# Rigidity

Rigidity is the ability of a solid to withstand deformation when it undergoes mechanical stress. It is mainly dependent on the geometry of the part and the elasticity moduli of the material.

For a homogeneous isotropic material we can express:

· tensile rigidity, from the product E times S, E being the Young modulus and S the cross section perpendicular to the axis along which the tensile force is applied (the straight section);

· bending rigidity, from the product E times Iyy or of E times Izz, where Iyy and/or Izz are the inertia of the component along the yy or zz axis (the xx axis being normal to the section considered).

· the shear rigidity from the product G times S, where G is the shear modulus of the material.

The coefficients of the matrix **C** (mathematical expression) for the behaviour law (**S** = **R**.**e**) of a linear elastic material, giving the stresses **S** as a function of the deformations **e**, are called the "rigidities". They are expressed as a function of the mechanical properties of the material (elasticity modulus, Poisson coefficients) but are independent of the geometry of the body considered.

In the case of composite materials, and in particular for a fold, the rigidities depend on the percentages of the various constituents, their orientations and their mechanical properties.