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Definition of Reproducing Kernel

Submitted by Yeo Jingjie on
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meshless
reproducing kernel

Hi all, I am currently beginning research as a graduate student on meshfree methods, focusing on RKPM right now. I have not been able to find an exact definition of what exactly a reproducing kernel means. Could someone kindly define a reproducing kernel? According to W.K Liu et al, a good example of a reproducing kernel is a Fourier transform, but I can't grasp why is that so.

Generating quadratic tetrahedral (tet10) meshes from .stl surface models

Submitted by sps4 on
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meshing
tet10
quadratic tetrahedra

Hi iMechanica-experts,

I'm working with soft tissue models of abdominal organs (e.g. liver) for surgery simulation. These models are alway constructed from segmented surface files (triangles, e.g. .stl). I'm devloping an algorithm that uses isometric quadratic tetrahedral (tet10) elements (mainly in order to reduce volume locking). Now I'd like to generate a tet10 mesh from the surface mesh.

How to get the elemental stiffness/damping matrix of a Maxwell spring-damper element?

Submitted by zhangxiaodong on
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Computational Mechanics Forum

A Maxwell spring-damper element consists of a nonlinear damper in series with a spring.

The force deformation relationship can ben found in the file attached . The problem is the constitutive relationship is in the form of  a PDE.

Does any on konw how to get the elemental stiffness/damping matrix?   Or can anyone suggest some reference?

Thanks a lot. 

 

 

Correct Average of Stress/Strain Microfields

Submitted by adz on
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homogenization
porous material
This is a general micromechanic question.

Suppose we have a microstructured 2-phases material with random inclusions (or a porous material with random pores) and we make a real tensile test (monoaxial loading in the vertical direction of a specimen with nominal length L). We want to model such tensile test with FEM (for instance with Abaqus) like in this pic:
 
 
 
 

Solving nonlinear equilibrium problem

Submitted by Bashir Venkatta on
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Nonlinear problem
Newton methods
numerical continuation

Hi!

I am trying to solve (for equilibrium points) a geometrically nonlinear problem of the form

f(u) = F

where u is the displacement and F is the load. At first I tried the plain

Newton method, with, perhaps obviously, limited success. I then tried to use

linesearch and trustregion strategies to improve the situation. Eventually, however,

I realized that I needed to use some form of continuation method. Though the most

commonly used methods in mechanics seems to be based on gradually increasing the

Naming of an "Epsilon Dot Zero" And a "Reference Strain Rate" of J-C Parameters in Abaqus/Explicit

Submitted by Martin Madaj on
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ABAQUS
strain rate
Johnson Cook Plasticity Model

Hello,

 
I'm a little bit confused with a naming convention of strain rates of Johnson-Cook plasticity and damage model in Abaqus. In J-C equations there are two parameters:  

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