November 20, 2019
Propagating Material Instabilities in Planar Architectured Materials
By Justin Dirrenberger (PIMM, Arts et Métiers, Paris)
Under tension low-carbon steels exhibit inhomogeneous plastic deformation. The Piobert-Lüders  instabilities create fronts of localized strain that propagate throughout the structure. From a modelling and simulation viewpoint, only simple geometries such as sheets and tubes have been considered in the literature. This work focuses on planar architectured materials, specifically 2D lattice structures which can be defined as a tessellation of unit-cells periodically distributed in space. This class of advanced materials enables new and/or improved functionality in comparison to monolithic materials due to their internal geometrical features, i.e. architecture.
We investigate the impact of the architecture on the global behaviour of the structure. Especially, how localization bands interact with the lattice, and the possibility of controlling initiation and propagation of localized strain with internal geometrical features. A nonlinear elastoplastic material model implemented within a full-field finite element framework [2,3] is used in order to simulate the Piobert-Lüders band formation and propagation. The model also considers a finite transformation framework with periodic boundary conditions .
Initiation and propagation of material instabilities depend on the geometry and the relative orientation of the solicitation. Propagating and non-propagating behaviours are identified for the localisation bands and related to the different geometrical archetypes considered. Material instabilities affect the mechanical behaviour of the structure as far as they are governed by the architecture. Simulation results have been compared to DIC tensile experiments conducted on laser-architectured ARMCO® pure iron samples .
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 Viard, A.-E., Dirrenberger, J., & Forest, S. (2019). Propagating material instabilities in planar architectured materials. Under review.