Micromechanical and macromechanical modelling of foams: Identification of Cosserat parameters

Diebels, Stefan; Geringer, A.

doi:10.1002/zamm.201200271

Cited by 13 publications

(7 citation statements)

References 22 publications

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“…In topdown, reverse modelling approaches, one uses the microscale model in very much the same manner as one would deal with experimental data: One measures the (here size-dependent) system-scale response and then tries to identify macroscopic parameters that reproduce the same behavior (see e.g. Diebels and Geringer (2014); Diebels and Steeb (2002); Mora and Waas (2007); Tekoglu and Onck (2008)). In bottom-up homogenization approaches one seeks to derive macroscopic, effective materials properties through averaging the micro-heterogeneous material response over a representative volume element (RVE).…”

Section: Discussionmentioning

confidence: 99%

Determining Cosserat constants of 2D cellular solids from beam models

Liebenstein

Zaiser

2018

Mater Theory

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We present results of a two-scale model of disordered cellular materials where we describe the microstructure in an idealized manner using a beam network model and then make a transition to a Cosserat-type continuum model describing the same material on the macroscopic scale. In such scale transitions, normally either bottom-up homogenization approaches or top-down reverse modelling strategies are used in order to match the macro-scale Cosserat continuum to the micro-scale beam network. Here we use a different approach that is based on an energetically consistent continuization scheme that uses data from the beam network model in order to determine continuous stress and strain variables in a set of control volumes defined on the scale of the individual microstructure elements (cells) in such a manner that they form a continuous tessellation of the material domain. Stresses and strains are determined independently in all control volumes, and constitutive parameters are obtained from the ensemble of control volume data using a least-square error criterion. We show that this approach yields material parameters that are for regular honeycomb structures in close agreement with analytical results. For strongly disordered cellular structures, the thus parametrized Cosserat continuum produces results that reproduce the behavior of the micro-scale beam models both in view of the observed strain patterns and in view of the macroscopic response, including its size dependence.

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Section: Discussionmentioning

confidence: 99%

Determining Cosserat constants of 2D cellular solids from beam models

Liebenstein

Zaiser

2018

Mater Theory

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“…But mostly, there is a more mathematical treatment to describe the behaviour of micro-heterogeneous materials, e. g. using higher gradients or additional degrees of freedom [2,16,22]. A new approach uses the connectivity as fundamental parameter to describe the ongoing damage in foams by an order-parameter model in order to taking account for micro-structural effects [14].…”

Section: Gedanken Experiments For a Phenomenological Spring Modelmentioning

confidence: 99%

Micro-structural motivated phenomenological modelling of metal foams: experiments and modelling

2014

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Cellular materials like metal foams are bio-inspired materials which exhibit great potential for application in lightweight construction or as kinetic energy absorber. Such cellular materials show a complex micro-structure which significantly affects the macroscopic global properties. Cellular materials exhibit localised deformation expressed in deformation bands under inelastic strain conditions. Engineering with metal foams requires material models which describe the material behaviour properly even for different load cases. In this work, a new modelling approach has been developed which phenomenologically accounts for microstructural effects by a representative volume element made of several springs. The model is experimentally validated, and its micro-structural motivated parameters are experimentally identified in quasi-static compression tests with unloading cycles. Using digital image correlation, it was possible to connect the micro-structural deformation with the global macroscopic stress-strain behaviour, evaluated locally for the front surface of the specimens.

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“…The model was applied to porous and granular media (e.g., [6] (Ehlers, 1997) [7,8]) and even to living tissues such as bones (e.g., [9][10][11][12][13]). The identification of the material parameters of the micropolar elastic model has also been the subject of a number of works (see e.g., [14,15]. Depth sensing indentation is, among others, a valuable experimental tool for the mechanical characterization of some of this materials.…”

Section: Introductionmentioning

confidence: 99%

Spherical Indentation of a Micropolar Solid: A Numerical Investigation Using the Local Point Interpolation–Boundary Element Method

et al. 2021

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The load-penetration curve in elastic nanoindentation of an elastic micropolar flat by a diamond spherical punch is analyzed. The presented results are obtained by a specifically developed numerical tool based on a judicious combination of the conventional boundary element method and strong form local point interpolation method. The results show that the usual linear relationship between the material depression and the square of the radius of the contact area is also valid in this case of micropolar elastic material. It is also shown that the relation between the indentation stress (applied load over the contact surface) and the indentation strain (ratio of contact radius by the punch radius) is linear. The proportionality coefficient which is none other than the indentation stiffness varies with the coupling factor of the micropolar elastic medium. A relation between the indentation stiffness of a micropolar solid and that of a conventional solid with the same Young modulus and Poisson ratio is derived.

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Micromechanical and macromechanical modelling of foams: Identification of Cosserat parameters

Cited by 13 publications

References 22 publications

Determining Cosserat constants of 2D cellular solids from beam models

Determining Cosserat constants of 2D cellular solids from beam models

Micro-structural motivated phenomenological modelling of metal foams: experiments and modelling

Spherical Indentation of a Micropolar Solid: A Numerical Investigation Using the Local Point Interpolation–Boundary Element Method

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