Compatible strain-based upper bound limit analysis model for masonry walls under in-plane loading

Abstract

We present a novel numerical model for the upper bound limit analysis of in-plane loaded masonry structures. The construction is represented as a continuum model composed of planar elements whose kinematics combines rigid body velocities and plastic strain rates. The global velocity field remains continuous and crack configurations are described via plastic strain rates. Homogenization ensures the compatibility between the continuum’s plastic strain rate field and the kinematics of the heterogeneous material: idealizing masonry as an assembly of rigid bricks and frictional zero-thickness joints, the associative flow rule is expressed through homogenized kinematic relations defining a domain of compatible plastic strain rates. The derived limit analysis problem is written as a linear programming problem, yielding an upper bound of the load-bearing capacity along with rigid body velocities and a compatible plastic strain rate field. Finally, a local mesh refinement strategy governed by the $L_2$-norm of plastic strain rates optimizes the mechanism representation. The presented formulation offers advantages over the conventional homogenized limit analysis methods by defining a failure domain via strain rates, rather than stress, providing a more compact and computationally efficient numerical approach. Its efficacy is proven through numerical examples and comparisons with well-established analytical and numerical models.