# xiashengxu's blog

## Input variables used in Abaqus UMAT: STRAN, STRESS and DSTRAN

I wonder the mathematical expressions for the variables: STRAN, STRESS, and DSTRAN which are used in UMAT.

## What is exactly the 'pressure' of a solid in thermodynamics?

Most literatures on thermodynamics are written or started with the language of 'ideal gas'.

This confuses me a lot when I switch to consider solids. For example, the enthalpy of a system
is defined as H = U + P*V, where P is the pressure of the 'system'. This definition is found to be convenient
when dealing with gas. But in terms of solids, I really doubt if the 'pressure' is meaningful. The volume makes
sense but its relation with energy should be expressed in another way when we consider for example cold-
work.

## PBC implementation in equilibrium equation

Hi, guys,

Do some of you know how Periodical Boundary Condition is implemented in equilibrium equation while using FEM:

div{ C:sym[grad(u)] } = 0 ,where the displacement u is periodical.

Is there any (detailed) documentation about this stuff?

Thank you very much!

## software for eigenstrain problem

Hi,

Is there some fem code or software that can handle eigenstrain while solving equilibrium equation?

Thanks!

## What is the best method now to solve advection equation?

I am solving the advection equation which is hyperbolic. Some basic techniques (shown on the page  http://www.cse.illinois.edu/iem/pde/discadvc/) are either of large oscillation or numerical diffusion.

I am striving to find a method without or with little of these problems. Or is there any post correction method to use?

Thank you all!

## What is the best way to numerically solve hyperbolic equation?

What is the best way to numerically solve the transport equation like(the least numerical diffusion phenomenon):

df/dt+v df/dx=0

Thank you

## Is two point tensor a REAL tensor?

Two-point tensor appears in some of continnuum mechanics reference books.

1. In wikipedia, two-point tensor is interperated as:" Two-point tensors, or double vectors, are tensor-like quantities which ... "

2.Physically speaking, a tensor is a quantity that should not be changed by coordinate transformation while two-point tensor seems to have essential relationship with coordinates.

## How to perform surface boundary integration in elasticity fem?

This is a basic question regard to elsticity fem.

How to compute traction boundary integration numerically in elasticity fem under general situation? That is:

\int_{\Gamma} [N][t] d\Gamma,   here [N] is shape function and [t] is surface traction

My E-mail: shengxu.xia@yahoo.com

Thanks a lot

## fem code for plasticity theory?

Is there any available fem source code for plasticity theory?

Thanks alot!

## Solve 2d diffusion equation

the problem described by these equations is: at time=0, N particles are dropped onto an infinite plane to diffuse. C(r,t) represents the concentration density of particles

The solution is very simple, but I want to see the procedure.

Thank you very much!

## the DEM's solutions for static mechanics seem strange

My own DEM(Discrete Element Method) program's solution for static problem seems strange.

I use my program to calculate the displacement of a cantilever under static pressure:

1. it seems my program shows convergence for static problem as the mesh gets denser. As the mesh grows denser(that means the particle becomes smaller), the displacement(of y direction)  of the free tip becomes smaller.

## Is there any computing module which can compute a heap of disk elements in DEM(discrete element method)?

Is there any computing module which can compute a heap of disk elements in DEM(discrete element method)?it'd be better if it is written in matlab or C/C++. I'm doing research on the combined DEM-FEM. I need such module so as to save my time.

Thank you 