Computer Science

A novel numerical approach to analyze the mechanical behavior within composite materials including the inelastic regime up to final failure is presented. Therefore, a second-gradient theory is combined with phase-field methods to fracture. In particular, we assume that the polymeric matrix material undergoes ductile fracture, whereas continuously embedded fibers undergo brittle fracture as it is typical e.g. for roving glass reinforced thermoplastics. A hybrid phase-field approach is developed and applied along with a modified Gurson-Tvergaard-Needelman GTN-type plasticity model accounting for a temperature-dependent growth of voids on microscale. The mechanical response of the arising microstructure of the woven fabric gives rise to additional higher-order terms, representing homogenized bending contributions of the fibers. Eventually, a series of tests is conducted for this physically comprehensive multifield formulation to investigate different kinds and sequences of failure within long fiber reinforced polymers.

We present a method for enforcing manufacturability constraints in generated parts such that they will be automatically ready for fabrication using a subtractive approach. We primarily target multi-axis CNC milling approaches but the method should generalize to other subtractive methods as well. To this end, we take as user input: the radius of curvature of the tool bit, a coarse model of the tool head and optionally a set of milling directions. This allows us to enforce the following manufacturability conditions: 1) surface smoothness such that the radius of curvature of the part does not exceed the milling bit radius, 2) orientation such that every part of the surface to be milled is visible from at least one milling direction, 3) accessibility such that every surface patch can be reached by the tool bit without interference with the tool or head mount. We will show how to efficiently enforce the constraint during level set-based topology optimization modifying the advection velocity such that at each iteration the topology optimization maintains a descent optimization direction and does not violate any of the manufacturability conditions. This approach models the actual subtractive process by carving away material accessible to the machine at each iteration until a local optimum is achieved.

Simulation of unsteady creeping flows in complex geometries has traditionally required the use of a time-stepping procedure, which is typically costly and unscalable. To reduce the cost and allow for computations at much larger scales, we propose an alternative approach that is formulated based on the unsteady Stokes equation expressed in the time-spectral domain. This transformation results in a boundary value problem with an imaginary source term proportional to the computed mode that is discretized and solved in a complex-valued finite element solver using Bubnov-Galerkin formulation. This transformed spatio-spectral formulation presents several advantages over the traditional spatio-temporal techniques. Firstly, for cases with boundary conditions varying smoothly in time, it provides a significant saving in computational cost as it can resolve time-variation of the solution using a few modes rather than thousands of time steps. Secondly, in contrast to the traditional time integration scheme with a finite order of accuracy, this method exhibits a super convergence behavior versus the number of computed modes. Thirdly, in contrast to the stabilized finite element methods for fluid, no stabilization term is employed in our formulation, producing a solution that is consistent and more accurate. Fourthly, the proposed approach is embarrassingly parallelizable owing to the independence of the solution modes, thus enabling scalable calculations at a much larger number of processors. The comparison of the proposed technique against a standard stabilized finite element solver is performed using two- and three-dimensional canonical and complex geometries. The results show that the proposed method can produce more accurate results at 1% to 11% of the cost of the standard technique for the studied cases.

This paper presents a two-stage method for beam hardening artifact correction of dental cone beam computerized tomography (CBCT). The proposed artifact reduction method is designed to improve the quality of maxillofacial imaging, where soft tissue details are not required. Compared to standard CT, the additional difficulty of dental CBCT comes from the problems caused by offset detector, FOV truncation, and low signal-to-noise ratio due to low X-ray irradiation. To address these problems, the proposed method primarily performs a sinogram adjustment in the direction of enhancing data consistency, considering the situation according to the FOV truncation and offset detector. This sinogram correction algorithm significantly reduces beam hardening artifacts caused by high-density materials such as teeth, bones, and metal implants, while tending to amplify special types of noise. To suppress such noise, a deep convolutional neural network is complementarily used, where CT images adjusted by the sinogram correction are used as the input of the neural network. Numerous experiments validate that the proposed method successfully reduces beam hardening artifacts and, in particular, has the advantage of improving the image quality of teeth, associated with maxillofacial CBCT imaging.

Adaptive structures are characterized by their ability to adjust their geometrical and other properties to changing loads or requirements during service. This contribution deals with a method for the design of quasi-static motions of structures between two prescribed geometrical configurations that are optimal with regard to a specified quality function while taking large deformations into account. It is based on a variational formulation and the solution by two finite element discretizations, the spatial discretization (the standard finite element mesh) and an additional discretization of the deformation path or trajectory. For the investigations, an exemplary objective function, the minimization of the internal energy, integrated along the deformation path, is used. The method for motion design presented herein uses the Newton-Raphson method as a second order optimization algorithm and allows for analytical sensitivity analysis. The proposed method is verified and its properties are investigated by benchmark examples including rigid body motions, instability phenomena and determination of inextensible deformations of shells.

Designing novel materials that possess desired properties is a central need across many manufacturing industries. Driven by that industrial need, a variety of algorithms and tools have been developed that combine AI (machine learning and analytics) with domain knowledge in physics, chemistry, and materials science. AI-driven materials design can be divided to mainly two stages; the first one is the modeling stage, where the goal is to build an accurate regression or classification model to predict material properties (e.g. glass transition temperature) or attributes (e.g. toxic/non-toxic). The next stage is design, where the goal is to assemble or tune material structures so that they can achieve user-demanded target property values based on a prediction model that is trained in the modeling stage. For maximum benefit, these two stages should be architected to form a coherent workflow. Today there are several emerging services and tools for AI-driven material design, however, most of them provide only partial technical components (e.g. data analyzer, regression model, structure generator, etc.), that are useful for specific purposes, but for comprehensive material design, those components need to be orchestrated appropriately. Our material design system provides an end-to-end solution to this problem, with a workflow that consists of data input, feature encoding, prediction modeling, solution search, and structure generation. The system builds a regression model to predict properties, solves an inverse problem on the trained model, and generates novel chemical structure candidates that satisfy the target properties. In this paper we will introduce the methodology of our system, and demonstrate a simple example of inverse design generating new chemical structures that satisfy targeted physical property values.

Surface integral equation (SIE) methods are of great interest for the efficient electromagnetic modeling of various devices, from integrated circuits to antenna arrays. Existing acceleration algorithms for SIEs, such as the adaptive integral method (AIM), enable the fast approximation of interactions between well-separated mesh elements. Nearby interactions involve the singularity of the kernel, and must instead be computed accurately with direct integration at each frequency of interest, which can be computationally expensive. In this work, a novel algorithm is proposed for reducing the cost-per-frequency associated with near-region computations for both homogeneous and layered background media. In the proposed extended AIM (AIMx), the SIE operators are decomposed into a frequency-independent term, which contains the singularity of the kernel, and a frequency-dependent term, which is a smooth function. The expensive near-region computations are only required for the frequency-independent term, and can be reused at each frequency point, leading to significantly faster frequency sweeps. The frequency-dependent term is accurately captured via the AIM even in the near region, as confirmed through error analysis. The accuracy and efficiency of the proposed method are demonstrated through numerical examples drawn from several applications, and CPU times are significantly reduced by factors ranging from three to 16.

Antibodies are capable of potently and specifically binding individual antigens and, in some cases, disrupting their functions. The key challenge in generating antibody-based inhibitors is the lack of fundamental information relating sequences of antibodies to their unique properties as inhibitors. We develop a pipeline, Antibody Sequence Analysis Pipeline using Statistical testing and Machine Learning (ASAP-SML), to identify features that distinguish one set of antibody sequences from antibody sequences in a reference set. The pipeline extracts feature fingerprints from sequences. The fingerprints represent germline, CDR canonical structure, isoelectric point and frequent positional motifs. Machine learning and statistical significance testing techniques are applied to antibody sequences and extracted feature fingerprints to identify distinguishing feature values and combinations thereof. To demonstrate how it works, we applied the pipeline on sets of antibody sequences known to bind or inhibit the activities of matrix metalloproteinases (MMPs), a family of zinc-dependent enzymes that promote cancer progression and undesired inflammation under pathological conditions, against reference datasets that do not bind or inhibit MMPs. ASAP-SML identifies features and combinations of feature values found in the MMP-targeting sets that are distinct from those in the reference sets.

We present an approach to solving problems in micromechanics that is amenable to massively parallel calculations through the use of graphical processing units and other accelerators. The problems lead to nonlinear differential equations that are typically second order in space and first order in time. This combination of nonlinearity and nonlocality makes such problems difficult to solve in parallel. However, this combination is a result of collapsing nonlocal, but linear and universal physical laws (kinematic compatibility, balance laws), and nonlinear but local constitutive relations. We propose an operator-splitting scheme inspired by this structure. The governing equations are formulated as (incremental) variational problems, the differential constraints like compatibility are introduced using an augmented Lagrangian, and the resulting incremental variational principle is solved by the alternating direction method of multipliers. The resulting algorithm has a natural connection to physical principles, and also enables massively parallel implementation on structured grids. We present this method and use it to study two examples. The first concerns the long wavelength instability of finite elasticity, and allows us to verify the approach against previous numerical simulations. We also use this example to study convergence and parallel performance. The second example concerns microstructure evolution in liquid crystal elastomers and provides new insights into some counter-intuitive properties of these materials. We use this example to validate the model and the approach against experimental observations.

This work investigates the performance of the on-demand machine learning (ODML) algorithm introduced in Leal et al. (2020) when applied to different reactive transport problems in heterogeneous porous media. ODML was devised to accelerate the computationally expensive geochemical reaction calculations in reactive transport simulations. We demonstrate that the ODML algorithm speeds up these calculations by one to three orders of magnitude. Such acceleration, in turn, significantly accelerates the entire reactive transport simulation. The numerical experiments are performed by implementing the coupling of two open-source software packages: Reaktoro (Leal, 2015) and Firedrake (Rathgeber et al., 2016).