20 research outputs found
The Peierls--Nabarro FE model in two-phase microstructures -- a comparison with atomistics
This paper evaluates qualitatively as well as quantitatively the accuracy of
a recently proposed Peierls--Nabarro Finite Element (PN-FE) model for
dislocations by a direct comparison with an equivalent molecular statics
simulation. To this end, a two-dimensional microstructural specimen subjected
to simple shear is considered, consisting of a central soft phase flanked by
two hard-phase regions. A hexagonal atomic structure with equal lattice spacing
is adopted, the interactions of which are described by the Lennard--Jones
potential with phase specific depths of its energy well. During loading, edge
dislocation dipoles centred in the soft phase are introduced, which progress
towards the phase boundaries, where they pile up. Under a sufficiently high
external shear load, the leading dislocation is eventually transmitted into the
harder phase. The homogenized PN-FE model is calibrated to an atomistic model
in terms of effective elasticity constants and glide plane properties as
obtained from simple uniform deformations. To study the influence of different
formulations of the glide plane potential, multiple approaches are employed,
ranging from a simple sinusoidal function of the tangential disregistry to a
complex model that couples the influence of the tangential and the normal
disregistries. The obtained results show that, qualitatively, the dislocation
structure, displacement, strain fields, and the dislocation evolution are
captured adequately. The simplifications of the PN-FE model lead, however, to
some discrepancies within the dislocation core. Such discrepancies play a
dominant role in the dislocation transmission process, which thus cannot
quantitatively be captured properly. Despite its simplicity, the PN-FE model
proves to be an elegant tool for a qualitative study of edge dislocation
behaviour in two-phase microstructures, although it may not be quantitatively
predictive.Comment: 29 pages, 11 figures, 5 tables, abstract shortened to fulfill 1920
character limit, small changes after revie
On Micromechanical Parameter Identification With Integrated DIC and the Role of Accuracy in Kinematic Boundary Conditions
Integrated Digital Image Correlation (IDIC) is nowadays a well established
full-field experimental procedure for reliable and accurate identification of
material parameters. It is based on the correlation of a series of images
captured during a mechanical experiment, that are matched by displacement
fields derived from an underlying mechanical model. In recent studies, it has
been shown that when the applied boundary conditions lie outside the employed
field of view, IDIC suffers from inaccuracies. A typical example is a
micromechanical parameter identification inside a Microstructural Volume
Element (MVE), whereby images are usually obtained by electron microscopy or
other microscopy techniques but the loads are applied at a much larger scale.
For any IDIC model, MVE boundary conditions still need to be specified, and any
deviation or fluctuation in these boundary conditions may significantly
influence the quality of identification. Prescribing proper boundary conditions
is generally a challenging task, because the MVE has no free boundary, and the
boundary displacements are typically highly heterogeneous due to the underlying
microstructure. The aim of this paper is therefore first to quantify the
effects of errors in the prescribed boundary conditions on the accuracy of the
identification in a systematic way. To this end, three kinds of mechanical
tests, each for various levels of material contrast ratios and levels of image
noise, are carried out by means of virtual experiments. For simplicity, an
elastic compressible Neo-Hookean constitutive model under plane strain
assumption is adopted. It is shown that a high level of detail is required in
the applied boundary conditions. This motivates an improved boundary condition
application approach, which considers constitutive material parameters as well
as kinematic variables at the boundary of the entire MVE as degrees of freedom
in...Comment: 37 pages, 25 figures, 2 tables, 2 algorithm
Extended Micromorphic Computational Homogenization for Mechanical Metamaterials Exhibiting Multiple Geometric Pattern Transformations
Honeycomb-like microstructures have been shown to exhibit local elastic
buckling under compression, with three possible geometric buckling modes, or
pattern transformations. The individual pattern transformations, and
consequently also spatially distributed patterns, can be induced by controlling
the applied compression along two orthogonal directions. Exploitation of this
property holds great potential in, e.g., soft robotics applications. For fast
and optimal design, efficient numerical tools are required, capable of bridging
the gap between the microstructural and engineering scale, while capturing all
relevant pattern transformations. A micromorphic homogenization framework for
materials exhibiting multiple pattern transformations is therefore presented in
this paper, which extends the micromorphic scheme of Roko\v{s} et al., J. Mech.
Phys. Solids 123, 119-137 (2019), for elastomeric metamaterials exhibiting only
a single pattern transformation. The methodology is based on a suitable
kinematic ansatz consisting of a smooth part, a set of spatially correlated
fluctuating fields, and a remaining, spatially uncorrelated microfluctuation
field. Whereas the latter field is neglected or condensed out at the level of
each macroscopic material point, the magnitudes of the spatially correlated
fluctuating fields emerge at the macroscale as micromorphic fields. We develop
the balance equations which these micromorphic fields must satisfy as well as a
computational homogenization approach to compute the generalized stresses
featuring in these equations. To demonstrate the potential of the methodology,
loading cases resulting in mixed modes in both space and time are studied and
compared against full-scale simulations. It is shown that the proposed
framework is capable of capturing the relevant phenomena, although the inherent
multiplicity of solutions entails sensitivity to the initial guess.Comment: 22 pages, 13 figures, Extreme Mechanics Letters, 8 April 202
Enriched Computational Homogenization Schemes Applied to Pattern-Transforming Elastomeric Mechanical Metamaterials
Elastomeric mechanical metamaterials exhibit unconventional mechanical
behaviour owing to their complex microstructures. A clear transition in the
effective properties emerges under compressive loading, which is triggered by
local instabilities and pattern transformations of the underlying cellular
microstructure. Such transformations trigger a non-local mechanical response
resulting in strong size effects. For predictive modelling of engineering
applications, the effective homogenized material properties are generally of
interest. For mechanical metamaterials, these can be obtained in an expensive
manner by ensemble averaging of the direct numerical simulations for a series
of translated microstructures, applicable especially in the regime of small
separation of scales. To circumvent this expensive step, computational
homogenization methods are of benefit, employing volume averaging instead.
Classical first-order computational homogenization, which relies on the
standard separation of scales principle, is unable to capture any size and
boundary effects. Second-order computational homogenization has the ability to
capture strain gradient effects at the macro-scale, thus accounting for the
presence of non-localities. Another alternative is micromorphic computational
homogenization scheme, which is tailored to pattern-transforming metamaterials
by incorporating prior kinematic knowledge. In this contribution, a systematic
study is performed, assessing the predictive ability of computational
homogenization schemes in the realm of elastomeric metamaterials. Three
representative examples with distinct mechanical loading are employed for this
purpose: uniform compression and bending of an infinite specimen, and
compression of a finite specimen. Qualitative and quantitative analyses are
performed for each of the load cases where the ensemble average solution is set
as a reference.Comment: 32 pages, 19 figures, 1 table, abstract shortened to fulfil 1920
character limi
Experimental Full-field Analysis of Size Effects in Miniaturized Cellular Elastomeric Metamaterials
Cellular elastomeric metamaterials are interesting for various applications,
e.g. soft robotics, as they may exhibit multiple microstructural pattern
transformations, each with its characteristic mechanical behavior. Numerical
literature studies revealed that pattern formation is restricted in (thick)
boundary layers causing significant mechanical size effects. This paper aims to
experimentally validate these findings on miniaturized specimens, relevant for
real applications, and to investigate the effect of increased geometrical and
material imperfections resulting from specimen miniaturization. To this end,
miniaturized cellular metamaterial specimens are manufactured with different
scale ratios, subjected to in-situ micro-compression tests combined with
digital image correlation yielding full-field kinematics, and compared to
complementary numerical simulations. The specimens' global behavior agrees well
with the numerical predictions, in terms of pre-buckling stiffness, buckling
strain and post-buckling stress. Their local behavior, i.e. pattern
transformation and boundary layer formation, is also consistent between
experiments and simulations. Comparison of these results with idealized
numerical studies from literature reveals the influence of the boundary
conditions in real cellular metamaterial applications, e.g. lateral
confinement, on the mechanical response in terms of size effects and boundary
layer formation.Comment: 20 pages, 6 figures, Materials & Design, 11 May 202
Level set based eXtended finite element modelling of the response of fibrous networks under hygroscopic swelling
Materials like paper, consisting of a network of natural fibres, exposed to
variations in moisture, undergo changes in geometrical and mechanical
properties. This behaviour is particularly important for understanding the
hygro-mechanical response of sheets of paper in applications like digital
printing. A two-dimensional microstructural model of a fibrous network is
therefore developed to upscale the hygro-expansion of individual fibres,
through their interaction, to the resulting overall expansion of the network.
The fibres are modelled with rectangular shapes and are assumed to be perfectly
bonded where they overlap. For realistic networks the number of bonds is large
and the network is geometrically so complex that discretizing it by
conventional, geometry-conforming, finite elements is cumbersome. The
combination of a level-set and XFEM formalism enables the use of regular,
structured grids in order to model the complex microstructural geometry. In
this approach, the fibres are described implicitly by a level-set function. In
order to represent the fibre boundaries in the fibrous network, an XFEM
discretization is used together with a Heaviside enrichment function. Numerical
results demonstrate that the proposed approach successfully captures the
hygro-expansive properties of the network with fewer degrees of freedom
compared to classical FEM, preserving desired accuracy.Comment: 27 pages, 22 figures, 4 tables, J. Appl. Mech. June 19, 202
A Newton Solver for Micromorphic Computational Homogenization Enabling Multiscale Buckling Analysis of Pattern-Transforming Metamaterials
Mechanical metamaterials feature engineered microstructures designed to
exhibit exotic, and often counter-intuitive, effective behaviour. Such a
behaviour is often achieved through instability-induced transformations of the
underlying periodic microstructure into one or multiple patterning modes. Due
to a strong kinematic coupling of individual repeating microstructural cells,
non-local behaviour and size effects emerge, which cannot easily be captured by
classical homogenization schemes. In addition, the individual patterning modes
can mutually interact in space as well as in time, while at the engineering
scale the entire structure can buckle globally. For efficient numerical
macroscale predictions, a micromorphic computational homogenization scheme has
recently been developed. Although this framework is in principle capable of
accounting for spatial and temporal interactions between individual patterning
modes, its implementation relied on a gradient-based quasi-Newton solution
technique. This solver is suboptimal because (i) it has sub-quadratic
convergence, and (ii) the absence of Hessians does not allow for proper
bifurcation analyses. Given that mechanical metamaterials often rely on
controlled instabilities, these limitations are serious. To address them, a
full Newton method is provided in detail in this paper. The construction of the
macroscopic tangent operator is not straightforward due to specific model
assumptions on the decomposition of the underlying displacement field pertinent
to the micromorphic framework, involving orthogonality constraints. Analytical
expressions for the first and second variation of the total potential energy
are given, and the complete algorithm is listed. The developed methodology is
demonstrated with two examples in which a competition between local and global
buckling exists and where multiple patterning modes emerge.Comment: 34 pages, 17 figures, 1 table, 1 algorithm, abstract shortened to
fulfill 1920 character limi