Yuri Bazilevs

University of California, San Diego | UCSD · Department of Structural Engineering

We develop a computational framework to model damage and delamination in laminated polymer composite structures incorporating the effects of temperature and moisture content. The framework is founded on a recently developed comprehensive multi-layer thin-shell formulation based on Isogeometric Analysis, which includes continuum damage, plasticity a...

A smoothed naturally stabilized conforming nodal integration (S-NSNI) for the reproducing kernel particle method (RKPM) is proposed for non-linear explicit dynamics. The Taylor series expansion of the nodal strains in the solid variational formulation is employed, which introduces stabilization by enriching the energy of the originally underintegra...

In recent years, architected materials and structures have gained significant popularity due to their ability to reach enhanced performance for use in multifunctional and multidisciplinary applications. Among numerous options investigated, architected structures based on Triply Periodic Minimal Surfaces (TPMS) have gained increasing attention becau...

This contribution is comprised of two parts. In the first part we provide an overview of the Dynamically Data-Driven Applications Systems (DDDAS) concept, with particular emphasis on the analytics of systems coming from the field of Applied Mechanics and focusing on the applications to aerospace structures. Aerospace composite materials and structu...

In this paper, we lay out a variational framework for correspondence‐based peridynamic (PD) formulations of solid mechanics. Using the framework, we address the numerical instabilities of the original version of correspondence‐based PD by developing a natural stabilization technique that avoids costly bond‐associated approaches and retains the stru...

Many aerospace applications involve complex multiphysics in compressible flow regimes that are challenging to model and analyze. Fluid–structure interaction (FSI) simulations offer a promising approach to effectively examine these complex systems. In this work, a fully coupled FSI formulation for compressible flows is summarized. The formulation is...

We present an isogeometric analysis (IGA) framework for structural vibrations involving complex geometries. The framework is based on the Complex-Geometry IGA Mesh Generation (CGIMG) method. The CGIMG process is flexible and can accommodate, without a major effort, challenging complex-geometry applications in computational mechanics. To demonstrate...

A smooth Crack Band Model (sCBM) is developed for anisotropic materials with both high and low magnitude of anisotropy. sCBM is primarily used as a regularization mechanism to enable capturing the correct size and shape of the fracture process zone (FPZ) as well as the smooth distribution of strain inside the zone. The versatility of the proposed s...

Flows with moving boundaries and interfaces (MBI) is a large class of problems that includes fluid-particle and fluid-structure interactions, and in broader terms, moving solid surfaces. It also includes multi-fluid flows, and as a special case of that, free-surface flows, sometimes in combination with moving solid surfaces. In some classes of MBI...

In this chapter, we present a workflow for Isogeometric Analysis (IGA) that incorporates an advanced mesh generation method Otoguro et al. (Comput Fluids 158:189–200, 2017). The process is flexible and can be easily adjusted to accommodate challenging applications in computational mechanics. In addition, IGA is compared to the finite element (FE) m...

Recent optimum fitting of the data from eleven different types of distinctive fracture tests of quasibrittle materials, including the gap tests and the size effect tests, revealed that the crack band model (CBM) with the M7 damage constitutive law outperforms all the other existing computational fracture models for concrete. This is attributed to p...

We study the drag on a centimetric sphere in a uniform flow in the presence of a free surface as a function of submergence depth. Through direct force measurements in a custom benchtop recirculating flume, we demonstrate that the drag can significantly exceed the corresponding drag in a single-phase flow and achieves a peak at submergence depths ju...

This work focuses on the heat flux prediction in hypersonic flow regimes using the finite-element based Streamline-Upwind Petrov–Galerkin formulation enhanced with a discontinuity-capturing operator and weak enforcement of the Dirichlet boundary condition. The numerical formulation is validated on several benchmark cases including Mach 14 compressi...

We present a novel formulation based on an immersed coupling of Isogeometric Analysis (IGA) and Peridynamics (PD) for the simulation of fluid–structure interaction (FSI) phenomena for air blast. We aim to develop a practical computational framework that is capable of capturing the mechanics of air blast coupled to solids and structures that undergo...

Modeling of structural damage, fracture, and disintegration into fragments due to blast loads, is a fluid–structure interaction (FSI) problem of great significance due to its relevance to national security and defense applications. However, its numerical modeling remains challenging due to the presence of underlying complex physics, such as high Ma...

We study the drag on a centimetric sphere in a uniform flow in the presence of a free surface as a function of submergence depth. Through direct force measurements in a custom benchtop recirculating flume, we demonstrate that the drag can significantly exceed the corresponding drag in a single-phase flow and achieves a peak at submergence depths ju...

We present a new formulation for the multilayer Isogeometric Kirchhoff--Love (KL) shells, where the individual layers are assumed to interact through no-penetration and frictional contact. This work is largely motivated by the experiments and analysis presented in [1]. We utilize a regularized version of Coulomb's friction law to model the tangenti...

The superior accuracy isogeometric analysis (IGA) brought to computations in fluid and solid mechanics has been yielding higher fidelity in computational aerodynamics. The increased accuracy we achieve with the IGA is in the flow solution, in representing the problem geometry, and, when we use the IGA basis functions also in time in a space–time (S...

In this paper we develop a modification of the recently proposed Taylor series expansion-based formulation for computational solids to satisfy a generalized patch test. To achieve this property, the parametric derivatives of the strain rate-velocity matrix accounting for non-affine isoparametric element mappings and Taylor series expansion based on...

In this lead article of the special issue, we provide a brief summary of the research developments in Isogeometric Analysis (IGA) for Computational Fluid Dynamics (CFD). We focus on the use of IGA in combination with stabilized and variational multiscale methods in fluids. We highlight the key developments and present results in IGA-based CFD that...

Physics-informed neural networks (PINN) can solve partial differential equations (PDEs) by encoding the mathematical information explicitly into the loss functions. In the context of plasticity, discussions of PINN have only focused on small-strain formulations. We present a framework of finite-strain elasto-plasticity for PINN, considering rate-in...

This work presents a strongly-coupled fluid–structure interaction (FSI) formulation for compressible flows that is developed based on an augmented Lagrangian approach. The method is suitable for handling problems that involve nonmatching fluid–structure interface discretizations. In this work, the fluid is modeled using a stabilized finite element...

A stabilized Isogeometric formulation of compressible flows is coupled to a large-deformation inelastic solid with an M7 Microplane constitutive model of concrete failure discretized in the framework of correspondence-based Peridynamics with bond-associated stabilization. The fluid–structure interaction (FSI) coupling makes use of a simple volumetr...

Isogeometric analysis (IGA) brought superior accuracy to computations in both fluid and solid mechanics. The increased accuracy has been in representing both the problem geometry and the variables computed. Beyond using IGA basis functions in space, with IGA basis functions in time in a space–time (ST) context, we can have increased accuracy also i...

We begin the article by summarizing some key developments in the field of Peridynamics (PD) and arrive at a conclusion that two schools of PD are emerging in recent years. One school takes a more traditional view of PD as a model of a nonlocal continuum, while another approaches PD as a discretization methodology for local continua where the nonloc...

In this work, we propose and validate a new stabilized compressible flow finite element framework for the simulation of aerospace applications. The framework is comprised of the streamline upwind/Petrov–Galerkin (SUPG)-based Navier–Stokes equations for compressible flows, the weakly enforced essential boundary conditions that act as a wall function...

We extend the recently proposed framework using reduced quadrature in the Finite Element and Isogeometric methods for solid mechanics to the nonlinear realm. The proposed approach makes use of the governing equations in the updated Lagrangian formulation in combination with the rate form of the constitutive laws. The key ingredient in the framework...

A good mesh moving method is an important part of flow computations with moving-mesh methods like the space–time (ST) and Arbitrary Lagrangian–Eulerian (ALE) methods. With a good mesh moving method, we can decrease the remeshing frequency even when the fluid–solid and fluid–fluid interfaces undergo large displacements, decrease the element distortion i...

We present a comprehensive rotation-free Kirchhoff–Love (KL) shell formulation for peridynamics (PD) that is capable of modeling large elasto-plastic deformations and fracture in thin-walled structures. To remove the need for a predefined global parametric domain, Principal Component Analysis is employed in a meshfree setting to develop a local par...

View Video Presentation: https://doi.org/10.2514/6.2022-1077.vid The objective of this work is to investigate and validate a new stabilized compressible flow finite element framework for the simulation of aerospace applications. The framework is comprised of the streamline upwind/Petrov–Galerkin (SUPG)-based Navier–Stokes equations for compressible...

This chapter reviews a class of methods for computational contact mechanics, where the contact problem is regularized using nonlocal interaction, to simplify discretization. This discussion is guided by an analogy to computational fracture mechanics, where nonlocal regularizations are widely employed to obtain robust computational models. Particula...

We present a novel formulation for the immersed coupling of isogeometric analysis and peridynamics for the simulation of fluid–structure interaction (FSI). We focus on air-blast FSI and address the computational challenges of immersed FSI methods in the simulation of fracture and fragmentation by developing a weakly volume-coupled FSI formulation b...

We present a novel formulation for the immersed coupling of Isogeometric Analysis (IGA) and Peridynamics (PD) for the simulation of fluid-structure interaction (FSI). We focus on air-blast FSI and address the computational challenges of immersed FSI methods in the simulation of fracture and fragmentation by developing a weakly volume-coupled FSI fo...

Generating quality body-fitting meshes for complex composite microstructures is a non-trivial task. In particular, micro-CT images of composites can contain numerous irregularly-shaped inclusions. Among the methods available, immersed boundary methods that discretize bodies independently provide potential for tackling these types of problems since...

We present a novel formulation based on an immersed coupling of Isogeometric Analysis (IGA) and Peridynamics (PD) for the simulation of fluidstructure interaction (FSI) phenomena for air blast. We aim to develop a practical computational framework that is capable of capturing the mechanics of air blast coupled to solids and structures that undergo...

We present a novel formulation based on an immersed coupling of Isogeometric Analysis (IGA) and Peridynamics (PD) for the simulation of fluid-structure interaction (FSI) phenomena for air blast. We aim to develop a practical computational framework that is capable of capturing the mechanics of air blast coupled to solids and structures that undergo...

We present a comprehensive rotation-free Kirchhoff-Love (KL) shell formulation for peridynam-ics (PD) that is capable of modeling large elasto-plastic deformations and fracture in thin-walled structures. To remove the need for a predefined global parametric domain, Principal Component Analysis is employed in a meshfree setting to develop a local pa...

We present large-eddy simulations (LES) of wind and wave-driven turbulent boundary layers in shallow water with Langmuir circulation using a variational multi-scale formulation of the Craik-Leibovich equations. The simulations are performed using Isogeometric Analysis (IGA) based on quadratic non-uniform rational basis spline (NURBS) basis function...

The overarching goal of this work is to develop an accurate, robust, and stable methodology for finite deformation modeling using strong-form peridynamics (PD) and the correspondence modeling framework. We adopt recently developed methods that make use of higher-order corrections to improve the computation of integrals in the correspondence formula...

The overarching goal of this work is to develop an accurate, robust, and stable methodology for finite deformation modeling using strong-form peridynamics (PD) and the correspondence modeling framework. We adopt recently developed methods that make use of higher-order corrections to improve the computation of integrals in the correspondence formula...

A stabilized finite element framework for high-speed compressible flows is presented. The Streamline-Upwind/Petrov–Galerkin formulation augmented with discontinuity-capturing (DC) are the main constituents of the framework that enable accurate, efficient, and stable simulations in this flow regime. Full- and reduced-energy formulations are employed...

We propose a framework to improve one-point quadrature and, more generally, reduced integration for finite element methods (FEM), Isogeometric Analysis (IGA), and immersed methods. The framework makes use of first- and higher-order Taylor expansion of the integrands involved in the principle of virtual work, and the analytical integration of the re...

A recently introduced NURBS mesh generation method for complex-geometry Isogeometric Analysis (IGA) is applied to building a high-quality mesh for a gas turbine. The compressible flow in the turbine is computed using the IGA and a stabilized method with improved discontinuity-capturing, weakly-enforced no-slip boundary-condition, and sliding-interf...

An earlier version of this article included a number of typesetting mistakes. These were corrected on October 16, 2020. The publisher apologizes for the errors made during production. The symbol “Λn” was incorrectly published as “Γn” in equations 46 and 47. The correct equations are provided in this correction.

We propose the use of Isogeometric Analysis (IGA) within the context of the Material Point Method (MPM), and refer to the approach as IGA-MPM. We use the idea of IGA, and its instantiation based on Non-Uniform Rational B-Splines (NURBS), to build higher-order accurate and smooth approximation for MPM. Higher-order smoothness yields a continuous rep...

This work couples high-fidelity moving-domain finite element compressible flow modeling with a Surrogate Management Framework (SMF) for optimization to effectively design a variable speed gas turbine stage. The superior accuracy of high-fidelity modeling, however, comes with relatively high computational costs, which are further amplified in the it...

The objective of this work is to computationally investigate the impact of an incidence-tolerant rotor blade concept on gas turbine engine performance under off-design conditions. When a gas turbine operates at an off-design condition such as hover flight or takeoff, large-scale flow separation can occur around turbine blades, which causes performa...

A residual-based variational multi-scale (VMS) modeling framework is applied to simulate atmospheric flow over complex environmental terrains. The VMS framework is verified and validated using two test cases using linear finite element (FEM) and quadratic non-uniform rational B-spline (NURBS) discretizations. First, the flow over the 3D, axisymmetr...

Many of the challenges encountered in computational analysis of wind turbines and turbomachinery are being addressed by the Arbitrary Lagrangian–Eulerian (ALE) and Space–Time (ST) Variational Multiscale (VMS) methods and isogeometric discretization. The computational challenges include turbulent rotational flows, complex geometries, moving boundari...

Computational cardiovascular analysis can provide valuable information to cardiologists and cardiovascular surgeons on a patient-specific basis. There are many computational challenges that need to be faced in this class of flow analyses. They include highly unsteady flows, complex cardiovascular geometries, moving boundaries and interfaces, such a...

Computational flow analysis is now playing a key role in aerospace, energy and transportation technologies, bringing solution in challenging problems such as aerodynamics of parachutes, thermo-fluid analysis of ground vehicles and tires, and fluid–structure interaction (FSI) analysis of wind turbines. The computational challenges include complex ge...

We present large-eddy simulations (LES) of wind and wave-driven turbulent boundary layers in shallow water with Langmuir circulation using a variational multi-scale formulation of the Craik-Leibovich equations. The simulations are performed using Isogeometric Analysis (IGA) based on quadratic non-uniform rational basis spline (NURBS) basis function...

With the recent advances in the variational multiscale (VMS) methods, computational ow analysis in aerospace, energy, and transportation technologies has reached a high level of sophistication. It is bringing solutions in challenging problems such as the aerodynamics ofparachutes, thermo-fluid analysis of ground vehicles and tires, and fluid-struct...

The overarching goal of this work is to develop an accurate, robust, and stable methodology for finite deformation modeling using strong-form peridynamics (PD) and the correspondence modeling framework. We adopt recently developed methods that make use of higher-order corrections to improve the computation of integrals in the correspondence formula...

The overarching goal of this work is to develop an accurate, robust, and stable methodology for finite deformation modeling using strong-form peridynamics (PD) and the correspondence modeling framework. We adopt recently developed methods that make use of higher-order corrections to improve the computation of integrals in the correspondence formula...

Heart valve fluid–structure interaction (FSI) analysis is one of the computationally challenging cases in cardiovascular fluid mechanics. The challenges include unsteady flow through a complex geometry, solid surfaces with large motion, and contact between the valve leaflets. We introduce here an isogeometric sequentially-coupled FSI (SCFSI) method...

We introduce a residual-based stabilized formulation for incompressible Navier–Stokes flow that maintains discrete (and, for divergence-conforming methods, strong) mass conservation for inf–sup stable spaces with H1-conforming pressure approximation, while providing optimal convergence in the diffusive regime, robustness in the advective regime, an...

The challenges encountered in computational analysis of wind turbines and turbomachinery include turbulent rotational flows, complex geometries, moving boundaries and interfaces, such as the rotor motion, and the fluid-structure interaction (FSI), such as the FSI between the wind turbine blade and the air. The Arbitrary Lagrangian-Eulerian (ALE) an...

This paper adapts the concept of residual-based shock-capturing viscosity to the setting of solid mechanics. To evaluate the residual of the momentum balance equation, one requires the divergence of the Cauchy stress. Solid constitutive models used in simulations of extreme events involving shocks typically specify the Cauchy stress in terms of a l...

The Waste Isolation Pilot Plant (WIPP) is a geologic repository for defense-related nuclear waste. If left undisturbed, the virtually impermeable rock salt surrounding the repository will isolate the nuclear waste from the biosphere. If humans accidentally intrude into the repository in the future, then the likelihood of a radionuclide release to t...

We introduce a residual-based stabilized formulation for incompressible Navier-Stokes flow that maintains discrete (and, for divergence-conforming methods, strong) mass conservation for inf-sup stable spaces with $H^1$-conforming pressure approximation, while providing optimal convergence in the diffusive regime, robustness in the advective regime,...

This paper reviews several existing peridynamic models for frictional contact (previously documented only in the gray literature), and extends them to remedy various shortcomings. In particular, we introduce a state-based nonlocal friction formulation that corrects for loss of angular momentum balance and objectivity in a widely used frictional ext...

For unsteady aerodynamics, the Arbitrary Lagrangian-Eulerian Variational Multi-Scale (ALE-VMS) formulation for incompressible flows has proven an accurate and powerful method. In this paper we present an overview of some of its applications to wind engineering of long-span bridges, including flutter and buffeting analysis and vortex-induced vibrati...

Computational cardiovascular flow analysis can provide valuable information to medical doctors in a wide range of patientspecific cases, including cerebral aneurysms, aortas and heart valves. The computational challenges faced in this class of flow analyses also have a wide range. They include unsteady flows, complex cardiovascular geometries, movi...

Computational fluid dynamics (CFD) and fluid-structure interaction (FSI) are growing disciplines in the aeroelastic analysis and design of long-span bridges, which, with their bluff body characteristics, offer major challenges to efficient simulation. In this paper, we employ isogeometric analysis (IGA) based on nonuniform rational B-splines (NURBS...

We propose new projection methods for treating near-incompressibility in small and large deformation elasticity and plasticity within the framework of particle and meshfree methods. Using the \(\overline{\mathbf {B}}\) and \(\overline{\mathbf {F}}\) techniques as our point of departure, we develop projection methods for the conforming reproducing k...

We present an immersogeometric analysis (IMGA) approach for the simulation of compressible flows around complex geometries. In this method, compressible flow simulations are performed directly on various boundary representations (B-reps) of mechanical designs, circumventing the labor-intensive and time-consuming cleanup of complex geometric models....