333 research outputs found
eXtended Variational Quasicontinuum Methodology for Lattice Networks with Damage and Crack Propagation
Lattice networks with dissipative interactions are often employed to analyze
materials with discrete micro- or meso-structures, or for a description of
heterogeneous materials which can be modelled discretely. They are, however,
computationally prohibitive for engineering-scale applications. The
(variational) QuasiContinuum (QC) method is a concurrent multiscale approach
that reduces their computational cost by fully resolving the (dissipative)
lattice network in small regions of interest while coarsening elsewhere. When
applied to damageable lattices, moving crack tips can be captured by adaptive
mesh refinement schemes, whereas fully-resolved trails in crack wakes can be
removed by mesh coarsening. In order to address crack propagation efficiently
and accurately, we develop in this contribution the necessary generalizations
of the variational QC methodology. First, a suitable definition of crack paths
in discrete systems is introduced, which allows for their geometrical
representation in terms of the signed distance function. Second, special
function enrichments based on the partition of unity concept are adopted, in
order to capture kinematics in the wakes of crack tips. Third, a summation rule
that reflects the adopted enrichment functions with sufficient degree of
accuracy is developed. Finally, as our standpoint is variational, we discuss
implications of the mesh refinement and coarsening from an energy-consistency
point of view. All theoretical considerations are demonstrated using two
numerical examples for which the resulting reaction forces, energy evolutions,
and crack paths are compared to those of the direct numerical simulations.Comment: 36 pages, 23 figures, 1 table, 2 algorithms; small changes after
review, paper title change
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
Microstructural topology effects on the onset of ductile failure in multi-phase materials - a systematic computational approach
Multi-phase materials are key for modern engineering applications. They are
generally characterized by a high strength and ductility. Many of these
materials fail by ductile fracture of the, generally softer, matrix phase. In
this work we systematically study the influence of the arrangement of the
phases by correlating the microstructure of a two-phase material to the onset
of ductile failure. A single topological feature is identified in which
critical levels of damage are consistently indicated. It consists of a small
region of the matrix phase with particles of the hard phase on both sides in a
direction that depends on the applied deformation. Due to this configuration, a
large tensile hydrostatic stress and plastic strain is observed inside the
matrix, indicating high damage. This topological feature has, to some extent,
been recognized before for certain multi-phase materials. This study however
provides insight in the mechanics involved, including the influence of the
loading conditions and the arrangement of the phases in the material
surrounding the feature. Furthermore, a parameter study is performed to explore
the influence of volume fraction and hardness of the inclusion phase. For the
same macroscopic hardening response, the ductility is predicted to increase if
the volume fraction of the hard phase increases while at the same time its
hardness decreases
A Variational Formulation of Dissipative Quasicontinuum Methods
Lattice systems and discrete networks with dissipative interactions are
successfully employed as meso-scale models of heterogeneous solids. As the
application scale generally is much larger than that of the discrete links,
physically relevant simulations are computationally expensive. The
QuasiContinuum (QC) method is a multiscale approach that reduces the
computational cost of direct numerical simulations by fully resolving complex
phenomena only in regions of interest while coarsening elsewhere. In previous
work (Beex et al., J. Mech. Phys. Solids 64, 154-169, 2014), the originally
conservative QC methodology was generalized to a virtual-power-based QC
approach that includes local dissipative mechanisms. In this contribution, the
virtual-power-based QC method is reformulated from a variational point of view,
by employing the energy-based variational framework for rate-independent
processes (Mielke and Roub\'i\v{c}ek, Rate-Independent Systems: Theory and
Application, Springer-Verlag, 2015). By construction it is shown that the QC
method with dissipative interactions can be expressed as a minimization problem
of a properly built energy potential, providing solutions equivalent to those
of the virtual-power-based QC formulation. The theoretical considerations are
demonstrated on three simple examples. For them we verify energy consistency,
quantify relative errors in energies, and discuss errors in internal variables
obtained for different meshes and two summation rules.Comment: 38 pages, 21 figures, 4 tables; moderate revision after review, one
example in Section 5.3 adde
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
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