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The photopolymerization-based additive manufacturing process, including 3D printing techniques such as stereolithography and digital light processing, has undergone considerable development over the last few decades. These techniques provide flexibility in the physical and chemical properties of 3D printed materials. The photopolymerization process is based on ultraviolet (UV) curing of liquid-state monomers/oligomers in the presence of photopolymerizable photoinitiators, which is known as the UV irradiation curing process. The UV light intensity has a significant effect on the reactivity and solidification process, modeling which has many challenges. In this work, we present a novel model that determines the required UV light intensity in the photopolymerization process. To make meaningful predictions of the UV light intensity influence on the curing process, it is essential to appropriately model the UV light waves. Maxwell’s equations are considered for this purpose. The photopolymerization process itself is described by the reaction-diffusion equation, which is coupled to Maxwell’s equations in a unit square of the resin. Isogeometric analysis is used to discretize the produced coupled system of equations. We present numerical results that demonstrate the light intensity influence on the UV curing process.

We propose an isogeometric approximation of the equations describing the propagation of an electrophysiologic stimulus over a thin cardiac tissue with the subsequent muscle contraction. The underlying method relies on the monodomain model for the electrophysiological sub-problem. This requires the solution of a reaction–diffusion equation over a surface in the three-dimensional space. Exploiting the benefits of the high-order NURBS basis functions within a curvilinear framework, the method is found to reproduce complex excitation patterns with a limited number of degrees of freedom. Furthermore, the curvilinear description of the diffusion term provides a flexible and easy-to-implement approach for general surfaces. At the discrete level, two different approaches for integrating the ionic current are investigated in the isogeometric analysis framework. The electrophysiological stimulus is converted into a mechanical load employing the well-established active strain approach. The multiplicative decomposition of the deformation gradient tensor is grafted into a classical finite elasticity weak formulation, providing the necessary tensor expressions in curvilinear coordinates. The derived expressions provide what is needed to implement the active strain approach in standard finite-element solvers without resorting to dedicated formulations. Such a formulation is valid for general three-dimensional geometries and isotropic hyperelastic materials. The formulation is then restricted to Kirchhoff–Love shells by means of the static condensation of the material tensor. The purely elastic response of the structure is investigated with simple static test-cases of thin shells undergoing different active strain patterns. Eventually, various numerical tests performed with a staggered scheme illustrate that the coupled electromechanical model can capture the excitation–contraction mechanism over thin tissues and reproduce complex curvature variations.

The production of lightweight metal lattice structures has received much attention due to the recent developments in additive manufacturing (AM). The design flexibility comes, however, with the complexity of the underlying physics. In fact, metal additive manufacturing introduces process-induced geometrical defects that mainly result in deviations of the effective geometry from the nominal one. This change in the final printed shape is the primary cause of the gap between the as-designed and as-manufactured mechanical behavior of AM products. Thus, the possibility to incorporate the precise manufactured geometries into the computational analysis is crucial for the quality and performance assessment of the final parts. Computed tomography (CT) is an accurate method for the acquisition of the manufactured shape. However, it is often not feasible to integrate the CT-based geometrical information into the traditional computational analysis due to the complexity of the meshing procedure for such high-resolution geometrical models and the prohibitive numerical costs. In this work, an embedded numerical framework is applied to efficiently simulate and compare the mechanical behavior of as-designed to as-manufactured octet-truss lattice structures. The parts are produced using laser powder bed fusion (LPBF). Employing an immersed boundary method, namely the Finite Cell Method (FCM), we perform direct numerical simulations (DNS) and first-order numerical homogenization analysis of a tensile test for a 3D printed octet-truss structure. Numerical results based on CT scan (as-manufactured geometry) show an excellent agreement with experimental measurements, whereas both DNS and first-order numerical homogenization performed directly on the 3D virtual model (as-designed geometry) of the structure show a significant deviation from experimental data.

To exploit the advantageous properties of isogeometric analysis (IGA) in a scan-based setting, it is important to extract a smooth geometric domain from the scan data (e.g., voxel data). IGA-suitable domains can be constructed by convoluting the grayscale data using B-splines. A negative side-effect of this convolution technique is, however, that it can induce topological changes in the process of smoothing when features with a size similar to that of the voxels are encountered. This manuscript presents an enhanced B-spline-based segmentation procedure using a refinement strategy based on truncated hierarchical (TH)B-splines. A Fourier analysis is presented to explain the effectiveness of local grayscale function refinement in repairing topological anomalies. A moving-window-based topological anomaly detection algorithm is proposed to identify regions in which the grayscale function refinements must be performed. The criterion to identify topological anomalies is based on the Euler characteristic, giving it the capability to distinguish between topological and shape changes. The proposed topology-preserving THB-spline image segmentation strategy is studied using a range of test cases. These tests pertain to both the segmentation procedure itself, and its application in an immersed IGA setting., Comment: Submitted to CMAME

Computational mechanics 66(5), 1131–1152 (2020). doi:10.1007/s00466-020-01888-0 special issue: "Special Issue: Modeling and Simulation of Infectious Diseases-Propagation, Decontamination and Mitigation / Issue editors: Tarek I. Zohdi, Ellen Kuhl", Published by Springer, Berlin ; Heidelberg

In this paper, we use isogeometric Kirchhoff plates to approximate composite laminates adopting the classical laminate plate theory. Both isogeometric Galerkin and collocation formulations are considered. Within this framework, interlaminar stresses are recovered through an effective post-processing technique based on the direct imposition of equilibrium in strong form, relying on the accuracy and the higher continuity typically granted by isogeometric discretizations. The effectiveness of the proposed approach is proven by extensive numerical tests., 28 pages, 11 figures, 13 tables

Often the employment of the full potentialities of laminated composite materials is restrained by the scarceness of cost-effective simulation strategies in the design stage. Albeit cheap modelling techniques exist, they typically prove ineffective in retrieving interlaminar stresses, the first responsible for the damage of laminates. In this paper, we propose a strategy to reconstruct the out-of-plane stress components in composite laminates, post-processing FEM data obtained with coarse models simplified according to the classical theory of laminates. The described approach relies on radial basis function interpolation and Kansa method to enforce equilibrium in strong form, within a meshless approach. The obtained results successfully compare with those from complete layup modeling for test cases where an analytical solution is available.

This work focuses on the study of several computational challenges arising when trimmed surfaces are directly employed for the isogeometric analysis of Kirchhoff–Love shells. To cope with these issues and to resolve mechanical and/or geometrical features of interest, we exploit the local refinement capabilities of hierarchical B-splines. In particular, we show numerically that local refinement is suited to effectively impose Dirichlet-type boundary conditions in a weak sense, where this easily allows to overcome the issue of over-constraining of trimmed elements. Moreover, we highlight how refinement can alleviate the spurious coupling stemming from disjoint supports of basis functions in the presence of “small” trimmed geometrical features such as thin holes. These phenomena are particularly pronounced in surface models defined by complex trimming patterns and with details at different scales. In this contribution we focus our effort on the analysis of single-patch geometries, where we show through several numerical examples the benefits and computational efficiency of the proposed methodology.

In this contribution, we coupled the isogeometric analysis to a reduced order modelling technique in order to provide a computationally efficient solution in parametric domains. In details, we adopt the free-form deformation method to obtain the parametric formulation of the domain and proper orthogonal decomposition with interpolation for the computational reduction of the model. This technique provides a real-time solution for any parameter by combining several solutions, in this case computed using isogeometric analysis on different geometrical configurations of the domain, properly mapped into a reference configuration. We underline that this reduced order model requires only the full-order solutions, making this approach non-intrusive. We present in this work the results of the application of this methodology to a heat conduction problem inside a deformable collector pipe.

In this work, we focus on the family of shell formulations referred to as "solid shells", where the simulation of shell-type structures is performed by means of a mesh of 3D solid elements, with typically only one element through the thickness. We propose a novel approach for alleviating the various locking phenomena, which typically appear in thin structures, based on the projection of strains onto discontinuous coarser polynomial spaces defined at element level. In particular, we present and investigate two different formulations based on this approach. Several numerical experiments prove the very good performance of both formulations. The main advantages of the presented approach compared to existing solid shell formulations are its simplicity and numerical efficiency., Comment: 11 pages, 12 figures

In the present paper, an innovative approach based on a curve reparameterization technique is developed to solve the natural frequency problem of free-form Euler–Bernoulli curved beams using isogeometric analysis (IGA). The method is beneficial in modifying the probably inappropriate initial parameterization of input geometries. For this purpose, a transformation from the initial parametric domain to a new reparameterized one is adopted, creating a pseudo arc-length parameterization that is suitable for IGA. An auxiliary one-dimensional B-spline curve is utilized as the parametric transfer function (PTF). A combination of curve rectification and B-spline approximation techniques is implemented to construct the PTF. The number of elements in the proposed approach is based on the knot vector of the PTF that is not dependent on the knot vector of the input NURBS curve defining the geometry. The method is tested on different numerical examples that prove the validity and applicability of the formulations.

The objective of the present work is to develop efficient, higher-order space- and time-accurate, methods for structural dynamics. To this end, we present a family of explicit isogeometric collocation methods for structural dynamics that are obtained from predictor–multicorrector schemes. These methods are very similar in structure to explicit finite-difference time-domain methods , and in particular, they exhibit similar levels of computational cost, ease of implementation, and ease of parallelization . However, unlike finite difference methods , they are easily extended to non-trivial geometries of engineering interest. To examine the spectral properties of the explicit isogeometric collocation methods, we first provide a semi-discrete interpretation of the classical predictor–multicorrector method. This allows us to characterize the spatial and modal accuracy of the isogeometric collocation predictor–multicorrector method, irrespective of the considered time-integration scheme, as well as the critical time step size for a particular explicit time-integration scheme. For pure Dirichlet problems, we demonstrate that it is possible to obtain a second-order-in-space scheme with one corrector pass, a fourth-order-in-space scheme with two corrector passes, and a fifth-order-in-space scheme with three corrector passes. For pure Neumann and mixed Dirichlet–Neumann problems, we demonstrate that it is possible to obtain a second-order-in-space scheme with one corrector pass and a third-order-in-space scheme with two corrector passes, and we observe that fourth-order-in-space accuracy may be obtained pre-asymptotically with three corrector passes. We then present second-order-in-time, fourth-order-in-time, and fifth-order-in-time fully discrete predictor–multicorrector algorithms that result from the application of explicit Runge–Kutta methods to the semi-discrete isogeometric collocation predictor–multicorrector method. We confirm the accuracy of the family of explicit isogeometric collocation methods using a suite of numerical examples.

A Skeleton-stabilized IsoGeometric Analysis (SIGA) technique is proposed for incompressible viscous flow problems with moderate Reynolds number. The proposed method allows utilizing identical finite dimensional spaces (with arbitrary B-splines/NURBS order and regularity) for the approximation of the pressure and velocity components. The key idea is to stabilize the jumps of high-order derivatives of variables over the skeleton of the mesh. For B-splines/NURBS basis functions of degree k with C α -regularity ( 0 ≤ α k ), only the derivative of order α + 1 has to be controlled. This stabilization technique thus can be viewed as a high-regularity generalization of the (Continuous) Interior-Penalty Finite Element Method. Numerical experiments are performed for the Stokes and Navier–Stokes equations in two and three dimensions. Oscillation-free solutions and optimal convergence rates are obtained. In terms of the sparsity pattern of the algebraic system, we demonstrate that the block matrix associated with the stabilization term has a considerably smaller bandwidth when using B-splines than when using Lagrange basis functions, even in the case of C 0 -continuity. This important property makes the proposed isogeometric framework practical from a computational effort point of view.

This paper introduces a cost-effective strategy to simulate the behavior of laminated plates by means of isogeometric 3D solid elements. Exploiting the high continuity of spline functions and their properties, a proper out-of-plane stress state is recovered from a coarse displacement solution using a post-processing step based on the enforcement of equilibrium in strong form. Appealing results are obtained and the method is shown to be particularly effective on slender composite stacks with a large number of layers. These are indeed the cases where traditional (e.g., “layerwise”) approaches are more computationally heavy and where researchers are more inclined to look for alternatives, making the proposed method a very attractive solution.

A key advantage of isogeometric discretizations is their accurate and well-behaved eigenfrequencies and eigenmodes . For degree two and higher, however, a few spurious modes appear that possess inaccurate frequencies, denoted as “outliers”. The outlier frequencies and corresponding modes are at the root of several efficiency and robustness issues in isogeometric analysis. One example is explicit dynamics where outlier frequencies unnecessarily reduce the critical time step. Another example is wave propagation where the inaccurate outlier modes may participate in the solution. In this paper, we first investigate the spurious outlier frequencies and corresponding modes of isogeometric discretizations of second- and fourth-order model problems and provide a complete characterization. We then devise a new approach that removes all outliers modes without negatively affecting the accuracy of the discretizations. Our approach is variationally consistent and works for a range of common boundary conditions on tensor product domains. We finally demonstrate that our approach allows a much larger critical time step, irrespective of polynomial degree , providing a pathway towards efficient higher-order explicit dynamics.

In Selective Laser Melting (SLM) processes, residual stress formation can substantially affect mechanical properties and geometric accuracy of the produced part. The process parameters together with the adopted laser scan strategy should be optimized in order to reduce residual stresses in the solidified artifact. Employing traditional numerical methods, i.e., boundary-conforming mesh finite elements, can be computationally very expensive when complex geometrical features are involved, since the capability of capturing solidified part shapes depends on the element size. Immersed boundary methods present a valid alternative to effectively predict residual stresses employing a rather coarse discretization without loosing accuracy in the solidified geometry representation. In the present work, the finite cell method, an immersed boundary method, is employed to predict residual stresses using a high-fidelity thermo-mechanical model resolving the melt-pool length scale. The thermal model is first validated with respect to experimental measurements from the literature, while the mechanical results are compared to boundary-conforming mesh analysis for the same geometrical accuracy. Finally, the numerical method is applied to study the influence on residual stresses of two different laser scan strategies on a 10-layer SLM structure. The proposed immersed boundary approach can lead to a remarkable improvement in terms of computational time and memory usage when the mesh generation step is the main burden of a thermo-mechanical SLM process simulation.

Funding Information: We gratefully acknowledge the support of Deutsche Forschungsgemeinschaft (DFG) through the project 414265976 - TRR 277 C-01 and TUM International Graduate School of Science and Engineering (IGSSE), GSC 81. This work was partially supported by the Italian Minister of University and Research through the MIUR-PRIN projects “A BRIDGE TO THE FUTURE: Computational methods, innovative applications, experimental validations of new materials and technologies” (No. 2017L7X3CS) and “XFAST-SIMS” (No. 20173C478N). The authors would like to acknowledge the project “MADE4LO - Metal ADditivE for LOmbardy” (No. 240963) within the POR FESR 2014-2020 program. We also kindly acknowledge Eng. Alberto Cattenone and Prof. Stefania Marconi of the 3DMetal laboratory of the Department of Civil Engineering and Architecture of the University of Pavia for providing facilities for additive manufacturing and experimental testing ( http://www-4.unipv.it/3d/laboratories/3dmetalunipv/ ). We further acknowledge Academy ofFinland through the project Adaptive isogeometric methods for thin-walled structures (decision number 304122) as well as the August-Wilhelm Scheer Visiting Professors Program established by TUM International Center and funded by the German Excellence Initiative. The authors also gratefully acknowledge the Gauss Centre for Supercomputing e.V. ( www.gauss-centre.eu ) for funding this project by providing computing time on the Linux Cluster CoolMUC-2 and on the GCS Supercomputer SuperMUC-NG at Leibniz Supercomputing Centre ( www.lrz.de ). Finally, the authors gratefully acknowledge Giorgio Vattasso from LaborMet Due ( http://www.labormetdue.it/ ) for his technical support in obtaining CT scan images. Publisher Copyright: © 2021 The Author(s) Copyright: Copyright 2021 Elsevier B.V., All rights reserved. Selective Laser Melting (SLM) technology has undergone significant development in the past years providing unique flexibility for the fabrication of complex metamaterials such as octet-truss lattices. However, the microstructure can exhibit significant variations due to the high complexity of the manufacturing process. Consequently, the mechanical behavior, in particular, linear elastic response, of these lattices is strongly dependent on the process-induced defects, raising the importance on the incorporation of as-manufactured geometries into the computational structural analysis. This, in turn, challenges the traditional mesh-conforming methods making the computational costs prohibitively large. In the present work, an immersed image-to-analysis framework is applied to efficiently evaluate the bending behavior of AM lattices. To this end, we employ the Finite Cell Method (FCM) to perform a three-dimensional numerical analysis of the three-point bending test of a lattice structure and compare the as-designed to as-manufactured effective properties. Furthermore, we undertake a comprehensive study on the applicability of dimensionally reduced beam models to the prediction of the bending behavior of lattice beams and validate classical and strain gradient beam theories applied in combination with the FCM. The numerical findings suggest that the octet-truss lattices exhibit size effects, thus, requiring a flexible framework to incorporate high-order continuum theories.

We present a reformulation of the classical Timoshenko beam problem, resulting in a single differential equation with the rotation as the only primal variable. We show that this formulation is equivalent to the standard formulation and the same types of boundary conditions apply. Moreover, we develop an isogeometric collocation scheme to solve the problem numerically. The formulation is completely locking-free and involves only half the degrees of freedom compared to a standard formulation. Numerical tests are presented to confirm the performance of the proposed approach. This is the authors' accepted and refereed manuscript to the article. The final publication is available at link.springer.com via http://dx.doi.org/10.1007%2Fs11012-017-0745-7 . Locked until 24 August 2018 due to copyright restrictions

Sixth-order boundary value problems of a one-parameter gradient-elastic Kirchhoff plate model are formulated in a weak form within an H 3 Sobolev space setting with the corresponding equilibrium equations and general boundary conditions. The corresponding conforming Galerkin method is proposed with error estimates for discretizations satisfying C 2 continuity requirements. Continuity, coercivity and consistency of the corresponding bilinear form are utilized for proving the theoretical results. Numerical computations with conforming isogeometric discretizations of C p − 1 -continuous NURBS basis functions of order p ≥ 3 confirm the theoretical results and illustrate the features of the problem for both statics and free vibrations. In particular, the effects of the additional boundary conditions and parameter-dependent boundary layers corresponding to the gradient elasticity theory are addressed by the numerical examples.

This paper focuses on the employment of analysis-suitable T-spline surfaces of arbitrary degree for performing structural analysis of fully nonlinear thin shells. Our aim is to bring closer a seamless and flexible integration of design and analysis for shell structures. The local refinement capability of T-splines together with the Kirchhoff–Love shell discretization, which does not use rotational degrees of freedom, leads to a highly efficient and accurate formulation. Trimmed NURBS surfaces, which are ubiquitous in CAD programs, cannot be directly applied in analysis, however, T-splines can reparameterize these surfaces leading to analysis-suitable untrimmed T-spline representations. We consider various classical nonlinear benchmark problems where the cylindrical and spherical geometries are exactly represented and point loads are accurately captured through local h -refinement. Taking advantage of the higher inter-element continuity of T-splines, smooth stress resultants are plotted without using projection methods. Finally, we construct various trimmed NURBS surfaces with Rhino, an industrial and general-purpose CAD program, convert them to T-spline surfaces, and directly use them in analysis.

In computational hemodynamics we typically need to solve incompressible fluids in domains given by curved pipes or network of pipes. To reduce the computational costs, or conversely to improve models based on a pure 1D (axial) modeling, an approach called “Hierarchical Model reduction” (HiMod) was recently proposed. It consists of a diverse numerical approximation of the axial and of the transverse components of the dynamics. The latter are properly approximated by spectral methods with a few degrees of freedom, while classical finite elements were used for the main dynamics to easily fit any morphology. However affine elements for curved geometries are generally inaccurate. In this paper we conduct a preliminary exploration of IsoGeometric Analysis (IGA) applied to the axial discretization. With this approach, the centerline is approximated by Non Uniform Rational B-Splines (NURBS). The same functions are used to represent the axial component of the solution. In this way we obtain an accurate representation of the centerline as well as of the solution with few axial degrees of freedom. This paper provides preliminary promising results of the combination of HiMod with IGA - referred to as HIGAMod approach - to be applied in any field involving computational fluid dynamics in generic pipe-like domains.

Thoracic endovascular repair (TEVAR) is a minimally invasive alternative to classical open-chest surgery for pathologies of thoracic aorta such as aneurysms or dissections. It consists of the deployment of one or more endografts to either exclude aneurysms pressurization or seal entry tears of dissection. It is a minimally invasive procedure, yet long-term efficacy is still to be demonstrated and analyzed, depending on the geometry and the consequent hemodynamics and remodeling induced by the intervention. In this paper we consider a TEVAR patient by an extensive computational analysis of pre-op, post-op, and one-year follow up data. We focus on both geometrical features like curvature, torsion and area variations, as well as near-wall and intravascular flow-related quantities (i.e., wall shear stress-based descriptors and helicity). Comparison of the different morphologies indicates a partial restoration of normal flow in the region of interest, even though low WSS are still present with the associated risks. Overall, this study demonstrates the efficacy of quantitative computational tools in understanding the long-term impact of TEVAR.

Prostate cancer and benign prostatic hyperplasia are common genitourinary diseases in aging men. Both pathologies may coexist and share numerous similarities, which have suggested several connections or some interplay between them. However, solid evidence confirming their existence is lacking. Recent studies on extensive series of prostatectomy specimens have shown that tumors originating in larger prostates present favorable pathological features. Hence, large prostates may exert a protective effect against prostate cancer. In this work, we propose a mechanical explanation for this phenomenon. The mechanical stress fields that originate as tumors enlarge have been shown to slow down their dynamics. Benign prostatic hyperplasia contributes to these mechanical stress fields, hence further restraining prostate cancer growth. We derived a tissue-scale, patient-specific mechanically coupled mathematical model to qualitatively investigate the mechanical interaction of prostate cancer and benign prostatic hyperplasia. This model was calibrated by studying the deformation caused by each disease independently. Our simulations show that a history of benign prostatic hyperplasia creates mechanical stress fields in the prostate that impede prostatic tumor growth and limit its invasiveness. The technology presented herein may assist physicians in the clinical management of benign prostate hyperplasia and prostate cancer by predicting pathological outcomes on a tissue-scale, patient-specific basis.

This paper analyzes the non-trivial influence of the material anisotropy on the structural behavior of an anisotropic multilayer planar beam. Indeed, analytical results available in literature are limited to homogeneous beams and several aspects has not been addressed yet, impeding an in-depth understanding of the mechanical response of anisotropic structural elements. This paper proposes an effective recovery of stress distribution and an energetically consistent evaluation of constitutive relations to be used within a planar Timoshenko beam model. The resulting structural-analysis tool highlights the following peculiarities of anisotropic beams: (i) the axial stress explicitly depends on transversal internal force, which can weigh up to 30% on the maximal magnitude of axial stress, and (ii) the anisotropy influences the beam displacements more than standard shear deformation and even for extremely slender beams. A rigorous comparison with analytical and accurate 2D Finite Element solutions confirms the accuracy of the proposed approach that leads to errors exceptionally greater than 5%.

A novel approach which combines isogeometric collocation and an equilibrium-based stress recovery technique is applied to analyze laminated composite plates. Isogeometric collocation is an appealing strong form alternative to standard Galerkin approaches, able to achieve high order convergence rates coupled with a significantly reduced computational cost. Laminated composite plates are herein conveniently modeled considering only one element through the thickness with homogenized material properties. This guarantees accurate results in terms of displacements and in-plane stress components. To recover an accurate out-of-plane stress state, equilibrium is imposed in strong form as a post-processing correction step, which requires the shape functions to be highly continuous. This continuity demand is fully granted by isogeometric analysis properties, and excellent results are obtained using a minimal number of collocation points per direction, particularly for increasing values of length-to-thickness plate ratio and number of layers.

We present an example-based exposition and review of recent advances in symbol-based spectral analysis. We consider constant- and variable-coefficient, second-order eigenvalue problems discretized through the (isogeometric) Galerkin method based on B-splines of degree p and smoothness For each discretized problem, we compute the so-called symbol, which is a function describing the asymptotic singular value and eigenvalue distribution of the associated discretization matrices. Using the symbol, we are able to formulate analytical predictions for the eigenvalue errors occurring when the exact eigenvalues are approximated by the numerical eigenvalues. In this way, we recover and extend previous analytical spectral results. We are also able to predict the existence of p-"optical", when discretizing the one-dimensional Laplacian eigenvalue problem. We provide explicit and implicit analytical expressions for these branches, and we quantify the divergence to infinity with respect to p of the largest optical branch in the case of smoothness (the case of classical finite element analysis).

Chemotherapy is a common treatment for advanced prostate cancer. The standard approach relies on cytotoxic drugs, which aim at inhibiting proliferation and promoting cell death. Advanced prostatic tumors are known to rely on angiogenesis, i.e. the growth of local microvasculature via chemical signaling produced by the tumor. Thus, several clinical studies have been investigating antiangiogenic therapy for advanced prostate cancer, either as monotherapy or in combination with standard cytotoxic protocols. However, the complex genetic alterations that originate and sustain prostate cancer growth complicate the selection of the best chemotherapeutic approach for each patient’s tumor. Here, we present a mathematical model of prostate cancer growth and chemotherapy that may enable physicians to test and design personalized chemotherapeutic protocols in silico. We use the phase-field method to describe tumor growth, which we assume to be driven by a generic nutrient following reaction–diffusion dynamics. Tumor proliferation and apoptosis (i.e. programmed cell death) can be parameterized with experimentally-determined values. Cytotoxic chemotherapy is included as a term downregulating tumor net proliferation, while antiangiogenic therapy is modeled as a reduction in intratumoral nutrient supply. An additional equation couples the tumor phase field with the production of prostate-specific antigen, which is a prostate cancer biomarker that is extensively used in the clinical management of the disease. We prove the well posedness of our model and we run a series of representative simulations leveraging an isogeometric method to explore untreated tumor growth as well as the effects of cytotoxic chemotherapy and antiangiogenic therapy, both alone and combined. Our simulations show that our model captures the growth morphologies of prostate cancer as well as common outcomes of cytotoxic and antiangiogenic mono therapy and combined therapy. Additionally, our model also reproduces the usual temporal trends in tumor volume and prostate-specific antigen evolution observed in experimental and clinical studies.

In the present work we introduce a complete set of algorithms to efficiently perform adaptive refinement and coarsening by exploiting truncated hierarchical B-splines (THB-splines) defined on suitably graded isogeometric meshes, that are called admissible mesh configurations. We apply the proposed algorithms to two-dimensional linear heat transfer problems with localized moving heat source, as simplified models for additive manufacturing applications. We first verify the accuracy of the admissible adaptive scheme with respect to an overkilled solution, for then comparing our results with similar schemes which consider different refinement and coarsening algorithms, with or without taking into account grading parameters. This study shows that the THB-spline admissible solution delivers an optimal discretization for what concerns not only the accuracy of the approximation, but also the (reduced) number of degrees of freedom per time step. In the last example we investigate the capability of the algorithms to approximate the thermal history of the problem for a more complicated source path. The comparison with uniform and non-admissible hierarchical meshes demonstrates that also in this case our adaptive scheme returns the desired accuracy while strongly improving the computational efficiency., 20 pages, 12 figures

The Modified Finite Particle Method (MFPM) is a meshless method belonging to the class of meshless method. Given the absence of a pre-determined connectivity among nodes, such methods are mainly used in applications where large deformations are involved, such as fluid-dynamics. In the present work we combine the Modified Finite Particle Method with a Weighted Least Square Residual Method, and use the combined version of the method for the solution of saddle point problems, such as the Stokes and Navier–Stokes equations for incompressible fluid flow simulations. The use of MFPM derivative approximation techniques in the framework of Least Square Residual Method permits a simple handling of the numerical difficulties typical of incompressible fluid simulations, avoiding problems such as pressure spurious oscillations, and preserving the convergence properties of the Modified Finite Particle Method also in presence of random collocation point distributions.

The present paper investigates the use of different knot placement techniques for isogeometric analysis of spatial curved beams, to enhance analysis results in cases when geometries are given in terms of data points. Focusing on analysis-aware modeling for structural static and vibration simulations of spatial free-form curved beams, the knot placement techniques based on uniformly spaced knots as well as on De Boor’s and Piegl and Tiller’s algorithms are studied. For this purpose, an isogeometric formulation for linear Euler–Bernoulli beams based on the Euler–Rodriguez transformation rule is implemented. Different case studies and numerical examples are presented and the results are validated against “overkill” solutions computed with a commercial finite element software. The results show that the De Boor’s knot placement algorithm typically leads to better approximation errors and is therefore the suggested strategy for this kind of problems.

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.

In the last decades, biomechanical computer models have been increasingly adopted in the cardiovascular field either to improve the knowledge of pathological conditions or to anticipate possible outcomes of therapeutic interventions in specific patients. The present chapter stems from this new paradigm, also known as predictive medicine, and aims at presenting the state of the art of computer-based simulations for transcatheter aortic valve implantation (TAVI). We show how numerical analyses may be used to predict possible complications after TAVI with the aim of supporting the operation planning procedure and help heart surgeons choose the optimal strategy (i.e., that providing the best possible performance) for a given patient. Both balloon-expandable and self-expandable devices are taken into consideration and the predictive ability of computer simulations is highlighted for real clinical cases.

We present an early version of a Susceptible–Exposed–Infected–Recovered–Deceased (SEIRD) mathematical model based on partial differential equations coupled with a heterogeneous diffusion model. The model describes the spatio-temporal spread of the COVID-19 pandemic, and aims to capture dynamics also based on human habits and geographical features. To test the model, we compare the outputs generated by a finite-element solver with measured data over the Italian region of Lombardy, which has been heavily impacted by this crisis between February and April 2020. Our results show a strong qualitative agreement between the simulated forecast of the spatio-temporal COVID-19 spread in Lombardy and epidemiological data collected at the municipality level. Additional simulations exploring alternative scenarios for the relaxation of lockdown restrictions suggest that reopening strategies should account for local population densities and the specific dynamics of the contagion. Thus, we argue that data-driven simulations of our model could ultimately inform health authorities to design effective pandemic-arresting measures and anticipate the geographical allocation of crucial medical resources.

The capability of correctly predicting part deflections after support removal is important to assess the quality of a final artifact produced by laser powder bed fusion (LPBF) technology. The finite element method is usually employed to perform part-scale thermo-mechanical analysis to estimate the final distortion of 3D printed parts. Due to the high flexibility of LPBF additive manufacturing, most of the components produced by means of such a technology have an optimized shape and complex geometrical features. Consequently, the process of generating an analysis suitable mesh starting from the original 3D virtual model turns out to be a non-trivial task. Immersed boundary methods represent a possible solution to perform accurate process simulation without the meshing burden. In this work, an immersed numerical framework to perform thermo-mechanical part-scale analysis is experimentally validated by means of part deflection measurements obtained for a single-cantilever structure after support removal. The comparison between simulation and experiment shows that the proposed numerical framework is able to deliver results with an almost perfect correlation to the measured data and a maximum relative error below 5%.

Prosthesis positioning in transcatheter aortic valve implantation procedures represents a crucial aspect for procedure success as demonstrated by many recent studies on this topic. Possible complications, device performance, and, consequently, also long-term durability are highly affected by the adopted prosthesis placement strategy. In the present work, we develop a computational finite element model able to predict device-specific and patient-specific replacement procedure outcomes, which may help medical operators to plan and choose the optimal implantation strategy. We focus in particular on the effects of prosthesis implantation depth and release angle. We start from a real clinical case undergoing Corevalve self-expanding device implantation. Our study confirms the crucial role of positioning in determining valve anchoring, replacement failure due to intra or para-valvular regurgitation, and post-operative device deformation.

In the last 20 years, a new approach has emerged to investigate the physiopathology of circulation. By merging medical images with validated numerical models, it is possible to support doctors’ decision-making process. The iCardioCloud project aims at establishing a computational framework to perform a complete patient-specific numerical analysis, specially oriented to aortic diseases (like dissections or aneurysms) and to deliver a compelling synthesis. The project can be considered a pioneering example of a Computer Aided Clinical Trial: i.e., a comprehensive analysis of patients where the level of knowledge extracted by traditional measures and statistics is enhanced through the massive use of numerical modeling. From a computer engineering point of view, iCardioCloud faces multiple challenges. First, the number of problems to solve for each patient is significantly huge – this is typical of computational fluid dynamics (CFD) – and it requires parallel methods. In addition, working in a clinical environment demands efficiency as the timeline requires rapid quantitative answers (as may happen in an emergency scenario). It is therefore mandatory to employ high-end parallel systems, such as large clusters or supercomputers. Here we discuss a parallel implementation of an application within the iCardioCloud project, built with a black-box approach – i.e., by assembling and configuring existing packages and libraries and in particular LifeV, a finite element library developed to solve CFD problems. The goal of this paper is to describe the software architecture underlying LifeV and to assess its performance and the most appropriate parallel paradigm. This paper is an extension of a previous work presented at the PBio 2015 Conference. This revision extends the description of the software architecture and discusses several new serial and parallel optimizations to the application. We discuss the introduction of hybrid parallelism in order to mitigate some performance problems previously experienced.

This paper deals with the use of analysis-suitable T-splines of arbitrary degree in combination with isogeometric collocation methods for the solution of second- and fourth-order boundary-value problems. In fact, analysis-suitable T-splines appear to be a particularly efficient locally refinable basis for isogeometric collocation, able to conserve the cost of only one point evaluation per degree of freedom typical of standard NURBS-based isogeometric collocation. Furthermore, T-splines allow to easily create highly non-uniform meshes without introducing elements with high aspect ratios; this makes it possible to avoid the numerical instabilities that may arise in the case of problems characterized by reduced regularity when Neumann boundary conditions are imposed in strong form and elements with high aspect ratio are used. The local refinement properties of T-splines can be also successfully exploited to approximate problems where point loads are applied. Finally, several numerical tests are herein presented in order to confirm all the above-mentioned features, as well as the good overall convergence properties of the combination of isogeometric collocation and analysis-suitable T-splines.

We investigate the variational structure of a phenomenological model for the coupled thermomechanical behavior of shape-memory polycrystalline materials. The nonisothermal evolution of the medium is reformulated as a generalized gradient flow of the entropy with respect to an entropy-production potential. Based on this reformulation, a semi-implicit time-discretization of the fully coupled thermomechanical problem is presented and proved to be unconditionally stable and convergent. The flexibility and robustness of the numerical method is assessed via both uniaxial and multiaxial computational tests.

We apply an “immersed” finite element approach discussed in [1] for the 2D steady incompressible Stokes equations to a 2D fluid-structure interaction problem in a tube with a thin (i.e., codimension 1) hinged rigid leaflet sets in motion by an incompressible unsteady flow. In order to change the minimal possible fraction of elements we remesh only the triangles that are cut by the structure. Furthermore, with this approach essential constraints between the fluid and the solid may be strongly enforced in the finite element spaces and it is fairly easy to allow the fluid stress to be discontinuous across the structure. An obvious consequence of the proposed remeshing strategy is the presence of anisotropic triangles, for which it is known that the standard finite element method may be used (see, e.g., [2]). However, for mixed elements most of the inf-sup stability proofs require isotropic meshes and only few results are available on distorted triangles. In [1], the inf-sup stability of the Hood-Taylor element with the present method has been discussed. It was shown that instabilities may occur but also that adding a bubble in the velocity space stabilizes the element. In the present work we apply and extend the results presented in [1] to a 2D fluid-structure problem with a codimension 1 structure immersed in the fluid domain. As a consequence, it may be convenient to use mixed elements with a discontinuous pressure. Indeed, with such elements the discontinuity in the pressure field across the structure is straightforwardly enforced. We discuss the use of the P2/P0 and the P2-bubble/P1-discontinuous elements with the proposed remeshing algorithm. However, we also consider the elements in [1] with a discontinuous pressure is across the structure. Numerical tests show that the two elements with a discontinuous pressure suffer inf-sup stability issues in a more severe way than the Hood-Taylor element. The P2/P0 and P2-bubble/P1-discontinuous elements show spurious modes along the structure, and thus not only in corners as in the case of the Hood-Taylor element. On the contrary, the Hood-Taylor element with an additional bubble do not show any spurious modes in the performed tests. The deleterious effects of inf-sup instabilities are also observed in the conditioning of the linear system. Furthermore, in [3] a similar fluid-structure interaction algorithm to the one presented here is employed using the P2-bubble/P1-discontinuous element. However, a smoothing strategy is used such that all triangles are isotropic. Our results show in particular the necessity of such a smoothing with that element.

Due to broad usage of anisotropic composite beams in modern engineering structures, the main goal of the present work is to examine their geometrically nonlinear vibration. To this end, a third–order shear deformation theory with a nonlinear von-Karman strain field is used for anisotropic beams and combined with the advantages of the isogeometric framework. The layup properties are assumed to be anisotropic in the depth direction and a transient tip follower force is considered. The governing nonlinear equations of vibration are integrated by means of the Newmark approach and solved with the Newton-Raphson method. Flutter loads as well as natural frequencies are obtained by eigenvalue analysis. The effects of various important factors such as non-prismatic shape, orientation of the composite fibers, critical follower force and bifurcation point are studied, using both h- and p-refinements. The results show that the nonlinear vibration and flutter characteristics of the anisotropic composite beams are completely different from those for orthotropic and isotropic ones. Thick beams with anisotropic layups are more sensitive to the shear parameter than conventional ones and deform primarily in shear mode rather than in bending. Anisotropic beams reveal a higher flutter instability force than other cases for a given shear parameter value. Another important phenomenon is that the stress distribution in anisotropic layups shows irregular patterns both in depth and time. Anisotropic layups with ply angles between 15 ∘ and 45 ∘ seem to present enhanced nonlinear performance with respect to other layup choices. A coarse mesh of quartic C 3 B-splines is observed to provide high accuracy for nonlinear deflections in anisotropic cases even for rather low shear parameters.

Isogeometric Kirchhoff–Love elements have been receiving increasing attention in geometrically nonlinear analysis of thin shells because they make it possible to meet the C 1 requirement in the interior of surface patches and to avoid the use of finite rotations. However, engineering structures of appreciable complexity are typically modeled using multiple patches and, often, neither rotational continuity nor conforming discretization can be practically obtained at patch interfaces. Simple penalty approaches for coupling adjacent patches, applicable to either smooth or non-smooth interfaces and either matching or non-matching discretizations, have been proposed. Although the problem dependence of the penalty coefficient can be reduced by scaling factors which take into account geometrical and material parameters, only high values of the penalty coefficient can guarantee a negligible coupling error in all possible cases. However, this can lead to an ill conditioned problem and to an increasing iterative effort for solving the nonlinear discrete equations. In this work, we show how to avoid this drawback by rewriting the penalty terms in an Hellinger–Reissner form, introducing independent fields work-conjugated to the coupling equations. This technique avoids convergence problems, making the analysis robust also for very high values of the penalty coefficient, which can be then employed to avert coupling errors. Moreover, a proper choice of the basis functions for the new fields provides an accurate coupling also for general non-matching cases, preventing overconstrained solutions. The additional variables are condensed out and then not involved in the global system of equations to be solved. A highly efficient approach based on a mixed integration point strategy and an interface-wise reduced integration rule makes the condensation inexpensive preserving the sparsity of the condensed stiffness matrix and the coupling accuracy.

We propose a mixed stress-displacement isogeometric collocation method for nearly incompressible elastic materials and for materials exhibiting von Mises plasticity. The discretization is based on isogeometric analysis (IGA) with non-uniform rational B-Splines (NURBS) as basis functions. As compared to conventional IGA Galerkin formulations, isogeometric collocation methods offer a high potential of computational cost reduction for higher-order discretizations as they eliminate the need for quadrature. In the proposed mixed formulation, both stress and displacement fields are approximated as primary variables with the aim of treating volumetric locking and instability issues, which occur in displacement-based isogeometric collocation for nearly incompressible elasticity and von Mises plasticity. The performance of the proposed approach is demonstrated by several numerical examples.

According to the American Cancer Society, prostate cancer (PCa) is the most common newly-diagnosed cancer and the second leading cancer-related cause of death among men in the US in 2019. The current clinical protocols of PCa are based on two key strategies: regular screening of men over fifty and patient triaging in risk groups. Prostatic tumors are usually detected at an early organ-confined stage, which poses a low to intermediate risk to the patient and may not produce any symptoms or require treatment for long time. However, most patients are prescribed a radical treatment immediately after diagnosis (e.g., surgery or radiation therapy), which may adversely impact their lives without necessarily prolonging their longevity or quality of life. Moreover, some patients who initially delay their treatment ultimately succumb to PCa due to an inaccurate initial diagnosis. Thus, while regular screening enables the detection of the majority of tumors at an early and mild stage, the limited individualization of patient monitoring and treatment has led to significant rates of both overtreatment and undertreatment. To overcome these fundamental limitations in the clinical management of PCa, we propose the use of a mechanistic mathematical model for which we can perform computer simulations to forecast patient-specific tumor growth. This computational model is based on a set of partial differential equations that describe the main mechanisms involved in organ-confined PCa growth. The model is parameterized using longitudinal multiparametric magnetic resonance (MR) images and the available clinical data for each patient. Tumor growth is simulated over the patient's prostate extracted from T2-weighted MR images. We use isogeometric analysis to accurately and efficiently address the computational challenges arising in this application. Our preliminary simulation results show that our computational technology can predict tumor growth and associated serum Prostate Specific Antigen (PSA, a key biomarker in clinical management of PCa) with reasonable accuracy. We also explore the potential of model parameters and variables to characterize tumor aggressivity. Thus, we believe that our imaging-based modeling approach could be a promising tool capable of being implemented in current PCa protocols to assist physicians in the clinical management of PCa. Citation Format: Guillermo Lorenzo, Thomas J. Hughes, Alessandro Reali, Hector Gomez, Thomas E. Yankeelov. An image-based mechanistic computational model for early prediction of organ-confined untreated prostate cancer growth [abstract]. In: Proceedings of the Annual Meeting of the American Association for Cancer Research 2020; 2020 Apr 27-28 and Jun 22-24. Philadelphia (PA): AACR; Cancer Res 2020;80(16 Suppl):Abstract nr 5483.

The main motivation for hierarchical B-Splines in Isogeometric Analysis is to perform a local refinement that is globally not a tensor product. Compared to standard knot insertion, this allows to increase refinement locality. Moreover, the implementation of hierarchical refinement on existing codes can be facilitated by Bezier extraction. This approach was initially developed for unrefined patches and then extended to local refinement. In case of B-Spline patches that are not locally refined, extraction and projection algorithms can be optimized by leveraging the tensor structure. However, these optimizations are not straightforwardly applicable to hierarchical B-Splines. In this contribution, we show an approach where all extraction operations are formulated to work directly on the univariate extraction operators, without explicitly computing and storing the full tensor product. In particular, we consider the extraction of functions, and projection of degrees of freedom for refinement and coarsening. A slightly modified Bezier projection is proposed to fully exploit the developed algorithms. We finally compare our approach to an explicit computation of the extraction operator in both a linear transient and a nonlinear example.

A computational framework is designed to accurately predict the elastic response of thin shells undergoing large displacements induced by local hydrodynamic forces, as well as to resolve the complex fluid pattern arising from its interaction with an incompressible fluid. Within the context of partitioned algorithms, two different approaches are employed for the fluid and structural domain. The fluid motion is resolved with a pressure projection method on a Cartesian structured grid. The immersed shell is modeled by means of a NURBS surface, and the elastic response is obtained from a displacement-based isogeometric analysis relying on the Kirchhoff–Love theory. The two solvers exchange data through a direct-forcing immersed-boundary approach, where the interpolation/spreading of the variables between Lagrangian and Eulerian grids is implemented with a Moving Least Squares approximation, which has proven to be very effective for moving boundaries. In this scenario, the isoparametric paradigm is exploited to perform an adaptive collocation of the Lagrangian markers, decoupling the local grid density of fluid and shell domains and reducing the computational expense. The accuracy of the method is verified by refinement analyses, segregating the Eulerian/Lagrangian refinement, which confirm the expected scheme accuracy in space and time. The effectiveness of the method is then validated against different test-cases of engineering and biologic inspiration, involving fundamentally different physical and numerical conditions, namely: (i) a flapping flag, (ii) an inverted flag, (iii) a clamped plate, (iv) a buoyant seaweed in a free stream. Both strong and loose coupling approaches are implemented to handle different fluid-to-structure density ratios, providing accurate results.

5 α -reductase inhibitors are regarded as a promising chemoprevention strategy to reduce the incidence and delay the progression of prostate cancer. Landmark clinical trials have shown the chemopreventive potential of these drugs, but they appear to be mostly effective in mild tumors and have also been correlated with a higher prevalence of advanced prostate cancer. Hence, the use of 5 α -reductase inhibitors for prostate cancer chemoprevention has become a controversial issue. The effects of these drugs on prostate cancer growth remain incompletely understood, but they are thought to promote apoptosis in the tumor. Additionally, 5 α -reductase inhibitors induce global prostate shrinkage, which decreases the tumor-inhibiting effect of the mechanical stress accumulated in prostatic tissue due to common prostate enlargement with age. Thus, the competition between this mechanical effect and apoptotic upregulation may explain the controversial outcomes of 5 α -reductase inhibitors on prostate cancer. Here, we extend our mechanically-coupled model of prostate cancer growth by including the mechanical and apoptotic action of 5 α -reductase inhibitors and explore their combined effect on an aggressive tumor in silico. Our simulations show that the apoptotic boost dominates in the first months of therapy but the long-term outcome of 5 α -reductase inhibitors depends on its competition with a decrease in hydrostatic stress caused by prostate shrinkage, which favors tumor growth. By combining moderate or strong prostate shrinkage with mild or intense apoptotic upregulation, our simulations show different tumor growth dynamics ranging from long-term inhibition of prostate cancer growth to rapidly growing large tumors, which may evolve towards advanced disease. Thus, our proposed mechanism for the action of 5 α -reductase inhibitors may contribute to resolve the controversy around the use of these drugs for chemoprevention and to gain insight on prostate cancer dynamics during its use. The computational technology used herein could also assist physicians to monitor prostatic tumors during 5 α -reductase inhibitor therapy and enable the early identification of responders from non-responders in a patient-specific manner.

In the present work we introduce a novel graded-material design based on phase-field and topology optimization. The main novelty of this work comes from the introduction of an additional phase-field variable in the classical single-material phase-field topology optimization algorithm. This new variable is used to grade the material properties in a continuous fashion. Two different numerical examples are discussed, in both of them, we perform sensitivity studies to asses the effects of different model parameters onto the resulting structure. From the presented results we can observe that the proposed algorithm adds additional freedom in the design, exploiting the higher flexibility coming from additive manufacturing technology.

The introduction of computational models in cardiovascular sciences has been progressively bringing new and unique tools for the investigation of the physiopathology. Together with the dramatic improvement of imaging and measuring devices on one side, and of computational architectures on the other one, mathematical and numerical models have provided a new, clearly noninvasive, approach for understanding not only basic mechanisms but also patient-specific conditions, and for supporting the design and the development of new therapeutic options. The terminology in silico is, nowadays, commonly accepted for indicating this new source of knowledge added to traditional in vitro and in vivo investigations. The advantages of in silico methodologies are basically the low cost in terms of infrastructures and facilities, the reduced invasiveness and, in general, the intrinsic predictive capabilities based on the use of mathematical models. The disadvantages are generally identified in the distance between the real cases and their virtual counterpart required by the conceptual modeling that can be detrimental for the reliability of numerical simulations.

The continuous technological improvements of medical instruments and devices make minimally-invasive approaches a real and valid alternative to standard open surgery in more and more cases. Recent developments in cardiovascular surgery, in particular, have led to the success of thoracic endovascular repair (TEVAR) and transcatheter aortic valve implantation (TAVI). If, on the one hand, minimally-invasive interventions induce shorter hospital stays, faster recovery, and thus reduced costs, on the other hand, since, for obvious reasons, the direct control of the operator on the procedure is much more limited, operation planning and decision-making steps cover a crucial importance. In this context, computational tools have demonstrated to play a remarkable role, providing the surgeon with predictive information regarding the potential optimality of the treatment strategy. In the present chapter, we aim at describing recent developments of TEVAR and TAVI modeling, from both the structural and fluid-dynamic point of view.