Laboratoire Angevin de Mécanique, Procédés et InnovAtion

Architected lattice materials inspired by biological structures are frequently described as bioinspired, yet the underlying functional principles governing their mechanical response are not always explicitly isolated. The hexactinellid spongeEuplectella aspergillumexhibits a distinctive skeletal organization based on a periodic square unit subdivided into four sub-squares, where two opposite regions are reinforced by paired diagonal struts while the remaining corners remain non-reinforced. This alternating reinforcement pattern introduces spatial heterogeneity in stiffness and connectivity at the unit-cell scale. While related geometries have been examined under compression and bending, their tensile elasto-plastic behavior and the specific mechanical role of this architectural coupling remain insufficiently understood. In this study, we isolate and quantify the contributions of (i) diagonal reinforcement and (ii) spatial cell alternation under uniaxial tension. PLA-based lattice variants were fabricated using fused filament fabrication to decouple these structural variables and were benchmarked against the full EA-sponge derived topology. Quasi-static tensile experiments, supported by linear elastic finite-element analysis, demonstrate that all configurations exhibit stretch-dominated elastic scaling. However, significant differences emerge in post-yield behavior. Fully plain and fully reinforced lattices show early strain localization and structurally brittle fracture modes, whereas alternating architectures promote stress redistribution and delay the formation of continuous failure bands. The EA-sponge topology, characterized by its checkerboard alternation and geometrically offset diagonals, exhibits the most stable structural elasto-plastic response, combining stiffness retention with progressive, non-catastrophic fracture behavior. These findings demonstrate that tensile performance is governed primarily by structural connectivity and spatial organization rather than relative density or material properties alone, establishing a topology-driven design principle derived from biological organization.

Rooted in the Monge and Kantorovich problems, optimal transport seeks to minimize transportation costs, as quantified by Wasserstein distances, facilitating the transformation of one distribution into another distribution. However, its application faces challenges in addressing non-convex geometries, especially in interpolating mid-way distributions along transportation paths. In such scenarios, particles may breach the original shape boundaries, creating infeasible solutions. The article addresses this by proposing three innovative solutions: geometry mapping, trajectory planning and graph planning. These solutions aim to overcome the inherent limitations of optimal transport in non-convex spaces by offering mathematical formulations and implementation strategies. Importantly, the article goes beyond theoretical considerations by applying these solutions to predict shrinkage porosity in aluminum casting. This application demonstrates the broader relevance and effectiveness of the proposed solutions.

A new numerical method for solving Volterra linear convolution integral equations (CVIEs) of the second kind is presented in this work. This new approach uses first-order infinite impulse response digital filters method (IIRFM). Three convolutive kernels were analyzed, the unit kernel and two singular kernels: the logarithmic and generalized Abel kernels. The IIRFM is based on the combined use of the Laplace transformation, a first-order decomposition, and a bilinear transformation. This approach often leads to simple analytical expressions of the approximate solutions, enabling efficient numerical calculation, even using single-precision floating-point numbers. When compared with the method of homotopic perturbations with Laplace transformation (HPM-L), the IIRFM approach does not present, in linear cases, the convergence difficulties inherent to iterative approaches. Unlike most solution methods based on the Laplace transform, the IIRFM has the dual advantage of not requiring the calculation of the Laplace transform of the source function, and of not requiring the systematic calculation of inverse Laplace transforms.

Abstract. The estimation of post-machining distortion of monolithic aeronautical parts induced by the redistribution of the bulk residual stresses (RS) during machining is one of the major challenges of aeronautical parts manufacturing. Since it is the main cause of thick parts post-machining distortion, it is essential to know the state of the initial RS so that the machining strategy can be modified to minimize distortion of each part. The problem is even more complex because the RS field is not identical from one part to another. Considering an average stress field provides satisfactory results only for parts with simple geometries and a highly repeatable manufacturing process, which is rarely the case in an industrial setting. By simulating the steps of the production of the laminated blank, the variability of RS field will be established. This variability can be used to determine the distribution of the RS field of each part during machining.