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Jayadeep U. B.'s blog

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Equilibrium equations in mechanics: why there are only two kinds?

Off late, I am not seing any random thoughts on iMechanica.  This is my humble attempt at reviving such discussions.  Please contribute with your comments...

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Principle of minimum potential energy -- why is it true?

Dear all,

Two fundamental concepts from thermodynamics are that systems try to minimise their potential energy, whereas the tendency is to maximise the entropy (ofcourse I am not at all precise in the above statement, but I hope I am able to convey the matter.  Further, the two can be combined in the form of a free enrgy as applicable to the system under consideration).

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Tensile stresses in an elastic body accelerated by an attractive body force

Dear all,

Can someone suggest me literature where the problem "tensile stresses developed in an elastic body accelerated by an attractive body force" is discussed.  The situation is similar to finding the stresses developed in a celestial body falling into black hole (though my interest is in impact with adhesive forces).

The problem is about solving the inhomogeneous wave equation, where inhomogeneous part is due to the attractive force.  So any helpful hints in that direction will also be useful. 

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Dynamic FEM: Can the timestep size be made extremely/arbitrarily small?

Dear all,

I am in the process of developing an FE code, and doing the analysis, for a class of highly nonlinear, dynamic problems in elasticity using Total Lagrangian formulation.  It is well-known that for the accuracy purposes, we need to use a small timestep size (stability is not an issue for me as I am using an unconditionally stable implicit scheme for timestepping).

My doubt is whether I can use arbitrarily/extremely small time steps in the analysis for a given mesh?

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Isotropy: Updated Lagrangian Vs Total Lagrangian

Dear All,

 I have seen it being mentioned that the material at an updated configuration in an Updated Lagrangian Formulation (say in FEM) may not remain isotropic, even if the reference configuration was isotropic.  However, I have not seen any detailed discussion on the matter.

Hence, I would request your comments on:

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"Classics" in iMechanica

Dear all,

While reading some "old" discussions in iMechanica, I have come across
a blog by Zhigang to have a collection of "classics" in iMechanica. 
Immediately, I searched for such a section, but couldn't locate it.  Is
it ever made?  If not, why not start it now?  I am sure there will be
many juniors like me, who are eager to read those classics.

Jayadeep U. B.'s picture

Continuum mechanics, Micromechanics and Nanomechanics

Hi all,

Can anyone explain me the characteristic features of continuum mechanics, micromechanics and nanomechanics?  My present level of understanding is:

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Symmetry of Infinitesimal (linear) strain tensor

Hello everyone,

 Why do we have the infinitesimal (linear) strain tensor to be symmetric? The reasons, which I have understood so far are:

1. It is defined to be symmetric so that it behaves like a tensor.

2. The stress tensor, which is its energy conjugate, is symmetric, and hence the skew-symmetric part has no contribution towards strain energy.

 Can anyone suggest more fundamental reason(s) for the symmetry of linear strain tensor, like the moment equlibrium leading to symmetry of the Cauchy stress tensor?

Thanks in advance,

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Finite Element Discretization in Time Direction

In the finite element analysis of a transient problem, the usual procedure is to discretize the space (domain) using finite elements, while in the time direction, a time-stepping scheme based on finite differences is used. Is it possible to use a finite element type discretization in time also?  Is there any work done in this manner?

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