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Derivatives of Tensors

Hi all,

I am looking for a general definition of the derivative of a tenorial product (e.g. when the expression for Stress contains nonlinear terms in deformation gradient, F ).

I start with a very simple example:

∂F_pq/∂F_mn = δ_pm  δ_qn , i.e. Kronecker delta with first index of F_pq and first index of  F_mn, and second Kronecker delta for second pair of indices q & n.

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Inverse of the 4th rank tensor

Hi all,

I am looking for an algorithm to get the inverse of a 4th rank tensor (e.g. the compliance tensor S_(ijkl) from elastic stiffness tensor C_(ijkl)) S_(ijkl)=C_(ijkl)^(-1)

I am programming in FORTRAN, and for this purpose I wasn't able to find neither any algorithm nor any existing subroutine.

If anyone at this forum has any idea about this inversion, kindly guide me.

Best regards,


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Physical Foundations of Continuum Mechanics

After many publications and lecture notes, Prof. Ian Murdoch has finally organized much of that material in the form of a book.

I am very hopeful that like Prof. Murdoch's lectures, this monograph will also help the readers to develop a better understanding of the physical aspects of mechanics. It will be a valuable addition to the researchers' personal collection. 


more details in the flyer attached.

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Advanced Finite Plasticity Textbooks

While reading the article

"An alternative approach to finite plasticity based on material isomorphisms " (1999) by Prof. Bertram, the first thing that attracted my attention was the quote [by Prof. Naghdi (late)]:

 “there is some degree of disagreements on nearly all of the main constitutive ingredients and features of plasticity in the presence of finite deformation... Some of the issues of disagreements are of basic and fundamental importance.”

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Strain Gradient Plasticity

Hi all,

I have a strange question that has puzzled me since last almost one year.

There are many SG-plasticity models in the technical literature, sometimes categorized as lower-order or higher-order models.

The problem is :

the constitutive models include the gradient of plastic parameters (e.g. plastic slip).

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Mechanics of Nanocrystalline Materials: From Discrete to Continuum

18th IUTAM Summer School on “Mechanics of Nanocrystalline Materials: From Discrete to Continuum”

September 10, 2012 — September 14, 2012


 International Centre for Mechanical Sciences (CISM), Udine , ITALY


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FEAP - history variables for Elements

Hi all,

my question is about the history data storage in FEAP.

I am writing element subroutine (elmt01) in FEAP 8.3  for a history dependent problem.

I have written the stiffness matrix subroutine (stiff01), but it needs the data from the previous solution steps (previous strains, stresses, plastic strains, dislocation densities .... nh1,nh2=30 per point).

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FEAP umat routines

Hi all,

I am using FEAP 8.2 in my university, and have to write a user material routine, but there is no clear guideline/example about which files to modify for this purpose. Sorry to say, the programmer's manual is very short, and very little detail is there.

The old tutorials/examples based on FEAP (7.x) are no longer helpful because the FEAP 8.2, 8.3 source code has changed considerably (atlease the files in user folder), hence the novice can get mad after trying for many weeks to figure out the way for doing this.

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CISM Course: Plasticity and Beyond

Dear all,

please find information about the 5 day - course on Plasticity and Microstructures at CISM Udine, Italy.

The link is:

Flyer is attached.

Best regards,



Original post from CISM website:

Plasticity and Beyond: Microstructures, Crystal-Plasticity and Phase Transitions

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Crystal Plasticity- overview

I read this article today, perhaps other beginners like me can also get some benefit from this:

Title: Overview of constitutive laws, kinematics, homogenization and multiscale methods in crystal plasticity finite-element modeling: Theory, experiments, applications.  

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Two-point Tensors

I am confused about the use of two-point tensors in elasticity. The deformation tensor F and first PK tensor are two point tensors, and the "two-point" property arises from use of two different Coordinate System When a continuum body is deformed, why it is necessary to move the Coordinate System as well? (or alternatively, why the coordinate system is attached to the body itself??, isn't it possible to use a general coordinate system which can represent the deformations and also account for the rigid body rotations of the continuum body?).

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Crystal Plasticity

I am interested in the computational crystal plasticity (elastic-viscoplastic models), and I intend to start working in this area. Therefore, I am looking for some review papers--

1- which provide an overview of the state-of-art in this area (a summary of the recognised single crystal plasticity models).

2- about the application of single crystal plasticity using micromechanics based  multiscale FEM for the prediction of texture evolution.


I will be very thankful if sombody can answer these queries.

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Multiscale Modelling- Introductory Literature

I am looking for introductory-level papers/texts on multiscale modelling of solids. Please suggest some titles which give introduction alongwith a summary about the latest advances in this field. I will be thankful for your suggestions.


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