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?

One problem I can think of is the growth of numerical errors with the increase in number of steps (though it might remain within bounds, due to the stability of the scheme).  Are there any other issues associated with extremely small time steps?

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:

1. Whether this aspect is actually considered in an updated Lagrangian formulation, or is it ignored as a negligibly small effect? 
2. Does it mean that Total Lagrangian Formulation is "the" correct approach, and updated Lagrangian method is only an approximation?

Links to any references, wherein this matter is discussed are also welcome.

Thanks in advance,

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.

Hi all,

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

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,

Jayadeep U. B.

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?