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Important variables of processes are, in many occasions, categorical, i.e. names or labels representing, e.g. categories of inputs, or types of reactors or a sequence of steps. In this work, we use Large Language Models (LLMs) to derive embeddings of such inputs that represent their actual meaning, or reflect the ``distances" between categories, i.e. how similar or dissimilar they are. This is a marked difference from the current standard practice of using binary, or one-hot encoding to replace categorical variables with sequences of ones and zeros. Combined with dimensionality reduction techniques, either linear such as Principal Components Analysis (PCA), or nonlinear such as Uniform Manifold Approximation and Projection (UMAP), the proposed approach leads to a \textit{meaningful}, low-dimensional feature space. The significance of obtaining meaningful embeddings is illustrated in the context of an industrial coating process for cutting tools that includes both numerical and categorical inputs. The proposed approach enables feature importance which is a marked improvement compared to the current state-of-the-art (SotA) in the encoding of categorical variables.

We present an approach to the coupling of mixed-dimensional continua by employing the mathematically enriched linear Cosserat micropolar model. The kinematical reduction of the model to lower dimensional domains leaves its fundamental degrees of freedom intact. Consequently, the degrees of freedom intrinsically agree even at the interface with a domain of a different dimensionality. Thus, this approach circumvents the need for intermediate finite elements or mortar methods. We introduce the derivations of all models of various dimensions using tangential differential calculus. The coupling itself is then achieved by defining a mixed-dimensional action functional with consistent Sobolev trace operators. Finally, we present numerical examples involving a three-dimensional silicone-rubber block reinforced with a curved graphite shell on its lower surface, a three-dimensional silver block reinforced with a graphite plate and beams, and lastly, intersecting silver shells reinforced with graphite beams.

Many real-world applications demand accurate and fast predictions, as well as reliable uncertainty estimates. However, quantifying uncertainty on high-dimensional predictions is still a severely under-invested problem, especially when input-output relationships are non-linear. To handle this problem, the present work introduces an innovative approach that combines autoencoder deep neural networks with the probabilistic regression capabilities of Gaussian processes. The autoencoder provides a low-dimensional representation of the solution space, while the Gaussian process is a Bayesian method that provides a probabilistic mapping between the low-dimensional inputs and outputs. We validate the proposed framework for its application to surrogate modeling of non-linear finite element simulations. Our findings highlight that the proposed framework is computationally efficient as well as accurate in predicting non-linear deformations of solid bodies subjected to external forces, all the while providing insightful uncertainty assessments.

Error control by means of a posteriori error estimators or indica-tors and adaptive discretizations, such as adaptive mesh refinement, have emerged in the late seventies. Since then, numerous theoretical developments and improvements have been made, as well as the first attempts to introduce them into real-life industrial applications. The present introductory chapter provides an overview of the subject, highlights some of the achievements to date and discusses possible perspectives.

Omics data analysis is crucial for studying complex diseases, but its high dimensionality and heterogeneity challenge classical statistical and machine learning methods. Graph neural networks have emerged as promising alternatives, yet the optimal strategies for their design and optimization in real-world biomedical challenges remain unclear. This study evaluates various graph representation learning models for case-control classification using high-throughput biological data from Parkinson's disease and control samples. We compare topologies derived from sample similarity networks and molecular interaction networks, including protein-protein and metabolite-metabolite interactions (PPI, MMI). Graph Convolutional Network (GCNs), Chebyshev spectral graph convolution (ChebyNet), and Graph Attention Network (GAT), are evaluated alongside advanced architectures like graph transformers, the graph U-net, and simpler models like multilayer perceptron (MLP). These models are systematically applied to transcriptomics and metabolomics data independently. Our comparative analysis highlights the benefits and limitations of various architectures in extracting patterns from omics data, paving the way for more accurate and interpretable models in biomedical research., Comment: Submitted to Machine Learning in Computational Biology 2024 as an extended abstract, 2 pages + 1 appendix

This work introduces a comprehensive approach utilizing data-driven methods to elucidate the deposition process regimes in Chemical Vapor Deposition (CVD) reactors and the interplay of physical mechanism that dominate in each one of them. Through this work, we address three key objectives. Firstly, our methodology relies on process outcomes, derived by a detailed CFD model, to identify clusters of "outcomes" corresponding to distinct process regimes, wherein the relative influence of input variables undergoes notable shifts. This phenomenon is experimentally validated through Arrhenius plot analysis, affirming the efficacy of our approach. Secondly, we demonstrate the development of an efficient surrogate model, based on Polynomial Chaos Expansion (PCE), that maintains accuracy, facilitating streamlined computational analyses. Finally, as a result of PCE, sensitivity analysis is made possible by means of Sobol' indices, that quantify the impact of process inputs across identified regimes. The insights gained from our analysis contribute to the formulation of hypotheses regarding phenomena occurring beyond the transition regime. Notably, the significance of temperature even in the diffusion-limited regime, as evidenced by the Arrhenius plot, suggests activation of gas phase reactions at elevated temperatures. Importantly, our proposed methods yield insights that align with experimental observations and theoretical principles, aiding decision-making in process design and optimization. By circumventing the need for costly and time-consuming experiments, our approach offers a pragmatic pathway towards enhanced process efficiency. Moreover, this study underscores the potential of data-driven computational methods for innovating reactor design paradigms.

This study introduces a machine learning framework tailored to large-scale industrial processes characterized by a plethora of numerical and categorical inputs. The framework aims to (i) discern critical parameters influencing the output and (ii) generate accurate out-of-sample qualitative and quantitative predictions of production outcomes. Specifically, we address the pivotal question of the significance of each input in shaping the process outcome, using an industrial Chemical Vapor Deposition (CVD) process as an example. The initial objective involves merging subject matter expertise and clustering techniques exclusively on the process output, here, coating thickness measurements at various positions in the reactor. This approach identifies groups of production runs that share similar qualitative characteristics, such as film mean thickness and standard deviation. In particular, the differences of the outcomes represented by the different clusters can be attributed to differences in specific inputs, indicating that these inputs are critical for the production outcome. Leveraging this insight, we subsequently implement supervised classification and regression methods using the identified critical process inputs. The proposed methodology proves to be valuable in scenarios with a multitude of inputs and insufficient data for the direct application of deep learning techniques, providing meaningful insights into the underlying processes.

The macroscopic behaviors of materials are determined by interactions that occur at multiple lengths and time scales. Depending on the application, describing, predicting, and understanding these behaviors require models that rely on insights from electronic and atomic scales. In such cases, classical simplified approximations at those scales are insufficient, and quantum-based modeling is required. In this paper, we study how quantum effects can modify the mechanical properties of systems relevant to materials engineering. We base our study on a high-fidelity modeling framework that combines two computationally efficient models rooted in quantum first principles: Density Functional Tight Binding (DFTB) and many-body dispersion (MBD). The MBD model is applied to accurately describe non-covalent van der Waals interactions. Through various benchmark applications, we demonstrate the capabilities of this framework and the limitations of simplified modeling. We provide an open-source repository containing all codes, datasets, and examples presented in this work. This repository serves as a practical toolkit that we hope will support the development of future research in effective large-scale and multiscale modeling with quantum-mechanical fidelity.

The Finite Element Method (FEM) is a well-established procedure for computing approximate solutions to deterministic engineering problems described by partial differential equations. FEM produces discrete approximations of the solution with a discretisation error that can be an be quantified with \emph{a posteriori} error estimates. The practical relevance of error estimates for biomechanics problems, especially for soft tissue where the response is governed by large strains, is rarely addressed. In this contribution, we propose an implementation of \emph{a posteriori} error estimates targeting a user-defined quantity of interest, using the Dual Weighted Residual (DWR) technique tailored to biomechanics. The proposed method considers a general setting that encompasses three-dimensional geometries and model non-linearities, which appear in hyperelastic soft tissues. We take advantage of the automatic differentiation capabilities embedded in modern finite element software, which allows the error estimates to be computed generically for a large class of models and constitutive laws. First we validate our methodology using experimental measurements from silicone samples, and then illustrate its applicability for patient-specific computations of pressure ulcers on a human heel.

Feature engineering is of critical importance in the field of Data Science. While any data scientist knows the importance of rigorously preparing data to obtain good performing models, only scarce literature formalizes its benefits. In this work, we will present the method of Statistically Enhanced Learning (SEL), a formalization framework of existing feature engineering and extraction tasks in Machine Learning (ML). The difference compared to classical ML consists in the fact that certain predictors are not directly observed but obtained as statistical estimators. Our goal is to study SEL, aiming to establish a formalized framework and illustrate its improved performance by means of simulations as well as applications on real life use cases.

Meshfree Lagrangian frameworks for free surface flow simulations do not conserve fluid volume. Meshfree particle methods like SPH are not mimetic, in the sense that discrete mass conservation does not imply discrete volume conservation. On the other hand, meshfree collocation methods typically do not use any notion of mass. As a result, they are neither mass conservative nor volume conservative at the discrete level. In this paper, we give an overview of various sources of conservation errors across different meshfree methods. The present work focuses on one specific issue: unreliable volume and mass definitions. We introduce the concept of representative masses and densities, which are essential for accurate post-processing especially in meshfree collocation methods. Using these, we introduce an artificial compression or expansion in the fluid to rectify errors in volume conservation. Numerical experiments show that the introduced frameworks significantly improve volume conservation behaviour, even for complex industrial test cases such as automotive water crossing.

We exploit level set topology optimization to find the optimal material distribution for metamaterial-based heat manipulators. The level set function, geometry, and solution field are parameterized using the non-uniform rational B-spline (NURBS) basis functions in order to take advantage of easy control of smoothness and continuity. In addition, NURBS approximations can produce conic geometries exactly and provide higher efficiency for higher-order elements. The values of the level set function at the control points (called expansion coefficients) are utilized as design variables. For optimization, we use an advanced mathematical programming technique, Sequential Quadratic Programming (SQP). Taking into account a large number of design variables and the small number of constraints associated with our optimization problem, the adjoint method is utilized to calculate the required sensitivities with respect to the design variables. The efficiency and robustness of the proposed method are demonstrated by solving three numerical examples. We have also shown that the current method can handle different geometries and types of objective functions. In addition, regularization techniques such as Tikhonov regularization and volume regularization have been explored to reduce unnecessary complexity and increase the manufacturability of optimized topologies.

Breast-conserving surgery is the most acceptable operation for breast cancer removal from an invasive and psychological point of view. Before the surgical procedure, a preoperative MRI is performed in the prone configuration, while the surgery is achieved in the supine position. This leads to a considerable movement of the breast, including the tumor, between the two poses, complicating the surgeon's task. In this work, a simulation pipeline allowing the computation of patient-specific geometry and the prediction of personalized breast material properties was put forward. Through image segmentation, a finite element model including the subject-specific geometry is established. By first computing an undeformed state of the breast, the geometrico-material model is calibrated by surface acquisition in the intra-operative stance. Using an elastic corotational formulation, the patient-specific mechanical properties of the breast and skin were identified to obtain the best estimates of the supine configuration. The final results are a Mean Absolute Error of 4.00mm for the mechanical parameters E_breast = 0.32 kPa and E_skin = 22.72 kPa, congruent with the current state-of-the-art. The Covariance Matrix Adaptation Evolution Strategy optimizer converges on average between 5 to 30 min depending on the initial parameters, reaching a simulation speed of 20s. To our knowledge, our model offers one of the best compromises between accuracy and speed. Satisfactory results were obtained for the estimation of breast deformation from preoperative to intra-operative configuration. Furthermore, we have demonstrated the clinical feasibility of such applications using a simulation framework that aims at the smallest disturbance of the actual surgical pipeline.

Soft biological tissues demonstrate strong time-dependent and strain-rate mechanical behavior, arising from their intrinsic visco-elasticity and fluid-solid interactions (especially at sufficiently large time scales). The time-dependent mechanical properties of soft tissues influence their physiological functions and are linked to several pathological processes. Poro-elastic modeling represents a promising approach because it allows the integration of multiscale/multiphysics data to probe biologically relevant phenomena at a smaller scale and embeds the relevant mechanisms at the larger scale. The implementation of multi-phasic flow poro-elastic models however is a complex undertaking, requiring extensive knowledge. The open-source software FEniCSx Project provides a novel tool for the automated solution of partial differential equations by the finite element method. This paper aims to provide the required tools to model the mixed formulation of poro-elasticity, from the theory to the implementation, within FEniCSx. Several benchmark cases are studied. A column under confined compression conditions is compared to the Terzaghi analytical solution, using the L2-norm. An implementation of poro-hyper-elasticity is proposed. A bi-compartment column is compared to previously published results (Cast3m implementation). For all cases, accurate results are obtained in terms of a normalized Root Mean Square Error (RMSE). Furthermore, the FEniCSx computation is found three times faster than the legacy FEniCS one. The benefits of parallel computation are also highlighted., Comment: https://github.com/Th0masLavigne/Dolfinx_Porous_Media.git

Deep learning surrogate models are being increasingly used in accelerating scientific simulations as a replacement for costly conventional numerical techniques. However, their use remains a significant challenge when dealing with real-world complex examples. In this work, we demonstrate three types of neural network architectures for efficient learning of highly non-linear deformations of solid bodies. The first two architectures are based on the recently proposed CNN U-NET and MAgNET (graph U-NET) frameworks which have shown promising performance for learning on mesh-based data. The third architecture is Perceiver IO, a very recent architecture that belongs to the family of attention-based neural networks--a class that has revolutionised diverse engineering fields and is still unexplored in computational mechanics. We study and compare the performance of all three networks on two benchmark examples, and show their capabilities to accurately predict the non-linear mechanical responses of soft bodies.

Clinical management of cancer has continuously evolved for several decades. Biochemical, molecular and genomics approaches have brought and still bring numerous insights into cancerous diseases. It is now accepted that some phenomena, allowed by favorable biological conditions, emerge via mechanical signaling at the cellular scale and via mechanical forces at the macroscale. Mechanical phenomena in cancer have been studied in-depth over the last decades, and their clinical applications are starting to be understood. If numerous models and experimental setups have been proposed, only a few have led to clinical applications. The objective of this contribution is to propose to review a large scope of mechanical findings which have consequences on the clinical management of cancer. This review is mainly addressed to doctoral candidates in mechanics and applied mathematics who are faced with the challenge of the mechanics-based modeling of cancer with the aim of clinical applications. We show that the collaboration of the biological and mechanical approaches has led to promising advances in terms of modeling, experimental design and therapeutic targets. Additionally, a specific focus is brought on imaging-informed mechanics-based models, which we believe can further the development of new therapeutic targets and the advent of personalized medicine. We study in detail several successful workflows on patient-specific targeted therapies based on mechanistic modeling.

In many cutting-edge applications, high-fidelity computational models prove to be too slow for practical use and are therefore replaced by much faster surrogate models. Recently, deep learning techniques have increasingly been utilized to accelerate such predictions. To enable learning on large-dimensional and complex data, specific neural network architectures have been developed, including convolutional and graph neural networks. In this work, we present a novel encoder-decoder geometric deep learning framework called MAgNET, which extends the well-known convolutional neural networks to accommodate arbitrary graph-structured data. MAgNET consists of innovative Multichannel Aggregation (MAg) layers and graph pooling/unpooling layers, forming a graph U-Net architecture that is analogous to convolutional U-Nets. We demonstrate the predictive capabilities of MAgNET in surrogate modeling for non-linear finite element simulations in the mechanics of solids.

Computer Aided Design (CAD) is widely used in the creation and optimization of various industrial systems and processes. Transforming a CAD geometry into a computational discretization that be used to solve PDEs requires care and a deep knowledge of the selected computational method. In this article, we present a novel integrated collocation scheme based on smart clouds. It allows us to transform a CAD geometry into a complete point collocation model, aware of the base geometry, with minimum effort. For this process, only the geometry of the domain, in the form of a STEP file, and the boundary conditions are needed. We also introduce an adaptive refinement process for the resultant smart cloud using an \textit{a posteriori} error indication. The scheme can be applied to any 2D or 3D geometry, to any PDE and can be applied to most point collocation approaches. We illustrate this with the meshfree Generalized Finite Difference (GFD) method applied to steady linear elasticity problems. We further show that each step of this process, from the initial discretization to the refinement strategy, is connected and is affected by the approach selected in the previous step, thus requiring an integrated scheme where the whole solution process should be considered at once.

This new approach allows the user to experiment with model choices easily and quickly without requiring in-depth expertise, as constitutive models can be modified by one line of code only. This ease in building new models makes SOniCS ideal to develop surrogate, reduced order models and to train machine learning algorithms for uncertainty quantification or to enable patient-specific simulations. SOniCS is thus not only a tool that facilitates the development of surgical training simulations but also, and perhaps more importantly, paves the way to increase the intuition of users or otherwise non-intuitive behaviors of (bio)mechanical systems. The plugin uses new developments of the FEniCSx project enabling automatic generation with FFCx of finite element tensors such as the local residual vector and Jacobian matrix. We validate our approach with numerical simulations such as manufactured solutions, cantilever beams, and benchmarks provided by FEBio. We reach machine precision accuracy and demonstrate the use of the plugin for a real-time haptic simulation involving a surgical tool controlled by the user in contact with a hyperelastic liver. We include complete examples showing the use of our plugin for simulations involving Saint Venant-Kirchhoff, Neo-Hookean, Mooney-Rivlin, and Holzapfel Ogden anisotropic models as supplementary material.

There has been a growing interest in controlled heat flux manipulation to increase the efficiency of thermal apparatus. Heat manipulators control and manipulate heat flow. A key to the effective performance of these heat manipulators is their thermal design. Such designs can be achieved by a periodic assembly of unit cells (known as metamaterials or meta-structure), whose geometry and material properties can be optimized for a specific objective. In this work, we focus on thermal metamaterial-based heat manipulators such as thermal concentrator (which concentrates the heat flux in a specified region of the domain). The main scope of the current work is to optimize the shape of the heat manipulators using Particle Swarm Optimization (PSO) method. The geometry is defined using NURBS basis functions due to the higher smoothness and continuity and the thermal boundary value problem is solved using Isogeometric Analysis (IGA). Often, nodes as design variables (as in Lagrange finite element method) generate the serrate shapes of boundaries which need to be smoothened later. For the NURBS-based boundary with the control points as design variables, the required smoothness can be predefined through knot vectors and smoothening in the post-processing can be avoided. The optimized shape generated by PSO is compared with the other shape exploited in the literature. The effects of the number of design variables, the thermal conductivity of the materials used, as well as some of the geometry parameters on the optimum shapes are also demonstrated.

Stress prediction in porous materials and structures is challenging due to the high computational cost associated with direct numerical simulations. Convolutional Neural Network (CNN) based architectures have recently been proposed as surrogates to approximate and extrapolate the solution of such multiscale simulations. These methodologies are usually limited to 2D problems due to the high computational cost of 3D voxel based CNNs. We propose a novel geometric learning approach based on a Graph Neural Network (GNN) that efficiently deals with three-dimensional problems by performing convolutions over 2D surfaces only. Following our previous developments using pixel-based CNN, we train the GNN to automatically add local fine-scale stress corrections to an inexpensively computed coarse stress prediction in the porous structure of interest. Our method is Bayesian and generates densities of stress fields, from which credible intervals may be extracted. As a second scientific contribution, we propose to improve the extrapolation ability of our network by deploying a strategy of online physics-based corrections. Specifically, we condition the posterior predictions of our probabilistic predictions to satisfy partial equilibrium at the microscale, at the inference stage. This is done using an Ensemble Kalman algorithm, to ensure tractability of the Bayesian conditioning operation. We show that this innovative methodology allows us to alleviate the effect of undesirable biases observed in the outputs of the uncorrected GNN, and improves the accuracy of the predictions in general., Comment: 68 pages; 52 figures

In this paper, we present a new model to simulate the formation, evolution, and break up of a thin film of fluid flowing over a curved surface. Referred to as the discrete droplet method (DDM), the model captures the evolution of thin fluid films by tracking individual moving fluid droplets. In contrast to existing thin film models that solve a PDE to determine the film height, here, we compute the film height by numerical integration based on the aggregation of droplets. The novelty of this approach in using droplets makes it suitable for simulating the formation of fluid films, and modelling thin film flows on partially wetted surfaces. The DDM is a Lagrangian approach, with a force balance on each droplet governing the motion, and derivatives approximated using a smoothed particle hydrodynamics (SPH) like approach. The proposed model is thoroughly validated by comparing results against analytical solutions, against the results of the shallow-water equations for thin film flow, and also against results from a full 3D resolved Navier Stokes model. We also present the use of the DDM on an industrial test case. The results highlight the effectiveness of the model for simulations of flows with thin films.

We develop a novel a posteriori error estimator for the $L^2$ error committed by the finite element discretization of the solution of the fractional Laplacian. Our a posteriori error estimator takes advantage of the semi-discretization scheme using rational approximations which allow to reformulate the fractional problem into a family of non-fractional parametric problems. The estimator involves applying the implicit Bank-Weiser error estimation strategy to each parametric non-fractional problem and reconstructing the fractional error through the same rational approximation used to compute the solution to the original fractional problem. In addition we propose an algorithm to adapt both the finite element mesh and the rational scheme in order to balance the discretization errors. We provide several numerical examples in both two and three-dimensions demonstrating the effectivity of our estimator for varying fractional powers and its ability to drive an adaptive mesh refinement strategy.

An adapted deflation preconditioner is employed to accelerate the solution of linear systems resulting from the discretization of fracture mechanics problems with well-conditioned extended/generalized finite elements. The deflation space typically used for linear elasticity problems is enriched with additional vectors, accounting for the enrichment functions used, thus effectively removing low frequency components of the error. To further improve performance, deflation is combined, in a multiplicative way, with a block-Jacobi preconditioner, which removes high frequency components of the error as well as linear dependencies introduced by enrichment. The resulting scheme is tested on a series of non-planar crack propagation problems and compared to alternative linear solvers in terms of performance.

For many novel applications, such as patient-specific computer-aided surgery, conventional solution techniques of the underlying nonlinear problems are usually computationally too expensive and are lacking information about how certain can we be about their predictions. In the present work, we propose a highly efficient deep-learning surrogate framework that is able to accurately predict the response of bodies undergoing large deformations in real-time. The surrogate model has a convolutional neural network architecture, called U-Net, which is trained with force-displacement data obtained with the finite element method. We propose deterministic and probabilistic versions of the framework. The probabilistic framework utilizes the Variational Bayes Inference approach and is able to capture all the uncertainties present in the data as well as in the deep-learning model. Based on several benchmark examples, we show the predictive capabilities of the framework and discuss its possible limitations

The uptake of machine learning (ML) approaches in the social and health sciences has been rather slow, and research using ML for social and health research questions remains fragmented. This may be due to the separate development of research in the computational/data versus social and health sciences as well as a lack of accessible overviews and adequate training in ML techniques for non data science researchers. This paper provides a meta-mapping of research questions in the social and health sciences to appropriate ML approaches, by incorporating the necessary requirements to statistical analysis in these disciplines. We map the established classification into description, prediction, and causal inference to common research goals, such as estimating prevalence of adverse health or social outcomes, predicting the risk of an event, and identifying risk factors or causes of adverse outcomes. This meta-mapping aims at overcoming disciplinary barriers and starting a fluid dialogue between researchers from the social and health sciences and methodologically trained researchers. Such mapping may also help to fully exploit the benefits of ML while considering domain-specific aspects relevant to the social and health sciences, and hopefully contribute to the acceleration of the uptake of ML applications to advance both basic and applied social and health sciences research.

Understanding static and dynamic phenomena in complex materials at different length scales requires reliably accounting for van der Waals (vdW) interactions, which stem from long-range electronic correlations. While the important role of many-body vdW interactions has been extensively documented when it comes to the stability of materials, much less is known about the coupling between vdW interactions and atomic forces. Here we analyze the Hessian force response matrix for a single and two vdW-coupled atomic chains to show that a many-body description of vdW interactions yields atomic force response magnitudes that exceed the expected pairwise decay by 3-5 orders of magnitude for a wide range of separations between the perturbed and the observed atom. Similar findings are confirmed for graphene and carbon nanotubes. This colossal force enhancement suggests implications for phonon spectra, free energies, interfacial adhesion, and collective dynamics in materials with many interacting atoms.

An innovative technique, called conversion, is introduced to model circumferential cracks in thin cylindrical shells. The semi-analytical finite element method is applied to investigate the modal deformation of the cylinder. An element including the crack is divided into three sub-elements with four nodes in which the stiffness matrix is enriched. The crack characteristics are included in the finite element method relations through conversion matrices and a rotational spring corresponding to the crack. Conversion matrices obtained by applying continuity conditions at the crack tip are used to transform displacements of the middle nodes to those of the main nodes. Moreover, another technique, called spring set, is represented based on a set of springs to model the crack as a separated element. Components of the stiffness matrix related to the separated element are incorporated while the geometric boundary conditions at the crack tip are satisfied. The effects of the circumferential mode number, the crack depth and the length of the cylinder on the critical buckling load are investigated. Experimental tests, ABAQUS modeling and results from literature are used to verify and validate the results and derived relations. In addition, the crack effect on the natural frequency is examined using the vibration analysis based on the conversion technique., Comment: 23 pages, 12 figures, and 5 tables

In breast surgical practice, drawing is part of the preoperative planning procedure and is essential for a successful operation. In this study, we design a pipeline to assist surgeons with patient-specific breast surgical drawings. We use a deformable torso model containing the surgical patterns to match any breast surface scan. To be compatible with surgical timing, we build an articulated model through a skinning process coupled with shape deformers to enhance a fast registration process. On one hand, the scalable bones of the skinning account for pose and morphological variations of the patients. On the other hand, pre-designed artistic blendshapes create a linear space for guaranteeing anatomical variations. Then, we apply meaningful constraints to the model to find a trade-off between precision and speed. The experiments were conducted on 7 patients, in 2 different poses (prone and supine) with a breast size ranging from 36A and 42C (US/UK bra sizing). The acquisitions were obtained using the depth camera Structure Sensor, and the breast scans were acquired in less than 1 minute. The result is a registration method converging within a few seconds (3 maximum), reaching a Mean Absolute Error of 2.3 mm for mesh registration and 8.0 mm for breast anatomical landmarks. Compared to the existing literature, our model can be personalized and does not require any database. Finally, our registered model can be used to transfer surgical reference patterns onto any patient in any position., Comment: 20 pages, 8 figures, submitted to Journal of Biomechanics