70 research outputs found
Accurate prediction of melt pool shapes in laser powder bed fusion by the non-linear temperature equation including phase changes - isotropic versus anisotropic conductivity
In this contribution, we validate a physical model based on a transient
temperature equation (including latent heat) w.r.t. the experimental set
AMB2018-02 provided within the additive manufacturing benchmark series,
established at the National Institute of Standards and Technology, USA. We aim
at predicting the following quantities of interest: width, depth, and length of
the melt pool by numerical simulation and report also on the obtainable
numerical results of the cooling rate. We first assume the laser to posses a
double ellipsoidal shape and demonstrate that a well calibrated, purely thermal
model based on isotropic thermal conductivity is able to predict all the
quantities of interest, up to a deviation of maximum 7.3\% from the
experimentally measured values.
However, it is interesting to observe that if we directly introduce, whenever
available, the measured laser profile in the model (instead of the double
ellipsoidal shape) the investigated model returns a deviation of 19.3\% from
the experimental values. This motivates a model update by introducing
anisotropic conductivity, which is intended to be a simplistic model for heat
material convection inside the melt pool. Such an anisotropic model enables the
prediction of all quantities of interest mentioned above with a maximum
deviation from the experimental values of 6.5\%.
We note that, although more predictive, the anisotropic model induces only a
marginal increase in computational complexity
Phase-field modeling of brittle fracture with multi-level hp-FEM and the finite cell method
The difficulties in dealing with discontinuities related to a sharp crack are
overcome in the phase-field approach for fracture by modeling the crack as a
diffusive object being described by a continuous field having high gradients.
The discrete crack limit case is approached for a small length-scale parameter
that controls the width of the transition region between the fully broken and
the undamaged phases. From a computational standpoint, this necessitates fine
meshes, at least locally, in order to accurately resolve the phase-field
profile. In the classical approach, phase-field models are computed on a fixed
mesh that is a priori refined in the areas where the crack is expected to
propagate. This on the other hand curbs the convenience of using phase-field
models for unknown crack paths and its ability to handle complex crack
propagation patterns. In this work, we overcome this issue by employing the
multi-level hp-refinement technique that enables a dynamically changing mesh
which in turn allows the refinement to remain local at singularities and high
gradients without problems of hanging nodes. Yet, in case of complex
geometries, mesh generation and in particular local refinement becomes
non-trivial. We address this issue by integrating a two-dimensional phase-field
framework for brittle fracture with the finite cell method (FCM). The FCM based
on high-order finite elements is a non-geometry-conforming discretization
technique wherein the physical domain is embedded into a larger fictitious
domain of simple geometry that can be easily discretized. This facilitates mesh
generation for complex geometries and supports local refinement. Numerical
examples including a comparison to a validation experiment illustrate the
applicability of the multi-level hp-refinement and the FCM in the context of
phase-field simulations
Immersed boundary parametrizations for full waveform inversion
Full Waveform Inversion (FWI) is a successful and well-established inverse
method for reconstructing material models from measured wave signals. In the
field of seismic exploration, FWI has proven particularly successful in the
reconstruction of smoothly varying material deviations. In contrast,
non-destructive testing (NDT) often requires the detection and specification of
sharp defects in a specimen. If the contrast between materials is low, FWI can
be successfully applied to these problems as well. However, so far the method
is not fully suitable to image defects such as voids, which are characterized
by a high contrast in the material parameters. In this paper, we introduce a
dimensionless scaling function to model voids in the forward and
inverse scalar wave equation problem. Depending on which material parameters
this function scales, different modeling approaches are presented,
leading to three formulations of mono-parameter FWI and one formulation of
two-parameter FWI. The resulting problems are solved by first-order
optimization, where the gradient is computed by an ajdoint state method. The
corresponding Fr\'echet kernels are derived for each approach and the
associated minimization is performed using an L-BFGS algorithm. A comparison
between the different approaches shows that scaling the density with
is most promising for parameterizing voids in the forward and inverse problem.
Finally, in order to consider arbitrary complex geometries known a priori, this
approach is combined with an immersed boundary method, the finite cell method
(FCM).Comment: 23 pages, 21 figure
On the Use of Neural Networks for Full Waveform Inversion
Neural networks have recently gained attention in solving inverse problems.
One prominent methodology are Physics-Informed Neural Networks (PINNs) which
can solve both forward and inverse problems. In the paper at hand, full
waveform inversion is the considered inverse problem. The performance of PINNs
is compared against classical adjoint optimization, focusing on three key
aspects: the forward-solver, the neural network Ansatz for the inverse field,
and the sensitivity computation for the gradient-based minimization. Starting
from PINNs, each of these key aspects is adapted individually until the
classical adjoint optimization emerges. It is shown that it is beneficial to
use the neural network only for the discretization of the unknown material
field, where the neural network produces reconstructions without oscillatory
artifacts as typically encountered in classical full waveform inversion
approaches. Due to this finding, a hybrid approach is proposed. It exploits
both the efficient gradient computation with the continuous adjoint method as
well as the neural network Ansatz for the unknown material field. This new
hybrid approach outperforms Physics-Informed Neural Networks and the classical
adjoint optimization in settings of two and three-dimensional examples
Direct structural analysis of domains defined by point clouds
This contribution presents a method that aims at the numerical analysis of
solids represented by oriented point clouds. The proposed approach is based on
the Finite Cell Method, a high-order immersed boundary technique that computes
on a regular background grid of finite elements and requires only
inside-outside information from the geometric model. It is shown that oriented
point clouds provide sufficient information for these point-membership
classifications. Further, we address a tessellation-free formulation of contour
integrals that allows to apply Neumann boundary conditions on point clouds
without having to recover the underlying surface. Two-dimensional linear
elastic benchmark examples demonstrate that the method is able to provide the
same accuracy as those computed with conventional, continuous surface
descriptions, because the associated error can be controlled by the density of
the cloud. Three-dimensional examples computed on point clouds of historical
structures show how the method can be employed to establish seamless
connections between digital shape measurement techniques and numerical
analyses
Efficient multi-level hp-finite elements in arbitrary dimensions
We present an efficient algorithmic framework for constructing multi-level
hp-bases that uses a data-oriented approach that easily extends to any number
of dimensions and provides a natural framework for performance-optimized
implementations. We only operate on the bounding faces of finite elements
without considering their lower-dimensional topological features and
demonstrate the potential of the presented methods using a newly written
open-source library. First, we analyze a Fichera corner and show that the
framework does not increase runtime and memory consumption when compared
against the classical p-version of the finite element method. Then, we compute
a transient example with dynamic refinement and derefinement, where we also
obtain the expected convergence rates and excellent performance in computing
time and memory usage
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