In psychology, rigidity refers to an obstacle to problem solving which arises from over-dependence on prior experience, which makes it difficult for a person with experience in a specific problem domain to recognize novel solution strategies. This phenomenon is also known as a mental set. A specific example is functional fixedness, which is a difficulty conceiving new uses for familiar objects.
In solid mechanics, "rigidity" refers to the degree of deforming ability of a solid material. Modulus of elasticity with moment of inertia (E·I) is the numeric value of rigidity. According to this expression, one can see only two criteria affect deformation, which are geometry and the material of an object.
In Accelerator Physics, "rigidity" refers to a particle beam's resistance to deflection by a magnetic field. It is defined as Bρ = A/Z * 3.33564 * p. B is the magnetic field, ρ is the radius of curvature (set by the accelerator in question), A is the atomic mass number, Z is the particle's charge and p is the particle momentum (in GeV/c). The units of Bρ are Tesla-Meters. It is frequently referred to as simply "Bρ".
Rigidity is also known as the material property of shear modulus which is a measure of force per unit area needed to change the shape of a material.