Indentation of functionally graded beams and its application to low-velocity impact response

The problem of contact between a rigid cylindrical indenter and a functionally graded (FG) beam is studied. The elastic modulus of the material varies in an exponential fashion across the thickness of the beam. For the sake of comparison indentation of a homogeneous beam is also considered. In the case of FG beams indentation of both soft and hard sides of the beam are studied. Results are presented for contact force–contact length relations and contact stresses in the three types of beams. Maximum normal strains and stresses and maximum transverse shear stresses are plotted as a function of strain energy (work done by the indenter) in the beam. The results are extended to low-velocity impact problems. It is seen that for a given impact energy in low-velocity impacts, the maximum stresses and strains are significantly lower in FG beams when the impact occurs on the softer side of the beam.