# How to detect the tensil and compression

1. Jan 20, 2010

### Zachary Liu

Hi, if i'm using the 3d element, i'm wondering how to detect the tensil and compression for a known stress state? the hydrostatic pressure p has been used before, but i don't think it is correct to all the cases.

2. Mar 9, 2010

3. Mar 9, 2010

### Astronuc

Staff Emeritus
Well if the strain is positive (+), it's tensile. If the strain is negative (-), it's compressive.

4. Mar 10, 2010

### Zachary Liu

what do you mean strain here? remember it is a 3D stress state. So the strain must be 3 dimension. Do you mean volumetric strain, e.g.

$$\epsilon_{v}=\frac{\epsilon_{11}+\epsilon_{22}+\epsilon_{33}}{3}$$

The question is it might be in compression in one direction and tensil in the other. I don't whether there is a simple way to distinguish this.

Last edited by a moderator: Mar 10, 2010
5. Mar 10, 2010

### Studiot

Without more detail it is difficult to know what you are after however the 3D stress has 9 components.
It is described by the stress tensor $$T$$

Just as a one dimensional stress may be decomposed into normal and tengential (shear) stress so may the the three dimensional version be decomposed into a uniform 'hydrostatic' normal stress, $${T_m}$$ and a set of 3D shear stresses, $${T_d}$$

The normal stress is often called the mean stress tensor and the shear stress tensor the deviator stress as it gives the deviation from uniformitivity, which is what I think you seek.

$$\begin{array}{l} {T_d}\quad = \quad \left( {\begin{array}{*{20}{c}} {\frac{{2{\sigma _{xx}} - {\sigma _{yy}} - {\sigma _{zz}}}}{3}} & {{\sigma _{xy}}} & {{\sigma _{xz}}} \\ {{\sigma _{xy}}} & {\frac{{2{\sigma _{yy}} - {\sigma _{xx}} - {\sigma _{zz}}}}{3}} & {{\sigma _{yz}}} \\ {{\sigma _{xz}}} & {{\sigma _{yz}}} & {\frac{{2{\sigma _{zz}} - {\sigma _{yy}} - {\sigma _{xx}}}}{3}} \\ \end{array}} \right) \\ {T_m}\quad = \quad \left( {\begin{array}{*{20}{c}} {{\sigma _m}} & 0 & 0 \\ 0 & {{\sigma _m}} & 0 \\ 0 & 0 & {{\sigma _m}} \\ \end{array}} \right) \\ T\quad = \quad {T_m}\quad + \quad {T_d} \\ \end{array}$$

6. Mar 10, 2010

### Zachary Liu

Thank you very much for your reply.

So you mean the $$T_d$$ could be used to diagnose the 'tensil' and 'compression' of a 3D stress state?

Actually what I'm seeking is a scalar parameter to distinguish the 'tensil' or 'compression' if possible.

You know, for some pressure dependent material, such as soil, ice etc. the strength in compression and tensile is quite different. Thus, a good material model should be able to treat the tensil and compression differently.

7. Mar 10, 2010

### Studiot

In order to point you in the right direction it would be really good to know what area you are workingin/studying.

The subjects of Rock Mechanics and Soil Mechanics might well be here you need to look, these disciplines are concerned with triaxial stress systems in everyday work.

Engineers in other disciplines (Structures, Mechanical etc ) tend to use simpler models in 1 or 2 D. They also tend to use finite element models rather than continuum mechanics ones.

There also some older graphical methods, based on Mohr Circles also used in stress analysis and soil mechanics. Many standard laboratory test methods are based on these.

8. Mar 11, 2010

### Zachary Liu

Yes, say i'm working on the geotechnical material modelling with solid elements. I want to simulate both tensil and compression failure. I've dived into several rock and soil books, but I found no answeres yet. Maybe someone here could give me a hint!

9. Mar 11, 2010

### Studiot

First of all soil and rock mechanics are big subjects so you really need a good book or three.

They are also different form ordinary continuum mechanics because rock geological materials contain fluid - usually water but sometimes oil etc. Ice and even rock act like a fluid at pressure.

This is vitally important because when you stress such a material much of the stress is carried by the pore fluid, not the material itself.

In soils literature in particular you will find the term 'effective stress' which is the stress left after the pore pressure has been subtracted, a bit like the decomposition I showed earlier. Pore pressure is much less important in rock mechanics.

Secondly the loading history of these materials greatly affects the response outcome.

So you need a good overview of the subject and its terminology to get up to speed, before applying theory from elsewhere.

When performing tests on these materials some more terms are important.

The 'triaxial test' can be confined or unconfined.
A confined test subjects the specimen to hydrostatic pressure in addition to a test loading so is truly triaxial.
An unconfined test does not do this and is, in fact uniaxial.
A test may be drained or undrained. This is where internal pore fluid is allowed to be squeezed out or not.

Some books I can recommend.

Mohr Circles, Stress Paths and Geotechnics by Parry

Discusses triaxial stress and its testing in great detail. Deals with both rocks and soils.

Elasticity, Fracture and Flow by Jaeger

A small book packed with useful geotechnical formulae by an applied mathematician.

Structural Geology by Twiss and Moores

Has comprehensive introductory chapters on stress ssytems and their application to geological situations

Rock Mechanics by Goodman

Wide ranging treatment by a practicing expert.

All these books give good treatment of failure criteria and information on real materials, which is what I think you are after.

10. Mar 11, 2010

### Zachary Liu

Thanks so much. A lot of reading is needed then.

As you mentioned the failure criterion, I'm trying to propose a pressure dependent failure criterion to invoke the erosion of elments. I think if a more advanced failure criterion taking into the real stress state of the 3D elments. it will be great! That's my intention.

But it always puzzles me whether the erosion technique is sufficient or proper to use.

11. Mar 11, 2010

### Studiot

What do you mean by erosion?

PM me if the answer is confidential.