adabistanesoophia said:
Strain is defined as "Measurement of deformation of a solid when stress is applied 2 it".
So where direction is invlved?
So can v say it is a scalar quantity or not?
Muhammad Rizwan Khalil
OK - that is an "beginner level" definition of strain. The whole truth is not so simple.
Strain is neither a scalar nor a vector. In the most general case it's a 2-dimensional symmetric tensor, defined by 9 numbers at any point. (Only 6 of the numbers are independent, because of the symmetry). Stress is also a tensor. The thing that corresponds to "Young's Modulus" is a 4-dimensional tensor with up to 21 independent constants for a general anisotropic material. (For an isotropic material there are only 2 independent constants, not 21. Young's Modulus and Poisson's Ratio are one pair of constants that define the stress-strain behaviour of an isotropic material).
When you are considering a problem like the axial stress in a rod producing an axial strain, the things you are calling "stress" and "strain" are single
components of the complete stress and strain tensors. The others are either zero, or you are not interested in them.
You don't need all this heavyweight tensor stuff to handle the simple cases like constant axial stress in a uniform rod. In the equations you have probably seen like
"stress" = force/area
"stress" = Youngs Modulus times "strain"
Extension = "strain" * length
the terms I put in quotes (like "stress") are actually single components of the full stress and strain tensors. They may look like scalars, but they are not.
Obviously until you have studied tensors some of this explanation won't mean much - but as an example, the product of a 2-D tensor times a vector is another vector. The product of the stress tensor with a unit vector gives the force vector on the plane normal to the unit vector. This is completely general and gives you the force on ANY plane section through a body with ANY state of stress in it. For a rod with axial tension, most of the terms in the tensor and the vector are zero, so you can use equations that
look like scalar equations, even though they are not really scalars.