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This web page acts as a portal into a series of Interactive Failure and Fracture Mechanics Resources.  These are intended to supplement undergraduate modules dealing with fatigue, fracture and failure analysis, or to support Continuing Professional Development short courses.  The aim was to improve student-centered learning in the integrative skill areas of linear elastic fracture mechanics and failure analysis.  Successful failure analysis depends on metallurgical/materials input as well as a good knowledge of design, stress analysis and fabrication.  It is therefore a high level engineering skill and case studies are an excellent means of achieving "authentic learning".

These resources have been developed over a number of years and are based on experience of the difficulties and pitfalls found by students in grappling with an inherently defect-based approach to engineering.  Further development is planned, particularly of the failure analysis case studies, although this depends on finding suitable time.  The case studies arose out my experience as a consulting failure analyst.

Use of these resources is open to any academic and student provided that they are not used for financial gain, and that appropriate acknowledgment is made to the author and to their provenance.  I would be interested to hear feedback on their use and to find out where they are being used.



Professor M N James' homepage can be accessed at:




vicky.nguyen's picture

Journal Club March 2010: Viscoelasticity of Soft Tissues

It is widely accepted that collagenous soft tissues exhibit viscoelastic behavior, which includes time-dependent creep and stress relaxation, rate-dependence, and hysteresis in a loading cycle. The hysteresis is less sensitive than the stiffness to the loading rate, and this phenomenon is generally found in soft tissues and elastomers (Fung 1993). The experiments of Boyce et al. (2007 2008) to characterize the viscoelastic response of the cornea and sclera spanned three orders of loading rates. They observed at higher rates little rate-dependence in the stress-strain curve during loading but significant hysteresis during unloading.

Zhigang Suo's picture

Fracture of Rubber. Lecture 2

Fracture mechanics without invoking any field theory. In Lecture 1 on Fracture of Rubber, we considered the extension of a crack in an elastic body subject to a load. Following Rivlin and Thomas (1953), we regarded the elastic energy stored in the body as a function of two independent variables: the displacement of the load, and the area of the crack. The partial derivative of the elastic energy with respect to the area of the crack defined the energy release rate.

Generate softening curve



I seek help from the forum regarding the following. Because I am very new to mechanics.

I have a continuum damage mechanics model with me. I have set up a problem of a typical three point bending test on a notched beam. The notch in the center of the specimen and extends from the bottom face up to the middle of the thickness. It is a plane stress problem. Now I want to simulate load-displacement curve obtained from the experiment (s).

knaumenko's picture

Postdoctoral Positions in the Post-Graduate School at the Otto-von-Guericke-University Magdeburg, Germany

A number of 3 year research schoolarships and PhD positions in the areas of mechanical engineering, process engineering and applied mathematics is available in the Post-Graduate School "Micro-Macro-Interactions in Structured Media and Particle Systems", Otto-von-Guericke-University Magdeburg, Germany.

Further information can be found at  http://www.uni-magdeburg.de/gkmm/free-position-new-gk.htm

Marine Current Turbine



I'm doing some investigation on a marine current turbine, for a project using the Lifting Line Theory. 

I found out some problems regarding some assumptions one has to make when projecting a turbine, such as cavitation number, tip speed ratio, Reynolds number, etc...

Any information of any bibliography you might have might became handy, so I appreciate if you share it.


Thank You!


Need an example of wave propagation in a plate using abaqus

Hi every body,I'm a senior student in mechanics and really I need an
example of wave propagation in a thin plate to conduct my project. At
now,main problem for me is how to apply load to get answers with
obvious wave propagtion contour plot without any thing more in just one

Thanks in advance,


How is this possible in ABAQUS?

I am trying to run UHYPER in ABAQUS 6.9EF1. I have the following questions:

1) How can I get the nodes
ID associated
with element# NOEL in UHYPER subroutine?

2) How can I get the
coordinates of the displaced nodes associated with element# NOEL in UHYPER
subroutine in the middle of the simulation? I tried to use GETVRN but it seems it does not work in

3) How can I get the deformation gradient tensor using
GETVRM for element# NOEL in UHYPER? I have also tried using USDFLD and
GETVRM but it returns zero for everything.

Hashem Mourad's picture

Postdoctoral Positions in Computational Solid Mechanics at Los Alamos National Laboratory

The Fluid Dynamics and Solid Mechanics group at Los Alamos National Laboratory is currently seeking candidates for two post-doctoral positions in the areas of theoretical and computational solid mechanics.

Further information and application instructions can be found at http://www.hr.lanl.gov/JobListing/SingleJobAd.aspx?JobNumber=218796

H Jerry Qi's picture

IMECE 2010 Student Travel Awards and Best Papers Contest

The AMD executive committee (EC) just announced the student travel awards and best paper contest for IMECE 2010. Between 10 and 15 students will be selected for travel grants of $750 each. The students who receive travel awards will also become eligible to participate in the best paper contest. This is a great opportunity for young students to present their work and meet other researchers during IMECE 2010.

Zhigang Suo's picture

Fracture of Rubber

A rubber band can be stretched several times its original length. This large deformation may hide its brittleness: the strain to rupture can be markedly reduced by the presence of a crack. This lecture describes fracture mechanic of highly deformable materials, such as rubbers and gels.

Demonstrate in class the effect of a crack on a rubber band. Use a wide rubber band. Show the class that the rubber band can be stretched several times its original length. Then use scissors to cut a crack into the rubber band. Pull the rubber band to rupture. Note that the strain to rupture is markedly reduced by the crack. Pass the scissors and some rubber bands around. Invite every student to try.

David R. Clarke's picture

Postdoctoral Fellowships in elastomers and related material sciences at Harvard

Applications are invited for one or more postdoctoral positions at the School of Engineering and Applied Sciences, Harvard University. The projects will be related to elastomer materials with relevance to their optical properties and device applications. Prior hands‐on experience in one or more areas such as polymer materials synthesis, optical measurements, polymer processing is required. The project will have a strong experimental focus and will encompass elastomer processing, physical characterization, mechanics as well as fabrication of devices based on actuation with elastomers.

Position Available - Solid Mechanics - Houston, TX

Please refer to job description. Thanks

Resumes can also be sent to : agrebe@smith.com



A post-doc position in the field of Composite materials (GNU, Korea)

A post-doc position is currently available at the Research centerfor Aircraft Parts Technology in Gyeongsang National University (Jinju, SouthKorea).

The research project will be based in the Research centerfor Aircraft Parts Technology in Gyeongsang National University. The researchwill be supervised by a principal investigator of the project (Prof. Jin-HweKweon).

The starting salary is 27,000 USD per year. For candidateswith excellent qualification, salary negotiation is also possible. Thisresearch position is guaranteed for several years depending on the researchresults.

navidtajik's picture

speckle pattern interferometry

I’m working on optical method for displacement measurement. and this is interesting to know more about application and development of these methods like ESPI , SHEAROGRAPHY anf HOLOGRAPHY . for example i face with a company that climb their product can give displacement and so strain field in many material and many geometry even in 3-D shapes!!

Jianliang Xiao's picture

Mechanics of in-surface buckling of one dimensional nanomaterials on elastomeric substrates

In this recently published paper on Nanotechnology, we studied the in-surface buckling mechanics of one dimensional nanomaterials on elastomeric substrates.  Simple analytical solutions are obtained for buckling wavelength and amplitude, which can be easily applied to the in-surface buckling of different nanomaterials, such as nanowires and nanotubes.  It is shown that in-surface buckling of nanomaterials has lower energy than out-of-surface buckling, which explains the experimental observance of in-surface buckling of silicon nanowires.  However, single-walled carbon nanotubes (SWNTs) are reported to buckle out-of-surface on PDMS substr

HCHan's picture

Postdoc position in vascular mechanics

The Cardiovascular Biomechanics Lab in the Department of Mechanical Engineering at The University of Texas at San Antonio (UTSA) is seeking a highly motivated postdoctoral fellow to join our research team. The position is supported by a research grant from the NIH to study the mechanical stability and tortuosity of blood vessels. Qualifications include a doctoral degree in BME or ME in computational fluid mechanics, or computational biomechanics.

Integrity of Scholarly Publishing under Attack


This issue of CAM digest re-published D.N. Arnold's article  "Integrity under Attack - the state of scholarly publishing". The orginal article is available via weblink


I feel the discussion (actually the journals mentioned in the article as well) is quite relevant to the mechanics community. While impact factors have no much meaning especially in mathematics, its role may not be easily dysfunctionalized by abusive publications/citations in a short run....

 X. Frank Xu     

Zhigang Suo's picture

Stress Corrosion

A glass may withstand a static load for a long time (days, weeks, or years) and then, without warning, breaks suddenly. Here are salient empirical observations:

  • The delay time depends on the magnitude of the load: The smaller the load, the longer the delay time.
  • The phenomenon is environment-sensitive. Glass suffers delayed fracture in moisture, but not in vacuum. The lower the humidity, the longer the delay time.
  • The phenomenon is thermally-activated. The lower the temperature, the longer the delay time.

The phenomenon occurs to all materials to some degree in some environments. The phenomenon is known variously as

thermal radiation analysis in ansys workbench 12

Hello everybody,

I have been assigned the task of performing thermal analysis of electronic components that involve conduction and radiation only and determine the temperature distribution on them. I am doing this in ansys workbench 12. Since I am doing thermal analysis for the first time so having problems.

Does anybody have tutorials related to performing thermal analysis in ansys workbench. Please share.

Thanks in advance.


Muhammad Yousuf Ayub

Qing Xiang PEI's picture

Postdoctoral Research Associate Position at IHPC of Singapore

We are seeking outstanding candidates for a Postdoctoral Research Associate Position at the Institute of High Performance Computing, Singapore. The position requires a Ph.D degree in physics, chemistry, materials science, chemical engineering, mechanical engineering or equivalent experience.

Additional requirements include:

. Knowledge in mechanics of materials

. Experience in molecular dynamics simulation . Proficiency in programming using Fortran and/or C/C++ . A record of technical publications is a plus . Must have strong oral and written communication skills in English

Rui Huang's picture

Effects of mismatch strain and substrate surface corrugation on morphology of supported monolayer graphene

In a previous work, substrate-modulated morphology of graphene was analyzed using a numerical Monte Carlo method. Here we present an analytical approach that explicitly relates the van der Waals interaction energy to the surface corrugation and the interfacial properties. Moreover, the effect of mismatch strain is considered, which predicts a strain-induced instability under a compressive strain and reduced corrugation under a tensile strain.

Henry Tan's picture

Subsea Integrity

I am teaching Subsea Integrity for the MSc students majoring in Subsea Engineering at the School of Engineering, University of Aberdeen. This is a course that combines the fundamental principles (corrosion, fracture, fatigue and material selection) with the industry applications (subsea integrity management and implementation, cathodic protection, case studies on subsea reliability and engineering assurance).

The teaching is recorded and posted with video and pdf files. The course website is at



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Please use this identifier to cite or link to this item: http://hdl.handle.net/1813/3075
Title: Lecture Notes on Fracture Mechanics
Authors: Zehnder, Alan
Keywords: fracture
fracture toughness
energy release rate
stress intensity factor
J integral
fracture criteria
ductile fracture
brittle fracture
cohesive zone
small scale yielding
large scale yielding
crack stability
plastic zone
crack tip
Dugdale model
toughness test
computational fracture
domain integral
modified crack closure
nodal release
Issue Date: 30-Jul-2009
Abstract: This book is written for students who want to understand, apply and contribute to the vast and growing field of fracture mechanics. The emphasis is on mechanics models for crack tip fields and energy flows. A brief discussion of computational fracture methods is given along with applied aspects such as fracture toughness testing and fracture criteria. As I intend to update the notes, I would be happy to take any suggestions or corrections and am open to collaboration to expand the coverage.
URI: http://hdl.handle.net/1813/3075
Appears in Collections:Theoretical and Applied Mechanics Papers and Monographs

Files in This Item:

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Conventional Failure Analysis

The most straightforward design consideration to avoid structural failure is obviously keep the maximum stress well under the posted material strength:

Maximum Stress Strength of Material

This maximum stress approach, although usually adequate when one principal stress dominates, may not be valid when the structure undergoes general multi-axial loadings. To address this issue, many failure criteria were proposed. Most of them are based on principal stresses, strains, or strain energy. By overlaying an "effective" strength of material and the loading conditions, one can determine the effectiveness of the structural elements.

Applied Stress Failure Criterion

Still, in reality, many more factors are to be considered. For example, the material is never flawless; the assembly may not be perfect; the loading may not be as designed; the environment may be harsh; the maintenance may be poor; and the service life may have to be very long. Traditionally these concerns were (hopefully) offset by a single safety factor; that engineers employ like a second nature. Unfortunately, history showed that many structures failed way below their designed capacity.

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Fracture Mechanics, a Brief History

From investigating fallen structures, engineers found that most failure began with cracks. These cracks may be caused by material defects (dislocation, impurities...), discontinuities in assembly and/or design (sharp corners, grooves, nicks, voids...), harsh environments (thermal stress, corrosion...) and damages in service (impact, fatigue, unexpected loads...). Most microscopic cracks are arrested inside the material but it takes one run-away crack to destroy the whole structure.

To analyze the relationship among stresses, cracks, and fracture toughness, Fracture Mechanics was introduced. The first milestone was set by Griffith in his famous 1920 paper that quantitatively relates the flaw size to the fracture stresses. However, Griffith's approach is too primitive for engineering applications and is only good for brittle materials.

  Applied Stress  
Fracture Toughness   Flaw Size

For ductile materials, the milestone did not come about until Irwin developed the concept of strain energy release rate, G, in 1950s. G is defined as the rate of change in potential energy near the crack area for a linear elastic material.

When the strain energy release rate reaches the critical value, Gc, the crack will grow. Later, the strain energy release rate G was replaced by the stress intensity factor K with a similar approach by other researchers.

After the fundamentals of fracture mechanics were established around 1960, scientists began to concentrate on the plasticity of the crack tips. In 1968, Rice modeled the plastic deformation as nonlinear elastic behavior and extended the method of energy release rate to nonlinear materials. He showed that the energy release rate can be expressed as a path-independent line integral, called the J integral. Rice's theory has since dominated the development of fracture mechanics in Unite States. Meanwhile, Wells proposed a parameter called crack tip opening displacement (CTOD), which led the fracture mechanics research in Europe.

Thereafter, many experiments were conducted to verify the accuracy of the models of fracture mechanics. Significant efforts were devoted to converting theories of fracture mechanics to fracture design guidelines.

Recent trends of fracture research include dynamic and time-dependent fracture on nonlinear materials, fracture mechanics of microstructures, and models related to local, global, and geometry-dependent fractures. Unlike existing major theories with a single-parameter approach (G, K, J, or CTOD), these recent research trends usually require more than one parameter to describe the behavior of the crack growth, which is beyond the scope of this text.

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