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Theory of Representations for Tensor Functions—A Unified Invariant Approach to Constitutive Equations

Hi,

I am looking for the following paper.

Theory of representations for tensor functions - A unified invariant approach to constitutive equations - Q -S Zheng, Applied Mechanics Reviews, 47(11), 545-587, 1994.

If anyone has this paper, I request you to share.

Thanking you,

Best regards,

- Ramadas

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iMechanica app in a smart phone

Hi all,

I am thinking that it is a good idea to have 'iMechanica' smart phone app (like facebook, twitter etc). We can post/check blogs using a smart phone.  I request moderators and imechanicians to comment on this.

Best regards,

- Ramadas

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Strain energy density function of a Transversely Isotropic Material

Hi all,

I was going through Constitutive Modeling in Continuum Mechanics. I came across the Transversely Isotropic Materials (TIM). I have a couple of doubts, which are listed in the attached pdf file. I request the Continuum Mechanicians to clarify.

Thank you in advance,

Best regards,

- Ramadas

 

 

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ANSYS-LSDYNA Tutorials

Hi all,

I am looking for ANSYS-LSDYNA tutorials. If anybody has, I request him/her to kindly share or post the links.

Thanking you,

With best regards,

- Ramadas

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Linear and non-linear buckling

Hi all,

When we do a non-linear buckling analysis, initially we introduce some imperfections (mode shapes of mode 1, 2 etc) from eigen buckling analysis. Then we multiply the load with eigenvalue of the first mode. This load is applied on the structure having imperfections. Now put on non-linear geometric option and run the analysis. At bifurcation point we get non-linear buckling load. Non-linear buckling load comes close to eigen buckling value.

Decription of my problem is as follows. 

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Non-linear buckling analysis - complex loading

Hi all,

I have attached a single slide ppt file with this blog. In this slide, there is a hollow cylinder subjected to internal pressure and non-uniform axial load. All the translations at the bottom of the cylinder are fixed. As a whole the cylinder is subjected to a complex loading. The cylinder is modeled using SHELL elements in ANSYS. Now I know how to carry out non-linear buckling analysis in ANSYS.

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Stress based FE is not popular. Why?

 

Hi all,

I have a doubt as follows.

"Why stress based Finite Element Analysis / Method is not popular compared to displacement based FE?"

I request you those who has some idea about this to comment.

With regards,

- Ramdas

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Hermite interpolation functions

Hi all!!!

In Finite Element Method (FEM), Hermite interpolation functions are used for interpolation of dependent variable and its derivative.

In FEM books, Hermite interpolation functions are directly written in terms of Lagrange interpolation functions. No derivations are given. I searched in Numerical methods books also for derivation of Hermite interpolation functions. I couldn't find.

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If there is no response.....then.....

In imechanica when a blog is posted, we get good response / discussion (or sharing ideas, knowledge etc) from members. This happens many times.

If there is no response for a particular blog even after many days...then....what? It may be updated (because some members might have missed it). Even then also if there is no response, what may be done???

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Delamination mode failure

Hi all!!!

General theories of failure of laminated composites are Tsai-Hu, Tsai-Hill, Maximum stress and maximum strain. These thoeries do not specify which component (fiber or matrix) of lamina fails.

Sigma_zz, sigma_xz and sigma_yz are out of plane stresses which cause delamination failure of laminated composite structures.

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Fourth order tensor

Hi all,

I have a fundamental question on Tensors. The length of a vector (firts order tensor) is independent of the reference co-ordinate system. In case of second order tensor (stress/strain), the invariants (I1, I2, I3) are independent of the co-ordinate system.

If I consider 4th order tensor (of course 3rd order also), say Cijkl, what parameters are constant? (Like length in vector and invariants in second order tensors).

Thanks in advance,

- Ramdas

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High SIF in plane stress

Hi all!!!

I have a very basic question in Fracture Mechanics. The question is as following.

"Stree Intensity Factor (SIF) is more in plane stress problems (plasic zone size is big) than in plane strain problems (plasic zone size is small). How do we explain this, without refering or invoking energy conecpt?"

I request to give some thoughtful explanation.

With regards,

- Ramdas

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Spectral Element

Hi all,

I have just started learning (working) on spectral element method for modeling elastic wave propagation. I wrote a small code for bar spectral element. There is some problem in reconstruction of signal. If anybody is working in this area may write back. I will send my code. If anybody is having a sample code, I requet them to kindly share.

With regards,

- Ramdas (rd_mech@yahoo.co.in)

 

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Theories of Failure in Strain space

Hi all!

In theories of failure (e.g von-Mises, Tresca, Max. principal stress etc), yield funcion,          f(sigma ij, Y) = 0 is plotted in principal stress space (sigma 1, sigma2 and sigma 3). Why shouldn't we express the same yield function, f(epsilon ij, epsilon Y) = 0 and plot in principal strain space?

Y = Yiled stress, sigma ij = stress ij, epsilon ij = strain ij. and espsilon Y = Yield strain = Y/E,   E = Young's modulus

Any thoughtful comments???

With regards,

- Ramdas

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Complementary Strain Energy - Non-linearity

Hi all!

I read that the "cmplementary starin energy of a structure is not equal to sum of the complementary strain energies of it's components, if there is non-linearity like geometric"

That means for e.g. if I consider a truss stucture subjected to loading so that it undergoes geometric non-linearity, then the sum of the complementary strain energies from members is not equal to complementary strain energy of the structure.

 I request somebody to explain why is it so??

 Thanks and regards,

- Ramdas

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Complmentary Strain Energy - Nonlinearity

Hi all!

I read that the "cmplementary starin energy of a structure is not equal to sum of the complementary strain energies of it's components, if there is non-linearity like geometric"

That means for e.g. if I consider a truss stucture subjected to loading so that it undergoes geometric non-linearity, then the sum of the complementary strain energies from members is not equal to complementary strain energy of the structure.

 I request somebody to explain why is it so??

 Thanks and regards,

- Ramdas

ramdas chennamsetti's picture

Complementary strain energy - Non-linearity

Hi all!

I read that the "cmplementary starin energy of a structure is not equal to sum of the complementary strain energies of it's components, if there is non-linearity like geometric"

That means for e.g. if I consider a truss stucture subjected to loading so that it undergoes geometric non-linearity, then the sum of the complementary strain energies from members is not equal to complementary strain energy of the structure.

 I request somebody to explain why is it so??

 Thanks and regards,

- Ramdas

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Why rate equations in Nonlinear FE?

Hi all!

I have a very fundamental question as follwing.

In Nonlinear FE formulations, we use rate equations (virtual work), but, in linear FE we don't use rate equations. Why???

Is it because Nonlinear solution is iterative solution (time may be virtual time).

I request those who have an idea to give some explanations.

Thanks in advance,

Regards,

- Ramdas

 

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Polar decomposition

Hi all,

I went through a topic on polar decomposition of deformation gradient. I understood the mathematics. I would like to know the physical significance and application of this. I request somebody to explain this.

Thanks in advance,

Regards,

- Ramdas

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Strain compatibility equation in non-linear solid mechanics!!!

We have six strain compatibility equations, which are obtained from strain-displacement relations by making an assumptions 'small strains'. Strain compatibility equations ensure a single valued and continuous displacemnet filed. These equations are used in stress based approach.

Now my queries are as following.

[1] Do we have strain compatibility equations for non-linear strain-displacement relations?

[2] Do we follow stress based approach in non-linear solid mechanics.

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Cubic symmetry

Hi all!!!

Could anybody please give some examples of materials possessing cubic symmetry (these materials need three independent elastic material properties).

Thanking you,

- R. Chennamsetti 

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Potential for Strain energy

Hi all,

When a conservative force does work, it is independent of the path, we define the potential and work done is given by  - (change in potential).

We define potentials for gravitational force, electrical force etc...

Assuming the body is linear elastic, internal forces, cause stresses in a body, are also conservative forces, whose work (strain energy) is independent of the path. Can we define potential for such internal forces? If so, we can calculate strain energy = -(change in potential).

You may kindly explain this.

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Body couples

Hi all,

We come across body loads such as gravitational, cenrifugal, magentic etc. Similary do we have body couples? If so, I request you to throw some light.

- Thanks & regards,

- Ramdas

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RMS Wave front

 

Hi all,

I just want to know how do we calculate the RMS wave front in frontal solver...

Thank you,

- Ramdas

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