powered by electrochemical batteries are taking a growing interest. In this work, we propose a different method to store the energy harvested from the ambient which is performed in the mechanical domain. Our mechanical storage concept is based on a spring which is loaded by the force associated to the energy source to be harvested [1]. The approach is based on pressing an array of fine wires (fws) grown vertically on a substrate surface. For the fine wires based battery, we have chosen ZnO fine wires due the fact that they could be grown using a simple and cheap process named hydrothermal method [2]. We have reported previous experiments changing temperature and initial pH of the solution in order to determine the best growth [3]. From new experiments done varying the compounds concentration the best results of fine wires were obtained. To characterize these fine wires we have considered that the maximum load we can apply to the system is limited by the linear buckling of the fine wires. From the best results we obtained a critical strain of εc = 3.72 % and a strain energy density of U = 11.26 MJ/m3, for a pinned-fixed configuration [4].

Investigation on Stress and Strain Singularity in LEFM

2006 ◽  
Vol 306-308 ◽  
pp. 31-36
Author(s):  
Zheng Yang ◽  
Wanlin Guo ◽  
Quan Liang Liu
Keyword(s):  
High Stress ◽  
Crack Tip ◽  
Plane Stress State ◽  
Stress And Strain ◽  
Linear Elastic ◽  
Geometrical Nonlinear ◽  
Maximum Crack ◽  
Elastic Fracture ◽  
Plain Strain ◽  
Strain Singularity

Stress and strain singularity at crack-tip is the characteristic of Linear Elastic Fracture Mechanics (LEFM). However, the stress, strain and strain energy at crack-tip may be infinite promoting conflicts with linear elastic hypothesis. It is indicated that the geometrical nonlinear near the crack-tip should not be neglected for linear elastic materials. In fact, the crack-tip blunts under high stress and strain, and the singularity vanishes due to the deformation of crack surface when loading. The stress at crack-tip may still be very high even though the singularity vanishes. The low bound of maximum crack-tip stress is the modulus of elastic in plane stress state, while in plain strain state, it is greater than the modulus of elastic, and will increase with the Poisson’s ratio.

Hybrid Analytical-Numerical Analysis of SAE 4150 Alloy Steel Rods Cooling

2014 ◽  
Vol 1082 ◽  
pp. 187-190 ◽  
Author(s):  
Marcelo Ferreira Pelegrini ◽  
Thiago Antonini Alves ◽  
Felipe Baptista Nishida ◽  
Ricardo A. Verdú Ramos ◽  
Cassio R. Macedo Maia
Keyword(s):  
Diffusion Equation ◽  
Alloy Steel ◽  
Integral Transform ◽  
Numerical Study ◽  
Physical Parameters ◽  
Analytical Treatment ◽  
Aspect Ratios ◽  
Rectangular Cylinders ◽  
Thermo Physical Properties ◽  
Integral Transform Technique

In this work, a hybrid analytical-numerical study was performed in cooling of rectangular rods made from SAE 4150 alloy steel (0.50% carbon, 0.85% chrome, 0.23% molybdenum, and 0.30% silicon). The analysis can be represented by the solution of transient diffusive problems in rectangular cylinders with variable thermo-physical properties in its domain under the boundary conditions of first kind (Dirichlet condition) and uniform initial condition. The diffusion equation was linearized through the Kirchhoff Transformation on the temperature potential to make the analytical treatment easier. The Generalized Integral Transform Technique (GITT) was applied on the diffusion equation in the domain in order to determine the temperature distribution. The physical parameters of interest were determined for several aspect ratios and compared with the results obtained through numerical simulations using the commercial software ANSYS/FluentTM15.

Linear elastic eigenstates of the compliance tensor for trigonal crystals

2000 ◽  
Vol 215 (1) ◽  
pp. 1-9 ◽  
Author(s):  
P.S. Theocaris ◽  
D.P. Sokolis
Keyword(s):  
Strain Energy ◽  
Elastic Strain Energy ◽  
Symmetric Tensor ◽  
Stress And Strain ◽  
Linear Elastic ◽  
Trigonal System ◽  
Compliance Tensor ◽  
Characteristic Values ◽  
Strain Tensors ◽  
Elastic Strain Energy Density

The spectral decomposition of the compliance fourth-rank tensor, representative of a trigonal crystalline or other anisotropic medium, is offered in this paper, and its characteristic values and idempotent fourth-rank tensors are established, with respect to the Cartesian tensor components. Consequently, it is proven that the idempotent tensors serve to analyse the second-rank symmetric tensor space into orthogonal subspaces, resolving the stress and strain tensors for the trigonal medium into their eigentensors, and, finally, decomposing the total elastic strain energy density into distinct, autonomous components. Finally, bounds on the values of the compliance tensor components for the trigonal system, dictated by the classical thermodynamical argument for the elastic potential to be positive definite, are estimated by imposing the characteristic values of the compliance tensor to be strictly positive.

scholarly journals Extension of Castigliano’s method for isotropic beams

2020 ◽  
Vol 231 (11) ◽  
pp. 4621-4640
Author(s):  
Juergen Schoeftner
Keyword(s):  
Shear Force ◽  
Strain Energy ◽  
Axial Stress ◽  
Bending Moment ◽  
Axial Direction ◽  
Present Contribution ◽  
Special Cases ◽  
Dummy Load ◽  
Complementary Strain ◽  
Castigliano’S Theorem

Abstract In the present contribution Castigliano’s theorem is extended to find more accurate results for the deflection curves of beam-type structures. The notion extension in the context of the second Castigliano’s theorem means that all stress components are included for the computation of the complementary strain energy, and not only the dominant axial stress and the shear stress. The derivation shows that the partial derivative of the complementary strain energy with respect to a scalar dummy parameter is equal to the displacement field multiplied by the normalized traction vector caused by the dummy load distribution. Knowing the Airy stress function of an isotropic beam as a function of the bending moment, the normal force, the shear force and the axial and vertical load distributions, higher-order formulae for the deflection curves and the cross section rotation are obtained. The analytical results for statically determinate and indeterminate beams for various load cases are validated by analytical and finite element results. Furthermore, the results of the extended Castigliano theory (ECT) are compared to Bernoulli–Euler and Timoshenko results, which are special cases of ECT, if only the energies caused by the bending moment and the shear force are considered. It is shown that lower-order terms for the vertical deflection exist that yield more accurate results than the Timoshenko theory. Additionally, it is shown that a distributed load is responsible for shrinking or elongation in the axial direction.

Recent Results on the Elasticity Theory of Inclusions

1994 ◽  
Vol 47 (1S) ◽  
pp. S10-S17 ◽  
Author(s):  
Jin H. Huang ◽  
T. Mura
Keyword(s):  
Composite Materials ◽  
Work Hardening ◽  
Strain Energy ◽  
Volume Fraction ◽  
Exact Formula ◽  
Stress And Strain ◽  
Inclusion Problems ◽  
Elastic Fields ◽  
Work Hardening Rate ◽  
Minimum Strain Energy

A method drawing from variational method is presented for the purpose of investigating the behavior of inclusions and inhomogeneities embedded in composite materials. The extended Hamilton’s principle is applied to solve many problems pertaining to composite materials such as constitutive equations, fracture mechanics, dislocation theory, overall elastic moduli, work hardening and sliding inclusions. Especially, elastic fields of sliding inclusions and workhardening rate of composite materials are presented in closed forms. For sliding inclusion problems, the sliding is modeled by adding the Somigliana dislocations along a matrix-inclusion interface. Exact formula are exploited for both Burgers vector and the disturbances in stress and strain due to sliding. The resulting expressions are obtained by utilizing the principle of minimum strain energy. Finally, explicit expressions are obtained for work-hardening rate of composite materials. It is verified that the work-hardening rate and yielding stress are independent on the size of inclusions but are dependent on the shape and the volume fraction of inclusions.

On the Ability of Structural and Phenomenological Hyperelastic Models to Predict the Mechanical Behavior of Biological Tissues Submitted to Multiaxial Loadings

2012 ◽  
Author(s):  
Mathieu Nierenberger ◽  
Yves Rémond ◽  
Saïd Ahzi
Keyword(s):  
Experimental Data ◽  
Mechanical Behavior ◽  
Strain Energy ◽  
Soft Tissues ◽  
Least Squares Method ◽  
Biological Tissues ◽  
Physical Parameters ◽  
Cauchy Stress ◽  
Specific Loading ◽  
Hyperelastic Models

Medical surgery is currently rapidly improving and requires modeling faithfully the mechanical behavior of soft tissues. Various models exist in literature; some of them created for the study of biological materials, and others coming from the field of rubber mechanics. Indeed biological tissues show a mechanical behavior close to the one of rubbers. But while building a model, one has to keep in mind that its parameters should be loading independent and that the model should be able to predict the behavior under complex loading conditions. In addition, keeping physical parameters seems interesting since it allows a bottom up approach taking into account the microstructure of the material. In this study, the authors consider different existing hyperelastic models based on strain energy functions and identify their coefficients successively on single loading stress-stretch curves. The experimental data used, come from a paper by Zemanek dated 2009 and concerning uniaxial, equibiaxial and plane tension tests on porcine arterial walls taken in identical experimental conditions. To achieve identification, the strain energy function of each model is derived differently to provide an expression of the Cauchy stress associated to each loading case. Firstly the parameters of each model are identified on the uniaxial tension curve using a least squares method. Then, keeping the obtained parameters, predictions are made for the two other loading cases (equibiaxial and plane tension) using the associated expressions of stresses. A comparison of these predictions with experimental data is done and allows evaluating the predictive capabilities of each model for the different loading cases. A similar approach is used after swapping the loading types. Since the predictive capabilities of the models are really dependent on the loading chosen to determine their parameters, another type of identification procedure is set up. It consists in adding the residues over the three loading cases during identification. This alternative identification method allows a better agreement between each model and the various types of experiments. This study evaluated the ability of some classical hyperelastic models to be used for a predictive scope after being identified on a specific loading type. Besides it brought to light some existing models which can describe at best the mechanical behavior of biological tissues submitted to various loadings.

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