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Thermal wave propagation in finite velocity

Hello All,

For the Cattaneo's hyperbolic heat equation with relaxation time,

usually a simple plane thermal wave Τ=T0 * exp[ ¡ (kx - ωt) ], with definition k is the (complex) wave number and ω is the the (real) frequency, is adopted to obtain the dispersion relations of the heat equation.

And consequently, the velocity is defined as: [ω / Re(k)].

 

My confusion is that is it necessary or obligatory to let k be complex and w be real?

If the answer is yes, then why?

If no, then it's possible to let both k and w are real?

 

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About UEL/VUEL for shell element

Hello, I'm trying to program a quadrilateral classical Mindlin flat shell element (full integration for membrane, bending and selective reduced integration for transverse shear).

Now, the situation is: 
for pure tension test, it works well (because only the membrane part works),
for pure bending test, it gives very bad result compared with S4R, and I find that's because the incremental rotations at each step are different.

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How to compile an UMAT wrote in C/C++?

Hi,

Does anyone know how to compiler an umat in c/c++ for abaqus under windows system?

The Umat wrote in fortran works well, but I do prefer using c/c++ to make program.

I have installed visual studio 2010 c++, intel fortran.

 

Or is it possible to use c/c++ for umat?

 

Thanks in advance.

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Should entropy and temperature be dual?

In Classical Continuum Mechanics, the entropy(s) and temperature(T) are considered to be dual in the second thermodynamics principle,

by define a relation between internal energy(e) and Helmhotz free energy(ψ): ψ = e - s * T .  As you can find it in many CM books, such as [2008][J.N.Reddy]Introduction to Continuum Mechanics.

 

Here is my questions:

1. Is the transformation between internal energy and Helmhotz free energy a Legendre Transform?

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Will the virtual work be valid in finite deformation?

"We see from the above that the virtual work statement is precisely the weak form of equilibrium equations and is valid for non-linear as well as linear stress-strain (or stress-strain rate) relations." --- written by O.C. Zienkiewicz etc. at Page 71 of <The Finite Element Method: Its Basis and Fundamentals  Sixth edition>

 

Here is my question: Will the virtual work still be valid for the case of non-linear strain-displacement relations (finite deformation)?

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How to understand the oscillating behaviour during calculating stress

Dear all,

Why we have an oscillating behaviour when calculating stress in FEM?

I saw the sentences in the paper:

'Another reason is that stresses are less accurately predicted than strains in FE simulations. Calculated stresses do also show a tendency for an oscillating behaviour, especially in dynamic explicit simulations.'

'stress is less accurate predicated than strain' is easier to understand, but I was wondering the existence of oscillating behaviour for calculating stress.

 

Any comments are welcome.

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Plasticity integration: satisfaction of the consistency requirement

Dear all,

I am trying to formulate the return mapping algorithm with Hill48 yield condition, isotropic hardening law and flow rule referenced to Simo & Hughes (Computational Inelasticity).

In section 2.2.2.1, equation (2.2.9) expresses the Kuhn-Tucker complementarity conditions:

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How to explain the coefficient of Hill 48 yield criterion?

Can someone help me to explain the derivation of the coefficent ?

 

 In the paper "A theory of the yielding and plastic flow of anisotropic metals", the Hill 48 yield criterion:

 The quadratic Hill yield criterion 

 

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Hi, iMechanica

Congratulations! This is the 1st entry.

Let me start with the self-introduction. 

Identity : A first-year Doctoral student of Dalian University of Technology.

Major : Solid Mechanics

Now, the simulation of sheet metal forming is focused on. 

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