Two-field variational formulations for a class of nonlinear mechanical models

A nonlinear boundary value problem arising from continuum mechanics is considered. The nonlinearity of the model arises from the constitutive law which is described by means of the subdifferential of a convex constitutive map. A bipotential [Formula: see text], related to the constitutive map and its Fenchel conjugate, is considered. Exploring the possibility to rewrite the constitutive law as a law governed by the bipotential [Formula: see text], a two-field variational formulation involving a variable convex set is proposed. Subsequently, we obtain existence and uniqueness results. Some properties of the solution are also discussed.

Compressive mechanical behavior and model of composite elastic-porous metal materials

This work presents the experimental characterization and theoretical modeling of composite elastic-porous metal materials (C-EPMM). C-EPMM is a novel porous metallic damping material made of wire mesh and wire helix. A series of quasi-static compressive experiments were carried out to investigate the stiffness and energy absorption ability of the C-EPMM with different mass ratios. The experimental results show that the mass ratios can significantly affect the stiffness and loss factor of C-EPMM. To efficiently predict the nonlinear mechanical properties of the C-EPMM a theoretical model of C-EPMM was proposed for the first time, the model was based on the manufacturing process. A comparison between the predicted data and the experimental data was conducted. The results show that the theoretical model can accurately predict the mechanical performance of C-EPMM. The conclusions derived from this work can provide a new method for adjusting the mechanical performance of EPMM in applications.