The stiffness of Li-ion batteries is defined as the derivative of force with respect to displacement. The existing constitutive models of the jellyroll of Li-ion batteries reveal that such stiffness keeps increasing as displacement increases. In this study, quasi-static mechanical abusive tests are performed on 18650 cylindrical Li-ion batteries at different state of charge. The experimental results indicate that three distinct stages are identified in the stiffness curve corresponding to densification stage, microscopic damage stage and macroscopic failure stage, and the stiffness only increases in the first stage and decreases in the latter two stages. Therefore, this paper proposes the improved constitutive model of the jellyroll of Li-ion batteries to describe their kinematics considering microscopic damage. An explicit finite element model of a Li-ion battery is established to validate the improved constitutive model. The voltages and temperatures of Li-ion batteries are also recorded to reveal their responses at different stages. It is found that Li-ion batteries at the fully charged state initiate internal short circuit before the end of the stage 2 (microscopic damage stage) whereas Li-ion batteries at low state of charge will only initiate internal short circuit at the stage 3 (macroscopic failure stage). (C) 2019 Elsevier Ltd. All rights reserved.