Based on the current density (CD) experimental results reported in a literature for the copper through-silicon vias (TSVs) arising in the Cu/Ti/SiO2/Si wafer structure, the CD solutions were obtained through simulations in the ANSYS/LS-DYNA software linked with the "Johnson-Cook (J-C) Constitutive Model" module in this study. The numerical schemes are developed to obtain the following contents: (1) the determinations of the unknown coefficients in the J-C model by conducting the microtensile tests for per each component of the TSV structure; (2) the earliest element failure caused by the thermal strain/stress; (3) the critical stress and time at potential failure location modeled by the J-C model; and (4) the evaluations of strain energy density (W-failure) required for element failures in the components and the effect of heat generation rate in per unit volume of Cu film on element failure. The numerical solutions predicted by the present models are confirmed to be very close to the reported experimental results, and thus validate the present predictions for temperature and time and the sequence of elements with the earliest failure in their component. The strain energy density (Wfailure) required to start the failure of an element is found to be dependent upon the TSV component material only, and is independent of the element's location in the same component. The heat generation in the Cu film is of importance to the order of the TSV components reaching its W-failure, the time to have W-failure increases along with the distance of the TSV component from the lateral surface of the Cu film. The smaller the distance is, the earlier the time that the W-failure of an element is reached. An appropriate combination of a Ti film with a large thickness and SiO2 film with a small thickness can reduce the maximum effective stress (sigma(max)) and provide an efficient barrier for copper diffusion into the Si wafer substrate. This study can provide an efficient method for the design and failure protection of TSV structures. (C) 2016 Elsevier B.V. All rights reserved.