| Abstract: |
| By using asymptotic analysis arguments, we derive and justify a two-dimensional contact model for linearly elastic elliptic membrane shells in adhesive contact with a deformable foundation. The process is assumed to be quasistatic, and therefore the effects of inertia are neglected.
Contact is modeled with normal compliance and the adhesion is modeled by introducing a surface auxiliary variable, the bonding function, the evolution of which is described by a nonlinear first order differential equation.
To do this, we consider the three-dimensional contact problem, introduce a change of variable to curvilinear coordinates, together with the right scaling of the unknowns and parameters of the problem, and when the thickness of the shell (small parameter of the problem) tends to zero we obtain a two-dimensional limit model, which we justify with a rigorous convergence theorem.
We will also show a fully discrete numerical scheme and results of some numerical simulations to test the performance of our model. |
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