Augmented Lagrangian Methods in Computational Mechanics

The goal of this project is to develop computational tools for the numerical modelling of problems with side conditions in the form of constraints.

The approach we wish to develop is the Augmented Lagrangian Method (ALM).Recent discoveries have made clear the relation between the ALM and stabilised Lagrangemultiplier methods in finite element discretisations of continua, which we aim to pursue:the possibility of replacing the Lagrange multiplier by its discretised physical counterpart  yields the possibility of eliminating the multiplier beforehand.

Further,ALM provides a solution to the variational inequality problem, as in a contact problem.

Here the ALM makes possible the replacement of the variational inequality by an equivalent nonlinearequality which has the potential to improve the efficiency of numerical solutions for a large class of variational inequality problems.

In the interest of versatileand efficient numerical methods we will also consider cut finite elment methods in the ALM framework, as well as hybridized ALM for interface and contact problems.The project includes mechanicalmodelling, development and implementation of numericalmodels, as well as analysis regarding the stability and convergenceproperties of the methods in order to establish the robustness ofresults obtained by numerical experiments.

Application to problemsin solid mechanics (contact, plasticity, thin structures) and fluid mechanics (cavitation,fluid-structure interaction) will be considered.