Question

Which one of the following represents ‘constitutive relationship’?
1. Vertical displacements in a structure
2. Rotational displacements in a structure
3. System of forces in equilibrium 
4. Stress – strain behaviour of a material

Answer 1

Correct Answer - Option 4 : Stress – strain behaviour of a material

The constitutive relationship is the relation between two physical quantities’ of material in such a way that their proportionality constant is function of property of material.

For example:

Stress (σ) in material is directly proportional to strain in that material (ϵ) and proportionality constant (also called Modulus of Elasticity, E) is the property of material i.e. for different materials, it is different.  This relation between Stress – strain i.e. σ = Eϵ called Constitutive Relationship.

Another example- Spring force (F_s) is directly proportional to change in its length (δx) and proportionality constant (also called spring constant, K) is the property of spring i.e. for different springs it is different.  This relation between spring and its change in length i.e. F_s = Kδx called Constitutive Relationship.