Stress Distribution in Front of the Crack - Analytical Solutions vs. Numerical. Can the Differences be Minimized?

2019 ◽  
Vol 810 ◽  
pp. 7-14
Author(s):  
Andrzej Neimitz ◽  
Sebastian Lipiec
Keyword(s):  
Stress Distribution ◽  
Analytical Solution ◽  
Large Strains ◽  
Stress Distributions ◽  
Fracture Criteria ◽  
Nonlinear Fracture Mechanics ◽  
The Real ◽  
Material Parameters ◽  
Nonlinear Fracture ◽  
Analytical Formulae

It is shown that it is possible to obtain such material parameters as α and Q, which, when used in the analytical formulae proposed by Hutchinson, Rice and Rosengren and O’Dowd and Shih, can lead to stress distributions similar to those obtained numerically (except for the region at the immediate crack front). The numerical solution obtained after calibration of the stress-strain uniaxial curve and assuming large strains is expected to be close to the “"real” stress distribution. Thus, the analytical solution is also close to the “real” stress distribution. These new values of α and Q can now be used in fracture criteria proposed within the scope of classical nonlinear fracture mechanics.

Kombinierte experimentelle und numerische Studie zur schwindinduzierten Rissbildung zementgebundener Werkstoffe / Combined Experimental and Numerical Study to assess Shrinkage Cracking of Cement-Based Materials

1998 ◽  
Vol 4 (5) ◽  
pp. 479-506 ◽  
Author(s):  
G. Martinola ◽  
H. Sadouki
Keyword(s):  
Numerical Study ◽  
Decisive Role ◽  
Shrinkage Cracking ◽  
Nonlinear Fracture Mechanics ◽  
Material Parameters ◽  
Nonlinear Fracture ◽  
Cement Based Materials ◽  
Different Types ◽  
Experimental Findings ◽  
Relevant Material

Abstract In this contribution, a combined experimental and numerical study to assess the cracking resistance of cement-based materials subjected to desiccation is outlined. Experimentally, the tendency to hygral cracking is determined by means of mortar ring specimens exposed to drying atmosphere. A numerical model based on the nonlinear theory of diffusion and nonlinear fracture mechanics is developed. The relevant hygral and mechanical parameters and laws needed for the model have been determined by means of adequate experiments analyzed by inverse analyses. The hygro-mechanical behaviour of two different types of mortar is studied. Numerical results have been compared to experimental findings. Furthermore, a parametric study has been carried out with the aim to characterize the relevant material parameters influencing shrinkage cracking. It can be concluded that a combination of experimental and numerical methods can play a decisive role in optimizing mortars or concretes with respect to predefined and required material properties. In this way, the durability of concrete structures can be significantly enhanced.

scholarly journals Simulation of the long-term behaviour of a fault with two asperities

2010 ◽  
Vol 17 (6) ◽  
pp. 777-784 ◽  
Author(s):  
M. Dragoni ◽  
S. Santini
Keyword(s):  
Phase Space ◽  
Stress Distribution ◽  
Analytical Solution ◽  
Infinite Number ◽  
Fault System ◽  
Seismic Events ◽  
Recurrence Pattern ◽  
Stress Distributions ◽  
The Difference

Abstract. A system made of two sliding blocks coupled by a spring is employed to simulate the long-term behaviour of a fault with two asperities. An analytical solution is given for the motion of the system in the case of blocks having the same friction. An analysis of the phase space shows that orbits can reach a limit cycle only after entering a particular subset of the space. There is an infinite number of different limit cycles, characterized by the difference between the forces applied to the blocks or, as an alternative, by the recurrence pattern of block motions. These results suggest that the recurrence pattern of seismic events produced by the equivalent fault system is associated with a particular stress distribution which repeats periodically. Admissible stress distributions require a certain degree of inhomogeneity, which depends on the geometry of fault system. Aperiodicity may derive from stress transfers from neighboring faults.

Complex study of the fracture processes in materials and structures

2018 ◽  
Vol 84 (11) ◽  
pp. 46-51 ◽  
Author(s):  
N. A. Makhutov
Keyword(s):  
Fracture Mechanics ◽  
Crack Resistance ◽  
Scientific Basis ◽  
Intensity Factors ◽  
Nonlinear Fracture Mechanics ◽  
Nonlinear Fracture ◽  
Linear Fracture ◽  
Science Technology ◽  
Fracture Processes

The results of comprehensive studies of multifactor processes, mechanisms and criteria for fracture at a variation of the crack-like defect state, loading conditions and mechanical properties of structural materials carried out in the 20th - 21st centuries are presented on the basis of monographic publications and articles published in the journal “Zavodskaya Laboratoriya. Diagnostika Materialov.” Crack resistance of materials and structures has become a key problem of the material science, technology, design, manufacture and service of structures. Fracture mechanics including estimation of the stress-strain and limiting states in a cracks tip formed a scientific basis of the crack resistance analysis Stress intensity factors (linear fracture mechanics) and strain intensity factors (nonlinear fracture mechanics) are accepted as the basic criteria of those states. The basic computational relations for construction of the fracture diagrammes which link the cracks growth with conditions of a static, cyclic, long-term, dynamic loading are presented. Parameters of computational relations are put into correspondence with the features of fracture processes on nano-, micro-, meso- and macrolevels. Prospects of the research and guidelines of further studing crack resistance are discussed.

Nonlinear Fracture Mechanics Analysis Considering Material Inhomogeneity of Welded Joints

Impact ◽  
2019 ◽  
Vol 2019 (10) ◽  
pp. 105-107
Author(s):  
Hiroshi Okada
Keyword(s):  
Fracture Mechanics ◽  
Solid Mechanics ◽  
Crack Nucleation ◽  
Intensity Factors ◽  
Nonlinear Fracture Mechanics ◽  
Material Inhomogeneity ◽  
Computational Fracture Mechanics ◽  
New Methods ◽  
Nonlinear Fracture ◽  
Mechanics Analysis

Professor Hiroshi Okada and his team from the Department of Mechanical Engineering, Faculty of Science and Technology, Tokyo University of Science, Japan, are engaged in the field of computational fracture mechanics. This is an area of computational engineering that refers to the creation of numerical methods to approximate the crack evolutions predicted by new classes of fracture mechanics models. For many years, it has been used to determine stress intensity factors and, more recently, has expanded into the simulation of crack nucleation and propagation. In their work, the researchers are proposing new methods for fracture mechanics analysis and solid mechanics analysis.

Finite Element Analysis of Poor Distal Contact of the Femoral Component of a Cementless Hip Endoprosthesis

1993 ◽  
Vol 207 (4) ◽  
pp. 255-261 ◽  
Author(s):  
M Taylor ◽  
E W Abel
Keyword(s):  
Finite Element ◽  
Stress Distribution ◽  
Influencing Factor ◽  
Three Dimensional ◽  
Stress Distributions ◽  
Element Analysis ◽  
Hip Endoprosthesis ◽  
Applied Loading ◽  
Femoral Geometry ◽  
Contact Models

The difficulty of achieving good distal contact between a cementless hip endoprosthesis and the femur is well established. This finite element study investigates the effect on the stress distribution within the femur due to varying lengths of distal gap. Three-dimensional anatomical models of two different sized femurs were generated, based upon computer tomograph scans of two cadaveric specimens. A further six models were derived from each original model, with distal gaps varying from 10 to 60 mm in length. The resulting stress distributions within these were compared to the uniform contact models. The extent to which femoral geometry was an influencing factor on the stress distribution within the bone was also studied. Lack of distal contact with the prosthesis was found not to affect the proximal stress distribution within the femur, for distal gap lengths of up to 60 mm. In the region of no distal contact, the stress within the femur was at normal physiological levels associated with the applied loading and boundary conditions. The femoral geometry was found to have little influence on the stress distribution within the cortical bone. Although localized variations were noted, both femurs exhibited the same general stress distribution pattern.

Stress Distribution Analysis of Different Types of Blade for a Fermentation System

2013 ◽  
Vol 479-480 ◽  
pp. 319-323
Author(s):  
Cheng Chi Wang ◽  
Po Jen Cheng ◽  
Kuo Chi Liu
Keyword(s):  
Stress Distribution ◽  
Maximum Stress ◽  
Effective Means ◽  
Materials Processing ◽  
Distribution Analysis ◽  
Stress Distributions ◽  
Fermentation System ◽  
Different Types ◽  
Inclined Angle ◽  
Key Parameter

Fermentation system is widely used for food manufacturing, materials processing and chemical reaction etc. Different types of blade in the tank for fermentation cause distinct stress distributions on the surface between fluid and blade, and appear various flow fields in the tank. So, this paper is mainly focused on analyzing the stress field of blades under different scales of blade with fixing rotational speed. The results show that the ratio of blade length to width influences stress distribution on the blades. At the same time, the inclined angle of blade is also the key parameter for the consideration of design and appropriate design will decrease the maximum stress. The results provide an effective means of gaining insights into the stress distribution of fermentation system.

Simple Model for Contact Stress of Strands Bent over Circular Saddles

2016 ◽  
Author(s):  
Sherif Mohareb ◽  
Arndt Goldack ◽  
Mike Schlaich
Keyword(s):  
Simple Model ◽  
Stress Distribution ◽  
Contact Force ◽  
Contact Stress ◽  
Flexural Rigidity ◽  
Strong Nonlinearity ◽  
Stress Distributions ◽  
Maximum Contact ◽  
Contact Stress Distribution ◽  
Peak Value

Cable-stayed and extra-dosed bridges are today widely used bridge types. Recently, saddles have been used to deviate strands of cables in the pylons. Up to now the mechanics of strands on saddles are not well understood. It was found, that typical longitudinal contact stress distributions between strand and saddle show a strong nonlinearity and a high peak value around the detachment point, where the strand meets the saddle. This paper presents a procedure to analyse the longitudinal contact stress distribution obtained by FEM calculations: This contact stress can be idealised as a constant contact stress according to the Barlow's formula and a contact force at the detachment point due to the flexural rigidity of the bent tension elements. An analytical model is provided to verify this contact force. Finally, a formula is presented to calculate the maximum contact stress. This study provides the basis for further research on saddle design and fatigue of strands.

scholarly journals A Non-Singular Analytical Technique for Reinforced Non-Circular Holes in Orthotropic Laminate

2020 ◽  
Vol 25 (1) ◽  
pp. 92-105
Author(s):  
Pradeep Mohan ◽  
R. Ramesh Kumar
Keyword(s):  
Stress Distribution ◽  
Analytical Solution ◽  
Power Series ◽  
Orthotropic Shell ◽  
Infinite Plate ◽  
Stress Singularity ◽  
Power Series Solution ◽  
Element Analysis ◽  
Full Field ◽  
Analytical Technique

AbstractThe intricacy in Lekhnitskii’s available single power series solution for stress distribution around hole edge for both circular and noncircular holes represented by a hole shape parameter ε is decoupled by introducing a new technique. Unknown coefficients in the power series in ε are solved by an iterative technique. Full field stress distribution is obtained by following an available method on Fourier solution. The present analytical solution for reinforced square hole in an orthotropic infinite plate is derived by completely eliminating stress singularity that depends on the concept of stress ratio. The region of validity of the present analytical solution on reinforcement area is arrived at based on a comparison with the finite element analysis. The present study will also be useful for deriving analytical solution for orthotropic shell with reinforced noncircular holes.

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