André Maués Brabo Pereira

This work proposes a memory-efficient strategy for plastic limit analysis, combining Linear Programming (LP) with a matrix-free implementation based on lattice models. Plastic limit analysis provides rigorous bounds for structural capacity; however, when formulated as LP, the explicit assembly of global matrices leads to prohibitive memory allocation demands as mesh sizes increase, even if in a sparse format. To overcome this limitation, a novel solver was developed based on the primal-dual interior-point method coupled with a block-diagonal preconditioner. This matrix-free approach eliminates the need to store the KKT system by executing algebraic operations directly on the mesh topology, which drastically reduces memory consumption. The numerical model incorporates a strict geometric calibration of the bar capacities, ensuring that the discrete lattice reproduces the continuous material behavior. Numerical experiments conducted on benchmark biphasic configurations and on a real nodular cast iron microstructure (via micro-CT) demonstrate that the proposed approach yields results equivalent to those of traditional sparse matrix formulations. Additionally, recent simulations involving the interaction of rigid symmetric hooks under different matrix strength ratios (0.1, 0.5, and 0.9) highlight the solver's capability to capture, with high fidelity, the transition from singular collapse bands to complex and diffuse failure topologies around re-entrant corners.

This paper presents an extension of the authors’ previously developed interface coupling technique for 2D problems to 3D problems. The method combines the strengths of the Discrete Element Method (DEM), known for its adeptness in capturing discontinuities and non-linearities at the microscale, and the Boundary Element Method (BEM), known for its efficiency in modelling wave propagation within infinite domains. The 3D formulation is based on spherical discrete elements and bilinear quadrilateral boundary elements. The innovative coupling methodology overcomes a critical limitation by enabling the representation of discontinuities within infinite domains, a pivotal development for large-scale dynamic problems. The paper systematically addresses challenges, with a focus on interface compatibility, showcasing the method’s accuracy through benchmark validation on a finite rod and infinite spherical cavity. Finally, a model of a column embedded into the ground illustrates the versatility of the approach in handling complex scenarios with multiple domains. This innovative coupling approach represents a significant leap in the integration of DEM and BEM for 3D problems and opens avenues for tackling complex and realistic problems in various scientific and engineering domains.