# Weijie Liu's blog

## 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?

## 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.

## 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?

## 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?

## 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.

## 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:

## 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:

## Hi, iMechanica

Congratulations! This is the 1st entry.

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

Major : Solid Mechanics

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

$1+sin(x)$