Analysing Cube Stress & Deformation in Figure A & B

Click For Summary
SUMMARY

The discussion focuses on analyzing stress and deformation in a cube with sides of 10mm, subjected to compression of 0.6MPa. Participants explore the stress state and relative deformation tensors for two scenarios: one with the cube alone and another with the cube in contact with an indeformable plate. Key points include the necessity of understanding the relationship between stress and deformation, particularly how the sum of relative deformations equals zero, and the implications of contact with the housing in Figure B.

PREREQUISITES
  • Understanding of stress and strain tensors in solid mechanics
  • Familiarity with Young's modulus and Poisson's ratio
  • Knowledge of basic principles of mechanics of materials
  • Ability to interpret and analyze mechanical diagrams
NEXT STEPS
  • Study the derivation of stress and strain tensors in solid mechanics
  • Learn about the implications of Poisson's ratio in material deformation
  • Research the effects of boundary conditions on stress distribution
  • Examine case studies involving compression in rigid body mechanics
USEFUL FOR

Mechanical engineers, materials scientists, and students studying solid mechanics who are interested in understanding stress analysis and deformation behavior in materials under compression.

zDrajCa
Messages
7
Reaction score
0
We have a cube with sides of 10mm (fig a) (in the same material than the exercice 1 (have poisson coef & young's modulus)

A- figure A
1- Write the stress state and the relatives values deformations (tensor)

2- Why the sum of relatives deformation is equal to 0?

B-Figure B
The cube is placed in a indeformable plate where a housing was realized inside. His dimension are on the figure B. The cube is already comprimed.
1- Thx to the results of A1, the x,y faces will be in contact with x,y, housing?
2- If we do the hypothesis of contact, determine the stress state and relatives values of deformation of thus cube.
3- What can you note analysing deformations.

C- The cube is comprimed with 0.6MPa but here is no space between the cube and the housing. write the tensor of deformation without calculus.

Well, sorry for my Bad english...

Where am I?
1)For me all stress values are equal to 0 except σzz= -0.6MPa? True ? I'm not sure cause σ=F/A=0.6/100 ? and deformation=σ/Young modulus ?

2)I didn't have to do more on this exercise. I won't have answers, i will try to do it this afternoon. But if you can give advices to know where i can start on the different questions, it can be good.

Thx a lot to read,and to give me your time.
 

Attachments

  • bla.png
    bla.png
    7 KB · Views: 471
Physics news on Phys.org
Sorry, I'm unable to understand your English, so I can't be of much help. But, for the case shown in figure A, is the Poisson ratio equal to 1/2?

Chet
 

Similar threads

  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 18 ·
Replies
18
Views
2K
  • · Replies 4 ·
Replies
4
Views
3K
  • · Replies 11 ·
Replies
11
Views
3K
Replies
4
Views
3K
  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 9 ·
Replies
9
Views
4K
  • · Replies 10 ·
Replies
10
Views
2K
  • · Replies 17 ·
Replies
17
Views
4K