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damage mechanics

Hi , I am a  working on a project of  Continuum Damage mechanics in Composite . But  I do not have much idea about Damage mechanics . I am getting lot of diffculites to understand this topic .

   So please  anyone let me know any basic literature, lecture notes where I can find all basic information about Damage mechanics .

Thanks in Advance,





Ying Li's picture

You can find some papers of him like follow:

X. Q. Feng and S. W. Yu, Damage and shakedown analysis of structures with strain-hardening, Int. J. Plasticity, 1995, 11(2), pp. 237-249.




I haven't done damage mechanics of composites in a while and don't
remember many of the details.  However, here are some pointers.

The basic idea is to degrade the material properties using a damage
variable as the strain increases.  The algorithms used to simulate damage
are therefore quite similar to those used for plasticity.  You should
first try to get some idea of how plasticity is numerically simulated.
Simo and Hughes book (the first part) is a good starting point.

Damage mechanics runs into additional problem because the initial-boundary
value problem becomes ill posed as the stress-strain curve changes slope
from positive to negative.  So you have to add a length scale to avoid
mesh dependence of the solution.  Usually some nonlocal or gradient terms
are added to take care of that problem.  There's a huge literature on the

If you are dealing with finite deformations then there are additional
complications that take quite some effort to understand - particularly for
composites.  This is because isotropy can no longer be assumed.

I have found the short papers in the collection "Numerical Modelling in
Damage Mechanics
" edited by Khemais Saanouni quite useful.  The book was
pubished by Kogan Page Science in 2003 and by Hermes Science Publications
in 2001.

The text book on damage mechanics by Kattan and Voyiadjis is
also quite useful as it takes you through the steps.  The book is called
Damage Mechanics With Finite Elements: practical applications with
computer tools
.  You will find a bibilography containing the early
literature and books on the subject.  You will have to be familiar with
finite elements and a bit of continuum mechanics to follow the book.


Thanks for your help..


phunguyen's picture


 Advanced course on

Modeling of
Localized Inelastic Deformation
taught by Milan Jirásek

in Prague, Czech Republic, on 24-28
September 2007

If you can attend that course, I think it's the best and shortest way to have basic knowledge on damage mechanics.

Hope that it was a little bit of help.



First of all thanks to everyone who gave me valueable raply...they are really helpful for guiding me towards right direction.

 anyone knows, in which paper prof.Ladevze explained Meso-damage model for composites or  where can I find all information about  basic meso damage model and  it`s related information

Thanks in advance,



Hi Nilesh,

For continuum damage mechanics (CDM), I would suggest you the following review paper by Dr. Ramesh Talreja:

Damage analysis for structural integrity and durability of composite materials, Fatigue & Fracture of Engineering Materials & Structures, Volume 29, Number 7, July 2006 , pp. 481-506(26)

I am also working on CDM (with Dr. Talreja) and we are extending the damage mechanics formulation to off-axis plies using a synergism between micromechanics based computational analysis and continuum damage mechanics formulation. As you would see, most of past work has been concentrated on  cross-ply laminates and researchers are now attempting to find ways to analyze damage in multidirectional laminates.

Basically, the idea in damage mechanics is as follows:

The composites on loading (tensile, fatigue or bending) develop multiple matrix cracks, which degrade the stiffness of the laminates and also give rise of more severe forms of damage such as delamination, interfacial debonding, sliding, fiber fracture etc. To model the performance degradation, damage models predict stiffness degradation with increasing crack density (# of transverse matrix cracks/mm) and also the damage progression rates (# of cracks as a function of applied stress). After combining the solution to these two inter-dependent problems, we arrive at the overall structural response (such as stress-strain response).

There are many models to predict stiffness degradation in cross-ply laminates, such as shear lag, self-consistent, variational, continuum damage mechanics etc. In particular, CDM tries to formulate the problem in form of the free energy of the damaged laminate with characterization of damage through introduction of internal variables (scalar, vector or tensor) , from which you can arrive at the constitutive relations (Double Differentiation of free energy function w.r.t. strain tensor will give you Cijkl).

If you need to discuss more, I would be happy to participate.



Chandra Veer Singh,

PhD Candidate,

Aerospace Engineering,

Texas A&M University


  Chandra Veer Singh,

 Thanks a lot for ur
valuable information. I would like to discuss further. Now days I am
working on mesodamge model for composite and ur
information is really helpful for me. Meanwhile from ur
reference I was searching courses on ur
university webpage and I found course No 616. Damage and Failure
in Composite Materials.

Mechanisms and models related to damage and failure in composite materials
subjected to mechanical loads. Prerequisite: Courses in composite materials,

So by any chance, could u give me softcopy of this lecture notes for study

Once again thanks for reply.

Best Regards,



Sorry for late reply. I don't think there is any softcopy of the damage mech course. Prof. Talreja teaches from papers, his notes etc. It is more like discussion, term papers etc. I agree there is no simple text/notes for this area.


Anyway, we can discuss on this depending on your specific problem. Think about the following things:

1. Are you using any specific damage model? What kind of composites you are dealing with, metal matrix, or ceramics or polymeric. Depending on those you may have to use different formulation. 

2. Is plasticity also involved? plasticity in metals is well knwon, but in case of polymeric composites, it is a different phenomenon known as crazing. So, for metal matrix composites undergoing plastic deformations, yield surface kind of plasticity laws can be adapted for composites; however the case will be different for polymeric composites, where yield surface doesn't make much physical sense.

3. What type of loading... tensile, bending, shear? it may change the type of formulation you may use.

4. What is the objective... Is it stress-strain response or change in stiffness properties or failure prediction or sth else?

5. Depending on your material... what are the dominant damage mechanisms involved (like matrix cracking, delamination, interfacial debonding, fiber fracture, microbuckling and so on )?

6. What is the length scale you are interested in? is it micro, meso-level or macro/structural? Are you intereseted in multiscale response? 

I hope answers to above questions will give you more insight into your specific problem and which damage model to use.


Good luck. 


Chandra Veer Singh,

PhD Candidate,

Aerospace Engineering,

Texas A&M University

ramdas chennamsetti's picture


I attended Prof. Talreja's lectures in IIT Bombay (I think it was in Dec' 2005). He mostly referred his papers. We got hard copy of PPTs only.

The lectures were very interesting.

Hi Veer, if you find any softcopy on damage mechanics (laminated composites) you may please forwrd us.

- Ramdas


I am aware of the DT for metalic structures, and i am having intrest to know about the DT analysis of Composite structures, but i can not able to found any material regarding this topic any ware..if any body is having any relevant material it will be very helpfukk for me...

my mail id:

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