https://hal-polytechnique.archives-ouvertes.fr/hal-01917356Kumar, SiddhantSiddhantKumarDanas, KostasKostasDanasLMS - Laboratoire de mécanique des solides - X - École polytechnique - Mines Paris - PSL (École nationale supérieure des mines de Paris) - PSL - Université Paris sciences et lettres - CNRS - Centre National de la Recherche ScientifiqueKochmann, DennisDennisKochmannEnhanced local maximum-entropy approximation for stable meshfree simulationsHAL CCSD2018meshfree/particle methodsupdated Lagrangianmaximum entropytensile instabilityfinite deformation[SPI.MECA.MEMA] Engineering Sciences [physics]/Mechanics [physics.med-ph]/Mechanics of materials [physics.class-ph][SPI.MECA.SOLID] Engineering Sciences [physics]/Mechanics [physics.med-ph]/Solid mechanics [physics.class-ph][SPI.MECA.MSMECA] Engineering Sciences [physics]/Mechanics [physics.med-ph]/Materials and structures in mechanics [physics.class-ph]Danas, Kostas2018-11-09 13:29:132022-10-22 04:55:462018-11-20 11:29:41enJournal articleshttps://hal-polytechnique.archives-ouvertes.fr/hal-01917356/document10.1016/j.cma.2018.10.030application/pdf1We introduce an improved meshfree approximation scheme which is based on the local maximum-entropy strategy as a compromise between shape function locality and entropy in an information-theoretical sense. The improved version is specifically designed for severe, finite deformation and offers significantly enhanced stability as opposed to the original formulation. This is achieved by (i) formulating the quasistatic mechanical boundary value problem in a suitable updated-Lagrangian setting, (ii) introducing anisotropy in the shape function support to accommodate directional variations in nodal spacing with increasing deformation and eliminate tensile instability, (iii) spatially bounding and evolving shape function support to restrict the domain of influence and increase efficiency, (iv) truncating shape functions at interfaces in order to stably represent multi-component systems like composites or polycrystals. The new scheme is applied to benchmark problems of severe elastic and elastoplastic deformation that demonstrate its performance both in terms of accuracy (as compared to exact solutions and, where applicable, finite element simulations) and efficiency. Importantly, the presented formulation overcomes the classical tensile instability found in most mesh-free interpolation schemes, as shown for stable simulations of, e.g., the inhomogeneous extension of a hyperelastic block up to 100% or the torsion of a hyperelastic cube by 200 •-both in an updated Lagrangian setting and without the need for remeshing.