We present formulations for compressible and incompressible hyperelastic thin shells which can use general 3D constitutive models. The necessary plane stress condition is enforced analytically for ...incompressible materials and iteratively for compressible materials. The thickness stretch is statically condensed and the shell kinematics are completely described by the first and second fundamental forms of the midsurface. We use C1-continuous isogeometric discretizations to build the numerical models. Numerical tests, including structural dynamics simulations of a bioprosthetic heart valve, show the good performance and applicability of the presented methods.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UL, UM, UPCLJ, UPUK
The interaction between thin structures and incompressible Newtonian fluids is ubiquitous both in nature and in industrial applications. In this paper we present an isogeometric formulation of such ...problems which exploits a boundary integral formulation of Stokes equations to model the surrounding flow, and a non linear Kirchhoff–Love shell theory to model the elastic behavior of the structure. We propose three different coupling strategies: a monolithic, fully implicit coupling, a staggered, elasticity driven coupling, and a novel semi-implicit coupling, where the effect of the surrounding flow is incorporated in the non-linear terms of the solid solver through its damping characteristics. The novel semi-implicit approach is then used to demonstrate the power and robustness of our method, which fits ideally in the isogeometric paradigm, by exploiting only the boundary representation (B-Rep) of the thin structure middle surface.
•We present an isogeometric FSI approach by combining fluid-BEM and shell analysis.•We assume Stokes flow and a large deformation shell model.•Both fluid and solid domain are fully described by the CAD model of the structure.•A semi-implicit solution algorithm combines high accuracy and stability with cost-efficiency.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UL, UM, UPCLJ, UPUK
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-Kármán 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 C3 B-splines is observed to provide high accuracy for nonlinear deflections in anisotropic cases even for rather low shear parameters.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
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.
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DOBA, EMUNI, FIS, FZAB, GEOZS, GIS, IJS, IMTLJ, IZUM, KILJ, KISLJ, MFDPS, NLZOH, NUK, OBVAL, OILJ, PILJ, PNG, SAZU, SBCE, SBJE, SBMB, SBNM, UILJ, UKNU, UL, UM, UPUK, VKSCE, ZAGLJ
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 shear and membrane 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 in terms of displacements and stresses. The main advantages of the presented approach compared to existing solid shell formulations are its simplicity and numerical efficiency.
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DOBA, EMUNI, FIS, FZAB, GEOZS, GIS, IJS, IMTLJ, IZUM, KILJ, KISLJ, MFDPS, NLZOH, NUK, OBVAL, OILJ, PILJ, PNG, SAZU, SBCE, SBJE, SBMB, SBNM, UILJ, UKNU, UL, UM, UPUK, VKSCE, ZAGLJ
We propose a variational principle combining a phase-field functional for structural topology optimization with a mixed (three-field) Hu–Washizu functional, then including directly in the formulation ...equilibrium, constitutive, and compatibility equations. The resulting mixed variational functional is then specialized to derive a classical topology optimization formulation (where the amount of material to be distributed is an a priori assigned quantity acting as a global constraint for the problem) as well as a novel topology optimization formulation (where the amount of material to be distributed is minimized, hence with no pre-imposed constraint for the problem). Both formulations are numerically solved by implementing a mixed finite element scheme, with the second approach avoiding the introduction of a global constraint, hence respecting the convenient local nature of the finite element discretization. Furthermore, within the proposed approach it is possible to obtain guidelines for settings proper values of phase-field-related simulation parameters and, thanks to the combined phase-field and Hu–Washizu rationale, a monolithic algorithm solution scheme can be easily adopted. An insightful and extensive numerical investigation results in a detailed convergence study and a discussion on the obtained final designs. The numerical results clearly highlight differences between the two formulations as well as advantages related to the monolithic solution strategy; numerical investigations address both two-dimensional and three-dimensional applications.
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EMUNI, FIS, FZAB, GEOZS, GIS, IJS, IMTLJ, KILJ, KISLJ, MFDPS, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, SBMB, SBNM, UKNU, UL, UM, UPUK, VKSCE, ZAGLJ
Numerous studies have suggested that medical image derived computational mechanics models could be developed to reduce mortality and morbidity due to cardiovascular diseases by allowing for ...patient‐specific surgical planning and customized medical device design. In this work, we present a novel framework for designing prosthetic heart valves using a parametric design platform and immersogeometric fluid–structure interaction (FSI) analysis. We parameterize the leaflet geometry using several key design parameters. This allows for generating various perturbations of the leaflet design for the patient‐specific aortic root reconstructed from the medical image data. Each design is analyzed using our hybrid arbitrary Lagrangian–Eulerian/immersogeometric FSI methodology, which allows us to efficiently simulate the coupling of the deforming aortic root, the parametrically designed prosthetic valves, and the surrounding blood flow under physiological conditions. A parametric study is performed to investigate the influence of the geometry on heart valve performance, indicated by the effective orifice area and the coaptation area. Finally, the FSI simulation result of a design that balances effective orifice area and coaptation area reasonably well is compared with patient‐specific phase contrast magnetic resonance imaging data to demonstrate the qualitative similarity of the flow patterns in the ascending aorta.
In this work, we present a framework for designing patient‐specific prosthetic heart valves using parametric design and immersogeometric fluid–structure interaction (FSI) analysis. Leaflet geometry is generated from several design parameters, while conforming to a medical image derived aortic root geometry at the attached edge. Each design is analyzed using our immersogeometric FSI methodology. A parametric study investigates the influence of geometry on valve performance. Simulation results are compared with phase contrast magnetic resonance imaging data.
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FZAB, GIS, IJS, IZUM, KILJ, NLZOH, NUK, OILJ, PILJ, PNG, SAZU, SBCE, SBMB, UL, UM, UPUK
The outbreak of COVID-19 in 2020 has led to a surge in interest in the mathematical modeling of infectious diseases. Such models are usually defined as compartmental models, in which the population ...under study is divided into compartments based on qualitative characteristics, with different assumptions about the nature and rate of transfer across compartments. Though most commonly formulated as ordinary differential equation models, in which the compartments depend only on time, recent works have also focused on partial differential equation (PDE) models, incorporating the variation of an epidemic in space. Such research on PDE models within a Susceptible, Infected, Exposed, Recovered, and Deceased framework has led to promising results in reproducing COVID-19 contagion dynamics. In this paper, we assess the robustness of this modeling framework by considering different geometries over more extended periods than in other similar studies. We first validate our code by reproducing previously shown results for Lombardy, Italy. We then focus on the U.S. state of Georgia and on the Brazilian state of Rio de Janeiro, one of the most impacted areas in the world. Our results show good agreement with real-world epidemiological data in both time and space for all regions across major areas and across three different continents, suggesting that the modeling approach is both valid and robust.
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EMUNI, FIS, FZAB, GEOZS, GIS, IJS, IMTLJ, KILJ, KISLJ, MFDPS, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, SBMB, SBNM, UKNU, UL, UM, UPUK, VKSCE, ZAGLJ
In this paper, IGA collocation methods are for the first time introduced for the solution of thin structural problems described by the Bernoulli–Euler beam and Kirchhoff plate models. In particular, ...a precise description of the proposed methods, of the relevant implementation details, and of the strategy to efficiently deal with different combinations of boundary conditions is given. Finally, several numerical experiments confirm that the proposed formulations represent an efficient and geometrically flexible tool for the simulation of thin structures.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UL, UM, UPCLJ, UPUK
Modeling multiscale mechanics in shape-shifting engineered tissues, such as organoids and organs-on-chip, is both important and challenging. In fact, it is difficult to model relevant tissue-level ...large non-linear deformations mediated by discrete cell-level behaviors, such as migration and proliferation. One approach to solve this problem is subcellular element modeling (SEM), where ensembles of coarse-grained particles interacting via empirically defined potentials are used to model individual cells while preserving cell rheology. However, an explicit treatment of multiscale mechanics in SEM was missing. Here, we incorporated analyses and visualizations of particle level stress and strain in the open-source software SEM++ to create a new framework that we call subcellular element modeling and mechanics or SEM2. To demonstrate SEM2, we provide a detailed mechanics treatment of classical SEM simulations including single-cell creep, migration, and proliferation. We also introduce an additional force to control nuclear positioning during migration and proliferation. Finally, we show how SEM2 can be used to model proliferation in engineered cell culture platforms such as organoids and organs-on-chip. For every scenario, we present the analysis of cell emergent behaviors as offered by SEM++ and examples of stress or strain distributions that are possible with SEM2. Throughout the study, we only used first-principles literature values or parametric studies, so we left to the Discussion a qualitative comparison of our insights with recently published results. The code for SEM2 is available on GitHub at https://github.com/Synthetic-Physiology-Lab/sem2.
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