Large-deflection axisymmetric deformation of circular clamped plates with different moduli in tension and compression

Ambartsumyan's bimodular model for isotropic materials deals with the principal stress state in a point, which is particularly useful in the analysis and design of structures. In this paper, based on the known flexural stiffness for a bimodular thin plate in small-deflection bending, we establish the von Kármán equations with different moduli in tension and compression and then use the perturbation method and the displacement variation method to solve the problem, respectively. The comparison shows that the perturbation solution based on the central deflection is valid. The analytical result shows that the bimodularity of the material will have an effect on the relation of load vs. deflection to a certain extent. We also investigate the yield conditions for a bimodular thin plate in large-deflection bending. It is concluded that this introduction of materials nonlinearity will eventually influence the yield stress at the edge and center of the plate, however, it does not change the yield order that when loading further, the edge of the plate will firstly yield and then the center of the plate. Moreover, during the transition from plate to membrane, the bimodular plate will gradually regress to the classical one. This work will be helpful for analyzing the mechanical behaviors of thin film materials with obvious bimodularity and with moderate thickness or hardness.

► We establish the von Kármán equations with different moduli in tension and compression.
► We use the perturbation technique and variation method to solve the problem, respectively.
► The comparison shows the perturbation solution based on the central deflection is valid.
► This bimodularity will not change the yield order that the edge firstly yield and then the center.
► The bimodular plate will gradually regress to the classical one when the membrane effect is dominant.