The ability of a material to resist deformation reflects either its modulus of rigidity under shearing or twisting stress or its modulus of elasticity under stretching stress. A modulus is the absolute value of a ratio expressing a physical attribute.
The modulus of rigidity, or shear modulus, measures stiffness. When an object experiences a force parallel to its length that is greater than its strength, it either slides against the source of the stress, or it slides internally, causing small changes to its volume. Bolts connecting two parts of an airplane must have a high modulus of rigidity to maintain their integrity during flight as the plates they fasten are pulled in opposite directions.
The modulus of elasticity, or Young's modulus, measures springiness. When an object is pulled perpendicularly to its length by strong forces, it reaches a point where it cannot return to its original dimensions. The wings of a plane must have a strong modulus of elasticity to withstand high winds without bending.
Military aircraft require materials with high rigidity and elasticity. Composite materials are made of thin plates sandwiched around a lightweight core. The core separates the plates enough to provide rigidity, and it prevent shear failure. It also has a high elasticity to prevent wrinkling.