Closed form vs. finite element analysis of laminated stacks

Recently, structural analysis of multi-layered stacks subjected to thermal loading has received considerable renewed interest. This is partly because of popular use of these structures in electronic packaging. In this paper a comparative analysis of these structures is presented. Comparisons between closed-form solution, elastic, viscoplastic and thermo-viscoplastic with damage analyses have been presented. A damage mechanics based constitutive model is proposed for finite element analysis (FEA) of multi-layered structures. Moreover, mesh sensitivity of the FEA in layered stack problems is studied. It is shown that the closed-form and elastic FEA can only be used for preliminary studies and elastic finite element method is highly mesh sensitive for this problem. In elastic analysis the stress singularity at the free edge makes mesh selection very difficult. On the other hand, inelastic analysis does not suffer from the stress singularity problem encountered in elastic analysis. The damage mechanics based constitutive model proposed in the study uses a thermodynamic internal state variable as a damage metric.