Mixed isogeometric collocation for geometrically exact 3D beams with elasto-visco-plastic material behavior and softening effects

Weeger, Oliver; Schillinger, Dominik; Müller, Ralf

doi:10.1016/j.cma.2022.115456

Cited by 21 publications

(10 citation statements)

References 58 publications

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“…It now appears highly relevant for the analysis of lattice structures given, in particular, its ability to incorporate spatially varying geometric parameters such as the beam thickness 59,60 and its extension to inelastic regimes. 68 Only the fundamentals are outlined in the following. For simplicity, we restrict ourselves to 2D and elasticity (but possibly with large deformations and rotations).…”

Section: Mechanical Analysis Of the Constructed Image-based Beam Latt...mentioning

confidence: 99%

“…Thus, we only provide a brief review of the considered isogeometric beam element here, which is the one introduced in Reference 58. It now appears highly relevant for the analysis of lattice structures given, in particular, its ability to incorporate spatially varying geometric parameters such as the beam thickness 59,60 and its extension to inelastic regimes 68 . Only the fundamentals are outlined in the following.…”

Section: Mechanical Analysis Of the Constructed Image‐based Beam Latt...mentioning

confidence: 99%

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Image‐based isogeometric twins of lattices with virtual image correlation for varying cross‐section beams

Passieux

Bouclier

Weeger

2023

Numerical Meth Engineering

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Cellular materials, in particular metal or polymer foams and beam lattices, are characterized by a complex architecture where the material is concentrated in slender struts. This study is concerned with the construction of numerically efficient sample-specific digital twin for the analysis and characterization of the mechanical behavior of such meta-materials. A method to build an explicit, light, and analysis-suitable isogeometric beam model directly from digital images is proposed. More precisely, as a main contribution, the virtual image correlation method is extended to the case of multiple interconnected beams with varying cross-sections. Special care is also given to the initialization for better efficiency and robustness. Synthetic and real examples of increasing complexity, that is, curved beams, lattices, and foams, are presented to account for the performance of the developed workflow from digital images to an isogeometric twin for mechanical modeling and simulation. K E Y W O R D Scellular materials, digital twin, image-based models, isogeometric analysis, lattices INTRODUCTIONCellular materials are currently gathering an important momentum in both the scientific and industrial communities. 1 They rely upon a simple idea: mimicking nature, such as bones and wood, which allows to achieve, in particular, unprecedented stiffness-to-weight ratios. 2 In practice, cellular materials are characterized by a complex micro-architecture. Most of times, the material is concentrated in small struts connected in different ways, at an intermediate scale between the constituents and the structure. Originally consisting of foams, 3,4 that is, exhibiting a random distribution of cells, the advent of additive manufacturing (AM) now pushes these materials to a new stage: it becomes possible to produce so-called lattices where well-designed unit-cells are periodically (or quasi-periodically 5 ) repeated all over a macro shape to obtain exceptional specific performances. Among others, lattices can be made highly stretchable, 6 auxetic, 7 and multi-functional, and therefore, besides being attractive for lightweight components, they appear of crucial interest for energy absorption, thermal management, design of medical implants, to name a few. [8][9][10][11] However, due to the coexistence of two very different scales, the prediction of the mechanical behavior of such materials remains an issue, especially in non-linear regimes. [12][13][14][15] Their global response is actually intimately related to the local architecture, which may not be perfectly known a priori, either because of the random aspect in foams, or because of the strut-level process-induced defects and uncertainties in lattices. [16][17][18] In view of characterizing the mechanical behavior of such materials, it thus appears of paramount importance to build a digital mechanical twin for each individual tested

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Section: Mechanical Analysis Of the Constructed Image-based Beam Latt...mentioning

confidence: 99%

Section: Mechanical Analysis Of the Constructed Image‐based Beam Latt...mentioning

confidence: 99%

Image‐based isogeometric twins of lattices with virtual image correlation for varying cross‐section beams

Passieux

Bouclier

Weeger

2023

Numerical Meth Engineering

Self Cite

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“…Based on these effective models, many metamaterials with excellent acoustic characteristics have been designed and studied [48][49][50][51] . Moreover, both Maxwell and Kelvin-Voigt materials show additional resistance to fast deformations [15][16][17] , providing models that can be extended to metamaterials [18][19][20][21][22] . For instance, based on the Kelvin-Voigt model, Janbaz et al used bi-beams composed of a hyperelastic beam and a visco-hyperelastic beam in parallel as the elements to design mechanical metamaterials with varying deformation characteristics and strain rate-dependent mechanical response 52 .…”

Section: Introductionmentioning

confidence: 99%

“…Metamaterials with tunable mechanical properties [11][12][13][14] , in particular having a rich dynamical behavior [15][16][17][18][19][20][21][22] or exhibiting non-reciprocity 23,24 , are extremely attractive for numerous applications, such as control of the propagation of acoustic and elastic waves [25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40] . Beyond the homogenization limit, the idea of dynamic shear, bulk, or mass density is commonly used and accepted for waves 41 .…”

Section: Introductionmentioning

confidence: 99%

Non-reciprocal and Non-Newtonian Mechanical Metamaterials

Wang

Martínez

Ulliac

et al. 2023

Preprint

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Non-Newtonian liquids are characterized by a stress and velocity-dependent dynamical response. In elasticity, and in particular in the field of phononics, reciprocity in the equations acts against obtaining a directional response for passive media. Active stimuli-responsive materials have been conceived to overcome it. Significantly, Milton and Willis have shown theoretically in 2007 that quasi-rigid bodies containing masses at resonance can display a very rich dynamical behavior, hence opening a route toward the design of non-reciprocal and non-Newtonian metamaterials. In this paper, we design a solid structure that displays unidirectional shock resistance, thus going beyond Newton’s second law in analogy to non-Newtonian fluids. We design the mechanical metamaterial with finite element analysis and fabricate it using 3D printing at the centimetric scale (with fused deposition modeling – FDM) and at the micrometric scale (with two-photon lithography – TPL). The non-Newtonian elastic response is measured via dynamical velocity-dependent experiments. Reversing the direction of the impact, we further highlight the intrinsic non-reciprocal response.

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“…In this regard, efforts have been made to develop effective inelastic constitutive models within the framework of geometrically exact Cosserat rod theory [7]. A similar aim was pursued by [27,28], where inelastic constitutive behaviour was considered in the modelling and simulation of manufactured composite materials, also described in terms of 3D Cosserat rods.…”

Section: Introductionmentioning

confidence: 99%

Data based constitutive modelling of rate independent inelastic effects in composite cables using Preisach hysteresis operators

et al. 2023

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This contribution aims at introducing first steps to develop hysteresis operator type inelastic constitutive laws for Cosserat rods for the simulation of cables composed of complex interior components. Motivated by the basic elements of Cosserat rod theory, we develop a specific approach to constitutive modelling adapted for this application. Afterwards, we describe the hysteretical behaviour arising from cyclic bending experiments on cables by means of the Preisach operator. As shown in pure bending experiments, slender structures such as electric cables behave inelastically, and open hysteresis loops arise with noticeable difference between the first load cycle and the following ones. The Preisach operator plays an important role in describing the input-output relation in hysteresis behaviours, and it can be expressed as a superposition of relay operators. Hence, a mathematical formulation of the problem is introduced, and a first attempt is made to determine the hysteresis behaviour that describes the relation between curvature and bending moment. Therefore, a suitable kernel function is identified in a way that its integration over the Preisach plane results in the bending moment of the specimen, and a comparison between different kernel functions is performed.

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Mixed isogeometric collocation for geometrically exact 3D beams with elasto-visco-plastic material behavior and softening effects

Cited by 21 publications

References 58 publications

Image‐based isogeometric twins of lattices with virtual image correlation for varying cross‐section beams

Image‐based isogeometric twins of lattices with virtual image correlation for varying cross‐section beams

Non-reciprocal and Non-Newtonian Mechanical Metamaterials

Data based constitutive modelling of rate independent inelastic effects in composite cables using Preisach hysteresis operators

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