# 1st, 2nd & 3rd principal strain vs. minimum and maximum principal strains

Hi All,

Non-maths person here struggling with the relationship between 1st, 2nd and 3rd principal strains generated by FEA software and minimum and maximum prinicipal strains often cited in the literature.

As i understand it the 1st principal strain is the most positive strain, 2nd and then 3rd most positive strains. For instance:

Case 1-

1st principal strain = +1000

2nd principal strain = +100

3rd principal strain = +50

Case 2-

1st principal strain = +500

2nd principal strain = -50

3rd principal strain = -100

Case 3 -

1st principal strain = -5

2nd principal strain = -50

3rd principal strain = -100

Am i right in thinking the  maximum strain is the same as the 1st principal strain in case 1 and 2 (+1000 & +500, respectively) but the 3rd principal strain in case 3 (-100). Similarly, am I also right in thinking the minimum strain is the 3rd prinicpal in case 1, 2nd principal in case 2 and 1st principal in case 3?

Case 1-

1st principal strain = +1000 (MAX)

2nd principal strain = +100

3rd principal strain = +50 (MIN)

Case 2-

1st principal strain = +500 (MAX)

2nd principal strain = -50 (MIN)

3rd principal strain = -100

Case 3 -

1st principal strain = -5 (MIN)

2nd principal strain = -50

3rd principal strain = -100 (MAX)

I have read some web sources that imply that the max is always the 1st and the minimum is always the 2nd - does not seem right and has confused me.

Any guidance

cheers

b

### Conventionally we assume

Conventionally we assume 1st > 2nd > 3rd. This sequence is sort by algebraic comparison instead of absolute value.