Efficient elasto-plastic modelling of reinforced concrete walls applying convex optimisation

The concept of finite element limit analysis (FELA) has demonstrated how the theory of rigid plasticity and convex optimisation algorithms can be used efficiently to determine the load-bearing capacity of e.g. reinforced concrete structures. While the method provides information on the collapse load and
mechanism, it does not consider the deformation of the structure before failure, which is a matter of importance in e.g. serviceability-limit-state verifications. This paper proposes a numerical framework based on convex optimisation for efficient elasto-plastic analysis of reinforced concrete structures in plane-stress conditions. The method uses the principle of minimum complementary energy and a hyperelastic material model to imitate the elasto-plastic behaviour of fully cracked reinforced concrete walls. With the use of stress-based finite elements, the problem is formulated as a convex optimisation problem that, in a non-incremental manner, finds the stresses and deformations associated with a pre-defined constant load imposed on the structure. As an illustrative example, the concept is applied to a deep beam with uniform, isotropic reinforcement, and the resulting load-displacement curve is compared to the analytical limit load based on rigid-plastic material behaviour. Finally, the advantages and validity domain of the method is touched upon along with its applicability in practical design scenarios.