# vinh phu nguyen's blog

## convergence of Newton Raphson for a Discontinuous Galerkin for linear elasticity

Hi all,

I have implemented a DG code for linear elasticity. If I solve Ku=f, then I obtained a correct result (compared with a continuous Galerkin method). However if I used a Newton-Raphson (NR) method to solve the equilibriuum equation, although I still got a correct result, the convergence of NR was bad: I needed 3 or 4 iterations for linear elasticity!!! The young modulus is 3e7 and the stabilization parameter is 3e9. If a larger value of 3e10 was used for the stabilization parameter, it converged in 2 iterations.

For your information, I am using the Symmetric Interior Penalty Method or Nitsche's method. And the material is compressible.

## meshless methods summer school (Cardiff University, UK)

Dear all,

Cardiff institute of Mechanics and Advanced Materials is organising the first UK Summer School on Meshless Methods in Mechanics on the 29th and 30th of July 2013. The schedule is below.

## Isogeometric Analysis (IGA)

The aim of this post is to give a brief introduction to the recently emerged isogeometric analysis (IGA) which was presented in the seminal paper " Hughes, T.J.R.; J.A. Cottrell, Y. Bazilevs (2005). "Isogeometric analysis: CAD, finite elements, NURBS,exact geometry and mesh refinement". Comput. Methods Appl. Mech. Engrg. (Elsevier) 194: 4135–4195." IGA refers to a computational framework in which the basis functions used to represent the geometry in CAD are used for approximating the unknown fields in FEA. In this regard, IGA also employs the well known isoparametric concept.

## Assistant Professor Position open at the Division of Computational Mechanics, Ton Duc Thang University, Vietnam

We are opening one or two Assistant Professor positions at the Division of Computational Mechanics, Ton Duc Thang University, Vietnam led by Prof. Hung Nguyen-Xuan and Dr. Trung Nguyen-Thoi. The candidates who hold a PhD degree on Mechanical Engineering, Civil Engineering or Computational Engineering are expected to work on some national projects on the field of computational fluid dynamics (CFD) and enhance the on-going research activities of the group.

Information on the Ton Duc Thang university can be found here

## A review on multiscale methods for material modeling

Dear all,

Please find enclosed our paper which is published on Journal of Multiscale Modelling
Vol. 3, No. 4 (2011) 1–
42 which gives an overview of state of the art multiscale techniques for material modeling.

The paper discusses the following topics: homogenization, Representative volume element, computational homogenization (Fe2 methods) for both both bulk materials and strong discontinuities.

I hope the paper is useful for beginners to the field.

All the bests,

## A free program to generate interface elements in an existing FE mesh

Hello all,

Last year when I started implementing interface elements to model material failure, I realized that the formulation is easy except how to generate a mesh with interface elements. I did a googling to search for such a free program. Amazingly, I did not find any although there are many researchers working on the fracture mechanics field.

So, I wrote a small object-oriented C++ program which reads a FE mesh, duplicates nodes and insert interface elements where asked. The program is able to

(1) insert 1D/2D interface elements everywhere in a FE mesh

(2) insert i1D/2D nterface elements along material interfaces, useful for delamination analysis or interface debonding

## Looking for a postdoctoral position in the field of (solid) computational mechanics

Hello,

My name is Nguyen Vinh Phu, a PhD student at Delft University of Technology, the Netherlands. I have been working with Prof. Bert Sluys on a project named "Coarse graining of failure in heterogeneous solids" since July 2007. I am finishing my work and therefore seeking for a postdoctoral position starting after July 2011.

My expertise in computational solid mechanics includes

(1) Finite elements, extended finite elements and meshless methods.

## Crack penetration in cohesive zone models

Hi all,

I am conducting some cohesive crack simulations within the framework of XFEM. The cohesive model is an initially rigid traction-separation law for mode I.  In order to deal with negative values of the normal sepration/jump, I use a penalty stiffness K.

The example is pretty simple: an un-notched three point bending test where a crack is initiated at the bottom edge of the beam and grow vertically upwards to the upper edge. During the simulation, some negative jumps are observed. The convergence is very much dependent on the penalty stiffness K used. Even for some cases, no convergence obtained at all. I tried K from 10^3 to 10^10.

Could you please share your experiences in dealing with crack penetration in crack grow simulation?

## Post-Doc in Computational Material Science or Computational Mechanics Institute of Structural Mechanics, Bauhaus Uni. Weima

Multiscale Methods for Fracture

Hello all

I have spent a large amount of time trying to undertstand the multiscale aggregating method (MAD) of Prof. Belytschko. Unfortunately, I still can not compltely understand the method.

Phu

## 2D approximation of heterogeneous 3D media

Dear All,

Could somebody indicate me some literature about the topic "2D
approximation of heterogeneous 3D media"?

In particular I am interested to address following issues:

1) Under which conditions averaging thermal conductivity and young
modulus (or more general, mechanical behaviour) on multiple 2D crossections of an heterogeneous "random"
material can be a good approximation for the behaviour of the real 3D
microstructure

2) Is there any  theorem which shows the equivalence between averaging
on n 2D crossections of a certain media and taking the single
real 3D structure for n sufficiently large?

Thank you very much in advance.

Phu

## solver for a very hetereogeneous system of equations

Hello everybody,

I am solving a FE problem on a hetereogeneous medium consisting of rigid phase (Young modulus of about 100 000 N/mm2), a softer phase (Young modulus of 20 000 N/mm2) and pore (Young modulus of 1 N/mm2). The reason that I have to mesh the pore is that there are some elements of rigid phase hanging out in the pores. So, if I do not mesh the pore, then my FE matrix is singular.

## free mesh generator based on imaging data

Dear all,

I am wondering if there exists a mesher that can generate finite element mesh (2D or 3D) from imaging data? It would be much nicer if there are somes and free.