15 research outputs found
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Micromechanics of ultra-high molecular weight polyethylene fibre composites
Ultra-high molecular weight polyethylene (UHMWPE) fibre composites are considered to be state-of-the-art materials for penetration and ballistic impact protection applications. The composites are made of strong UHMWPE fibres with a soft compliant matrix. The extreme anisotropy caused by the mismatch between the stiffness and strength of the fibres and the matrix resulted in unique deformation and failure mechanisms which cannot be found in conventional engineering materials. Therefore, the thesis contributes towards understanding the governing mechanisms of UHMWPE composites that resulted in their high penetration and impact resistance, as well as characterizing their mechanical response under dynamic loading.
In the first part of the thesis, we focus on the quasi-static penetration response of UHMWPE composites by sharp-tipped punches. It is shown that the punch penetrates the composites without fibre fracture but by the formation of mode-I cracks along the fibre directions. The results indicate that the high penetration resistance of the composites by sharp-tipped punches is attributed to the high toughnesses of the composites. In the second part of the thesis, failure mechanism maps are developed to illustrate the mechanisms by which failure can initiate in UHMWPE composite beams impacted by blunt projectiles. We reveal that beams with low shear strengths fail by the indirect tension mode at high impact velocities while beams with high shear strengths fail by the bending mode at significantly lower impact velocities. The study thus provides a mechanistic understanding of the experimental observations that high ballistic performance composites require low matrix shear strength. Finally, in the third part of the thesis we investigate the dynamic in-plane compressive response of the composites. It is revealed that compressive deformation of the composites occurs by ply level kink band formation. Additionally, the study shows that the composites become strongly strain rate dependent at strain rates above 100 s^{-1} and the observed strain rate dependency is mainly attributed to that of the matrix.
The findings presented throughout this thesis reveal the key mechanisms and material parameters of the UHMWPE composites which governs their impact and penetration resistance, hence open new avenues and additional routes towards the design of composite materials with ultimate performance
Fourier Neural Operator with Learned Deformations for PDEs on General Geometries
Deep learning surrogate models have shown promise in solving partial
differential equations (PDEs). Among them, the Fourier neural operator (FNO)
achieves good accuracy, and is significantly faster compared to numerical
solvers, on a variety of PDEs, such as fluid flows. However, the FNO uses the
Fast Fourier transform (FFT), which is limited to rectangular domains with
uniform grids. In this work, we propose a new framework, viz., geo-FNO, to
solve PDEs on arbitrary geometries. Geo-FNO learns to deform the input
(physical) domain, which may be irregular, into a latent space with a uniform
grid. The FNO model with the FFT is applied in the latent space. The resulting
geo-FNO model has both the computation efficiency of FFT and the flexibility of
handling arbitrary geometries. Our geo-FNO is also flexible in terms of its
input formats, viz., point clouds, meshes, and design parameters are all valid
inputs. We consider a variety of PDEs such as the Elasticity, Plasticity,
Euler's, and Navier-Stokes equations, and both forward modeling and inverse
design problems. Geo-FNO is times faster than the standard numerical
solvers and twice more accurate compared to direct interpolation on existing
ML-based PDE solvers such as the standard FNO
Learning macroscopic internal variables and history dependence from microscopic models
This paper concerns the study of history dependent phenomena in heterogeneous
materials in a two-scale setting where the material is specified at a fine
microscopic scale of heterogeneities that is much smaller than the coarse
macroscopic scale of application. We specifically study a polycrystalline
medium where each grain is governed by crystal plasticity while the solid is
subjected to macroscopic dynamic loads. The theory of homogenization allows us
to solve the macroscale problem directly with a constitutive relation that is
defined implicitly by the solution of the microscale problem. However, the
homogenization leads to a highly complex history dependence at the macroscale,
one that can be quite different from that at the microscale. In this paper, we
examine the use of machine-learning, and especially deep neural networks, to
harness data generated by repeatedly solving the finer scale model to: (i) gain
insights into the history dependence and the macroscopic internal variables
that govern the overall response; and (ii) to create a computationally
efficient surrogate of its solution operator, that can directly be used at the
coarser scale with no further modeling. We do so by introducing a recurrent
neural operator (RNO), and show that: (i) the architecture and the learned
internal variables can provide insight into the physics of the macroscopic
problem; and (ii) that the RNO can provide multiscale, specifically FE2,
accuracy at a cost comparable to a conventional empirical constitutive
relation
Multipole Graph Neural Operator for Parametric Partial Differential Equations
One of the main challenges in using deep learning-based methods for simulating physical systems and solving partial differential equations (PDEs) is formulating physics-based data in the desired structure for neural networks. Graph neural networks (GNNs) have gained popularity in this area since graphs offer a natural way of modeling particle interactions and provide a clear way of discretizing the continuum models. However, the graphs constructed for approximating such tasks usually ignore long-range interactions due to unfavorable scaling of the computational complexity with respect to the number of nodes. The errors due to these approximations scale with the discretization of the system, thereby not allowing for generalization under mesh-refinement. Inspired by the classical multipole methods, we purpose a novel multi-level graph neural network framework that captures interaction at all ranges with only linear complexity. Our multi-level formulation is equivalent to recursively adding inducing points to the kernel matrix, unifying GNNs with multi-resolution matrix factorization of the kernel. Experiments confirm our multi-graph network learns discretization-invariant solution operators to PDEs and can be evaluated in linear time
Markov Neural Operators for Learning Chaotic Systems
Chaotic systems are notoriously challenging to predict because of their
instability. Small errors accumulate in the simulation of each time step,
resulting in completely different trajectories. However, the trajectories of
many prominent chaotic systems live in a low-dimensional subspace (attractor).
If the system is Markovian, the attractor is uniquely determined by the Markov
operator that maps the evolution of infinitesimal time steps. This makes it
possible to predict the behavior of the chaotic system by learning the Markov
operator even if we cannot predict the exact trajectory. Recently, a new
framework for learning resolution-invariant solution operators for PDEs was
proposed, known as neural operators. In this work, we train a Markov neural
operator (MNO) with only the local one-step evolution information. We then
compose the learned operator to obtain the global attractor and invariant
measure. Such a Markov neural operator forms a discrete semigroup and we
empirically observe that does not collapse or blow up. Experiments show neural
operators are more accurate and stable compared to previous methods on chaotic
systems such as the Kuramoto-Sivashinsky and Navier-Stokes equations
Fourier Neural Operator for Parametric Partial Differential Equations
The classical development of neural networks has primarily focused on learning mappings between finite-dimensional Euclidean spaces. Recently, this has been generalized to neural operators that learn mappings between function spaces. For partial differential equations (PDEs), neural operators directly learn the mapping from any functional parametric dependence to the solution. Thus, they learn an entire family of PDEs, in contrast to classical methods which solve one instance of the equation. In this work, we formulate a new neural operator by parameterizing the integral kernel directly in Fourier space, allowing for an expressive and efficient architecture. We perform experiments on Burgers' equation, Darcy flow, and the Navier-Stokes equation (including the turbulent regime). Our Fourier neural operator shows state-of-the-art performance compared to existing neural network methodologies and it is up to three orders of magnitude faster compared to traditional PDE solvers
Multipole Graph Neural Operator for Parametric Partial Differential Equations
One of the main challenges in using deep learning-based methods for
simulating physical systems and solving partial differential equations (PDEs)
is formulating physics-based data in the desired structure for neural networks.
Graph neural networks (GNNs) have gained popularity in this area since graphs
offer a natural way of modeling particle interactions and provide a clear way
of discretizing the continuum models. However, the graphs constructed for
approximating such tasks usually ignore long-range interactions due to
unfavorable scaling of the computational complexity with respect to the number
of nodes. The errors due to these approximations scale with the discretization
of the system, thereby not allowing for generalization under mesh-refinement.
Inspired by the classical multipole methods, we propose a novel multi-level
graph neural network framework that captures interaction at all ranges with
only linear complexity. Our multi-level formulation is equivalent to
recursively adding inducing points to the kernel matrix, unifying GNNs with
multi-resolution matrix factorization of the kernel. Experiments confirm our
multi-graph network learns discretization-invariant solution operators to PDEs
and can be evaluated in linear time
Physics-Informed Neural Operator for Learning Partial Differential Equations
Machine learning methods have recently shown promise in solving partial
differential equations (PDEs). They can be classified into two broad
categories: approximating the solution function and learning the solution
operator. The Physics-Informed Neural Network (PINN) is an example of the
former while the Fourier neural operator (FNO) is an example of the latter.
Both these approaches have shortcomings. The optimization in PINN is
challenging and prone to failure, especially on multi-scale dynamic systems.
FNO does not suffer from this optimization issue since it carries out
supervised learning on a given dataset, but obtaining such data may be too
expensive or infeasible. In this work, we propose the physics-informed neural
operator (PINO), where we combine the operating-learning and
function-optimization frameworks. This integrated approach improves convergence
rates and accuracy over both PINN and FNO models. In the operator-learning
phase, PINO learns the solution operator over multiple instances of the
parametric PDE family. In the test-time optimization phase, PINO optimizes the
pre-trained operator ansatz for the querying instance of the PDE. Experiments
show PINO outperforms previous ML methods on many popular PDE families while
retaining the extraordinary speed-up of FNO compared to solvers. In particular,
PINO accurately solves challenging long temporal transient flows and Kolmogorov
flows where other baseline ML methods fail to converge
Strengthening magnesium by design: integrating alloying and dynamic processing
Magnesium (Mg) has the lowest density of all structural metals and has
excellent potential for wide use in structural applications. While pure Mg has
inferior mechanical properties; the addition of further elements at various
concentrations has produced alloys with enhanced mechanical performance and
corrosion resistance. An important consequence of adding such elements is that
the saturated Mg matrix can locally decompose to form solute clusters and
intermetallic particles, often referred to as precipitates. Controlling the
shape, number density, volume fraction, and spatial distribution of solute
clusters and precipitates significantly impacts the alloy's plastic response.
Conversely, plastic deformation during thermomechanical processing can
dramatically impact solute clustering and precipitation. In this paper, we
first discuss how solute atoms, solute clusters, and precipitates can improve
the mechanical properties of Mg alloys. We do so by primarily comparing three
alloy systems: Mg-Al, Mg-Zn, and Mg-Y-based alloys. In the second part, we
provide strategies for optimizing such microstructures by controlling
nucleation and growth of solute clusters and precipitates during
thermomechanical processing. In the third part, we briefly highlight how one
can enable inverse design of Mg alloys by a more robust Integrated
Computational Materials Design (ICMD) approach