X‐ray computed tomography‐based modeling of polymeric foams: The effect of finite element model size on the large strain response

Wismans, Jgf Joris; Govaert, Leon Le; Dommelen, van Jaw Hans

doi:10.1002/polb.22055

Cited by 29 publications

(13 citation statements)

References 36 publications

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“…Most of the research focuses on the mechanical/deformation behaviour but other properties are also considered. Amongst the recent studies, some are dedicated to cellular materials in general, 362,[376][377][378][379][380] others focus on specific types of cellular materials including metals, 372,[381][382][383][384][385][386][387][388][389][390] ceramics, 257,[391][392][393][394] polymers, [395][396][397] carbon, 398 nuclear graphite 399 and even bread. 400 In some cases FE simulations have been run side by side with in situ deformation under CT observation to compare their predictive capability both locally on a strut-by-strut basis and globally in terms of Poisson's ratio and Young's modulus, for example for conventional versus auxetic open cell foams.…”

Section: Image Based Modelling Of Cellular/porous Materialsmentioning

confidence: 99%

Quantitative X-ray tomography

Maire¹,

Withers²

2013

International Materials Reviews

1,089

601

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X-ray computer tomography (CT) is fast becoming an accepted tool within the materials science community for the acquisition of 3D images. Here the authors review the current state of the art as CT transforms from a qualitative diagnostic tool to a quantitative one. Our review considers first the image acquisition process, including the use of iterative reconstruction strategies suited to specific segmentation tasks and emerging methods that provide more insight (e.g. fast and high resolution imaging, crystallite (grain) imaging) than conventional attenuation based tomography. Methods and shortcomings of CT are examined for the quantification of 3D volumetric data to extract key topological parameters such as phase fractions, phase contiguity, and damage levels as well as density variations. As a non-destructive technique, CT is an ideal means of following structural development over time via time lapse sequences of 3D images (sometimes called 3D movies or 4D imaging). This includes information needed to optimise manufacturing processes, for example sintering or solidification, or to highlight the proclivity of specific degradation processes under service conditions, such as intergranular corrosion or fatigue crack growth. Besides the repeated application of static 3D image quantification to track such changes, digital volume correlation (DVC) and particle tracking (PT) methods are enabling the mapping of deformation in 3D over time. Finally the use of CT images is considered as the starting point for numerical modelling based on realistic microstructures, for example to predict flow through porous materials, the crystalline deformation of polycrystalline aggregates or the mechanical properties of composite materials.

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Section: Image Based Modelling Of Cellular/porous Materialsmentioning

confidence: 99%

Quantitative X-ray tomography

Maire¹,

Withers²

2013

International Materials Reviews

1,089

601

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“…al used 2D sections to model a closed cell polymeric foam [15]. A limitation of these studies was that the mechanical properties of the constituent materials were not known and so material parameters were assumed.…”

Section: Introductionmentioning

confidence: 99%

Deformation Mechanics of a Non-Linear Hyper-Viscoelastic Porous Material, Part II: Porous Material Micro-Scale Model

Salisbury

Cronin

Lien

2015

J. dynamic behavior mater.

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Foam materials are widely used for energy absorbing applications, and are often addressed in a modeling environment at a macroscopic or continuum level by measuring the mechanical properties, which may be size dependent, and implementing the properties in a continuum-level constitutive model. However, foams are known to exhibit a characteristically low wave speed and an understanding of the deformation mechanics of foams at the micro-scale and dependence on morphology are essential to understand the performance of foam material in impact scenarios. In this study, experimental testing and finite element modeling were used to investigate a viscoelastic polychloroprene closed-cell foam at the cell level, subject to large deformation and high deformation rates. A numerical model was created with solid hexahedral elements and a repeated tetrakaidecahedron cell structure using measured foam cell size and wall thickness, and mechanical properties measured from non-porous polychloroprene. The finite element model predictions were evaluated using experimental compression tests on the foam material at high deformation rates. The enclosed nitrogen in the closed cell foam was modeled using an Arbitrary Lagrange-Eulerian method so that this contribution could be included or removed, and demonstrated the significant effect of the enclosed gas on the mechanical response of the foam. The foam cell dimensions were varied to investigate morphological factors including cell size, cell aspect ratio and cell wall thickness.Increasing wall thickness, decreasing cell size and decreasing the cell aspect ratio resulted in increased material stiffness, with wall thickness having the most significant effect. Investigation of the wave transmission speed demonstrated a low value compared to the constituent materials, which was explained by the path of the stress wave through the foam structure and wave reflections within the cells, attenuating the stress wave. The consequence of this low wave speed was non-uniform deformation of the foam sample demonstrating that the measured mechanical properties of porous foams depend on the sample thickness, an important consideration for foam material testing and characterization.

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“…This section provides a unified finite element resolution of the weak form (29) within a non-linear finite element framework. The vector-matrix notations are used in this section instead of the tensor ones.…”

Section: Finite Element Resolution Of the Microscopic Bvpmentioning

confidence: 99%

“…The weak form (29) combined with the linear constraints system given in Eq. (74) results in the non-linear system of equations [59,13] …”

Section: Iterative Resolutionmentioning

confidence: 99%

“…However, a real material is generally more complex and consists of different constituents which are randomly distributed. In this case, the RVEs can be constructed from micro-structural images using either the direct image processing [29,30] or from the microstructure reconstruction [31,32]. In general, the homogenized properties are shown to approach the effective values when increasing the RVE size with a rate which depends not only on the nature of the underlying microstructure (properties of constituents, their distribution, and their interaction), but also on the proper choice of the microscopic boundary conditions [26].…”

Section: Introductionmentioning

confidence: 99%

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Unified treatment of microscopic boundary conditions and efficient algorithms for estimating tangent operators of the homogenized behavior in the computational homogenization method

Nguyễn

Noels

2016

Comput Mech

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Unified treatment of microscopic boundary conditions and efficient algorithms for estimating tangent operators of the homogenized behavior in the computational homogenization method Van-Dung Abstract This work provides a unified treatment of arbitrary kinds of microscopic boundary conditions usually considered in the multi-scale computational homogenization method for nonlinear multi-physics problems. An efficient procedure is developed to enforce the multi-point linear constraints arising from the microscopic boundary condition either by the direct constraint elimination or by the Lagrange multiplier elimination methods. The macroscopic tangent operators are computed in an efficient way from a multiple right hand sides linear system whose left hand side matrix is the stiffness matrix of the microscopic linearized system at the converged solution. The number of vectors at the right hand side is equal to the number of the macroscopic kinematic variables used to formulate the microscopic boundary condition. As the resolution of the microscopic linearized system often follows a direct factorization procedure, the computation of the macroscopic tangent operators is then performed using this factorized matrix at a reduced computational time.

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X‐ray computed tomography‐based modeling of polymeric foams: The effect of finite element model size on the large strain response

Cited by 29 publications

References 36 publications

Quantitative X-ray tomography

Quantitative X-ray tomography

Deformation Mechanics of a Non-Linear Hyper-Viscoelastic Porous Material, Part II: Porous Material Micro-Scale Model

Unified treatment of microscopic boundary conditions and efficient algorithms for estimating tangent operators of the homogenized behavior in the computational homogenization method

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