文档介绍：2 Strain analyses
Definition of strain
Small deformation
patibility equations
Principal strains
Strain rates and strain rate tensor
Elastic work or strain energy
1
Definition of strain
(a) Tensile, (b) compressive, and (c) shear.
All deformation processes in manufacturing involve strains of these types.
2
If the position of a point in a body is changed, we say that the point has been displaced. When the relative position of any two points in a continuous body is changed, then the body is said to be deformed or strained. When the distance between every pair of points in a body remains constant during displacement, the the body is referred as a rigid body. The displacements of a rigid body may be either translation or rotation which are known as rigid body displacements. A body may be displaced and strained, but a displaced body does not necessarily mean that the body is strained, as in the case of a rigid body displacement.
Displaced
Displaced and strained
3
Engineering strain:
True strain is more convenient for large strains,,
Definition of strain
After integrating:
(3-1)
(3-2)
(3-3)
Strain analyses
Normal strain
Shear strain
4
Definition of strain
If the strain is small, then true and engineering strain are nearly equal.
(3-4)
Strain analyses
(1) True strains for equivalent deformation in tension pression are identical except in sign.
(2) True strains are additive, the total strain being equal to the sum of the incremental strains.
(3) The volume change is related to the sum of the three normal strains, and with volume constancy
The features of true strain expression:
A series expansion result in
so as
5
Definition of strain
Definition of strain
Engineering shear strain is defined as the change in a right angle.
x
y
(3-5)
Strain analyses
For small shear strains
6
Small deformation
Direct strain at a point
Strain analyses
Assuming that u, v are displacement functions of