# Solve Volumetric Strain | Question 3 on http://img201.imageshack.us/my.php

• johnboy14
In summary, the conversation discusses how to solve for volumetric strain in a given block and what equations are needed to do so. The volumetric strain is equal to the change in volume over the original volume, and can be calculated by adding the principal strains together. The constants for the stress-strain relations are given as E = 200x10^9 and v = 0.3. The conversation also mentions calculating the principal stresses and using them to find the principal strains.
johnboy14

## Homework Statement

How do I solve the following block to find the volumetric strain. Its question 3 on the link

http://img201.imageshack.us/my.php?image=file0001pf0.jpg

I know that volumetric strain is equal to change in volume EV/ origninal volume(V)

Is Ev = Ex + Ey + Ev equal to volumetric strain.

I was told that the volumetric strain should be about 6.8 x 10^-4

Any help would be appreciated people.

I am used to seeing volume dilation as the sum of the principal strains.

$$D = [\epsilon_1 + \epsilon_2 + \epsilon_3] = J_1$$ where $$J_1$$ is the first strain invariant.

I would tackle the problem that way. Calculate the principal strains and add them together.

EDIT: After looking at the problem, it is in a state of zero shear. Therefore $$\sigma_x$$, $$\sigma_y$$ and $$\sigma_z$$ are going to be the principal stresses. So, if you calculate the strains from the principal stresses you will be calculating the principal strains. Things should be pretty straight forward. I ended up calculating $$6.5 x 10^{-4}$$

Do you know the 3 dimensional stress-strain relations that involve E and $$\nu$$?

Last edited:
yes I do

E = 200x10^9
v = 0.3

Those are constants, not the relations themselves. I meant the entire relations, i.e. equations.

Hint: There are three equations you're looking for and each equation will have one strain element and all three stress elements.

Last edited:

## What is volumetric strain?

Volumetric strain is a measure of the change in volume of a material due to a stress or strain. It is calculated by dividing the change in volume by the original volume of the material.

## How is volumetric strain calculated?

Volumetric strain is calculated by dividing the change in volume by the original volume of the material. The formula for volumetric strain is (ΔV/V), where ΔV is the change in volume and V is the original volume of the material.

## What causes volumetric strain?

Volumetric strain is caused by a stress or strain applied to a material. This can be due to factors such as compression, tension, or shear forces.

## What are the units of volumetric strain?

Volumetric strain is a dimensionless quantity and therefore has no units. It is expressed as a ratio or percentage.

## How is volumetric strain used in engineering?

Volumetric strain is an important concept in engineering, particularly in the study of materials and their response to stress and strain. It is used to analyze the behavior of materials under different conditions and to design structures that can withstand these forces.

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