In this study, an Adaptive Mesh Refinement (AMR) method is applied in order to conduct reliable solids mechanics studies with acceptable computing times when local phenomena are under consideration. The Local Defect Correction (LDC) method is performed, which enables us to validate the AMR philosophy for homogeneous linear elastic behaviour. The test case under study outcomes from an industrial situation: the pellet-cladding interaction in pressurized water reactors. A simplified model focused on the cladding response is used.