A level set topology optimization (LSTO) using the stabilized nodally integrated reproducing kernel particle method (RKPM) to solve the governing equations is introduced in this paper. This methodology allows for an exact geometry description of a structure at each iteration without remeshing and without any interpolation scheme. Moreover, useful characteristics of the RKPM such as the easily controlled

Damage models have been successfully employed for many decades in the modelling of tensile failure, where the crack surfaces separate as a crack grows. The advantage of this approach is that crack trajectories can be computed simply and efficiently on a fixed finite element mesh without explicit tracking. The development of damage models for shear failure in compression, where the crack faces slide

We describe a stable finite element formulation for advection–diffusion–reaction problems that allows for the easy implementation of robust automatic adaptivity. We consider locally vanishing, heterogeneous, and anisotropic diffusivities, as well as advection-dominated diffusion problems. We apply a general stabilized finite element framework (Calo et al., 2020) that seeks a discrete solution through

Cracking in quasi-brittle geomaterials is a complex mechanical phenomenon, driven by various dissipation mechanisms across multiple length scales. While some recent promising works have employed the phase-field method to model the damage and fracture of geomaterials, several open questions still remain. In particular, capturing frictional sliding along the lips of microcracks, incorporating lower scale

Fluid–structure interactions (FSI) are very common in many natural processes and engineering applications. However, modeling FSI with large structural deformations and turbulence flows under high Reynolds number (Re) is still a challenging task. Here, we present a hybrid 3D model that combines the advantages of Lattice Boltzmann Method (LBM) in solving complex flow problems and the capability of Material

It is well known that domain-decomposition-based multiscale mixed methods rely on interface spaces, defined on the skeleton of the decomposition, to connect the solution among the non-overlapping subdomains. Usual spaces, such as polynomial-based ones, cannot properly represent high-contrast channelized features such as fractures (high permeability) and barriers (low permeability) for flows in heterogeneous

Material and structural non-destructive evaluations using guided-wave (GW) testing techniques rely on the knowledge of wave dispersion characteristics. When studying coupled fluid–solid waveguides having complex geometries using the semi-analytical finite element (SAFE) method, an excessive computational effort may be required, especially at high-frequency ranges. In this paper, we show the robustness

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 a matching discretization is not needed. However, these

Phase field method has proven capable of producing complex crack patterns in solids. It introduces a continuous phase field to regularize the sharp crack discontinuities. However, the applicability of this method to engineering problems is hindered by its computational costs. In this work, we proposed a mapped phase field method as a possible route to resolve this issue. The core of this method is

Process-induced defects are the leading cause of discrepancies between as-designed and as-manufactured additive manufacturing (AM) product behavior. Especially for metal lattices, the variations in the printed geometry cannot be neglected. Therefore, the evaluation of the influence of microstructural variability on their mechanical behavior is crucial for the quality assessment of the produced structures

In this paper, we propose a new algorithm for computing planar multi-patch domain parameterizations which are suitable for consequent numerical computations based on isogeometric analysis. Firstly, a so-called fat skeleton of the given domain, represented by a multi-patch NURBS parameterization, is constructed, which determines the topology of a multi-patch NURBS parameterization suitable for the given

We propose an Exponential DG approach for numerically solving partial differential equations (PDEs). The idea is to decompose the governing PDE operators into linear (fast dynamics extracted by linearization) and nonlinear (the remaining after removing the former) parts, on which we apply the discontinuous Galerkin (DG) spatial discretization. The resulting semi-discrete system is then integrated using

We derive a continuum sharp-interface model for moving contact lines with soluble surfactants in a thermodynamically consistent framework. The model consists of the isothermal two-phase incompressible Navier–Stokes equations for the fluid dynamics and the bulk/surface convection–diffusion equations for the surfactant transportation. The interface condition, the slip boundary condition, the dynamic

This paper extends the static contact problem of crack faces to include dynamic contact and crack propagation based on the relevant literature (Zhang et al., 2018). The scaled boundary finite element method is used to solve dynamic crack face contact and crack propagation problems. Based on the scaled boundary finite element shape function considering side-face loads, the system dynamic equilibrium

In this paper, we propose two novel Robin-type domain decomposition methods based on the two-grid techniques for the coupled Stokes–Darcy system. Our schemes firstly adopt the existing Robin-type domain decomposition algorithm to obtain the coarse grid approximate solutions. Then two one-step modified domain decomposition methods are further constructed on the fine grid by utilizing the framework of

A Theory-guided Auto-Encoder (TgAE) framework is proposed for surrogate construction, and is further used for uncertainty quantification and inverse modeling tasks. The framework is built based on the Auto-Encoder (or Encoder–Decoder) architecture of the convolutional neural network (CNN) via a theory-guided training process. In order to incorporate physical constraints for achieving theory-guided

A meshless shell method for large deformation and a linear relation between the Cauchy stress tensor and the Almansi strain tensor based on the corrective smoothed particle method (CSPM) is presented in this paper. Due to the use of the shell theory, only one layer of particles in the reference plane is required to discretize the shell model. The CSPM combining the kernel estimate with the Taylor series

The kinetic energy of a flow is proportional to the square of the L2(Ω) norm of the velocity. Given a sufficient regular velocity field and a velocity finite element space with polynomials of degree r, then the best approximation error in L2(Ω) is of order r+1. In this survey, the available finite element error analysis for the velocity error in L∞(0,T;L2(Ω)) is reviewed, where T is a final time. Since

Physics-constrained data-driven computing is an emerging computational paradigm that allows simulation of complex materials directly based on material database and bypass the classical constitutive model construction. However, it remains difficult to deal with high-dimensional applications and extrapolative generalization. This paper introduces deep learning techniques under the data-driven framework

We propose a gauge theoretic model for quantifying and evolving spatial defects in the form of micro-cracks in deforming solids. A non-trivial affine connection — the gauge connection, is introduced to accommodate local changes in the configuration due to spatial defects. The gauge connection enables defining the covariant derivative, a procedure known as the minimal replacement. The configuration

The Physics-Informed Neural Network (PINN) framework introduced recently incorporates physics into deep learning, and offers a promising avenue for the solution of partial differential equations (PDEs) as well as identification of the equation parameters. The performance of existing PINN approaches, however, may degrade in the presence of sharp gradients, as a result of the inability of the network

We propose a new phase-field model formulated within the system of lattice Boltzmann (LB) equation for simulating solidification and dendritic growth with fully coupled melt flow and thermosolutal convection–diffusion. With the evolution of the phase field and the transport phenomena all modeled and integrated within the same LB framework, this method preserves and combines the intrinsic advantages

In this paper, a multi-objective version of the recently proposed marine predator algorithm (MPA) is presented, which is called the multi-objective marine predator algorithm (MOMPA). In this algorithm, an external archive component is introduced to store the non dominated Pareto optimal solutions found so far. Based on the elite selection method, a top predator selection mechanism is proposed, which

We consider finite element discretizations of Maxwell’s equations coupled with a non-local hydrodynamic Drude model that accurately accounts for electron motions in metallic nanostructures. Specifically, we focus on a posteriori error estimation and mesh adaptivity, which is of particular interest since the electromagnetic field usually exhibits strongly localized features near the interface between

We construct a nonconforming virtual element method (ncVEM) based on approximation spaces that are enriched with special singular functions. This enriched ncVEM is tailored for the approximation of solutions to elliptic problems, which have singularities due to the geometry of the domain. Differently from the traditional extended Galerkin method approach, based on the enrichment of local spaces with

The use of nonlinear projector matrix in co-rotational (CR) analysis was pioneered by Rankin and Nour-Omid in 1990s (Rankin and Nour-Omid, 1988; Nour-Omid and Rankin, 1991), and has almost became a standard manner for CR formulations deduction over the past thirty years. This matrix however relies heavily on a hysterical and sophisticated derivation of the variation of the local displacements to the

We outline a continuum approach for treating discrete granular flows that holds across multiple scales: from experiments that focus on centimeter-size control volumes, to tests that involve landslides and large buildings. The time evolution of the continuum used to capture the granular dynamics is resolved in space via the smoothed particle hydrodynamics (SPH) method. The interaction between the granular

The least-squares finite element method (LSFEM) has drawn much attention with desirable properties, such as always symmetric positive-definite stiffness matrix and approximation of primal and non-primal variables with equivalent accuracy. Despite a condition number comparable to that of Galerkin FEM, of O(h−2), it is sometimes found that LSFEM with low-order elements does not show a satisfactory accuracy

In this paper, we develop and study approximately smooth basis constructions for isogeometric analysis over two-patch domains. One key element of isogeometric analysis is that it allows high order smoothness within one patch. However, for representing complex geometries, a multi-patch construction is needed. In this case, a C0-smooth basis is easy to obtain, whereas C1-smooth isogeometric functions

In this paper, a computational framework for simulating ductile fracture in multipatch shell structures is presented. A ductile fracture phase-field model at finite strains is combined with an isogeometric Kirchhoff–Love shell formulation. For the application to complex structures, we employ a penalty approach for imposing, at patch interfaces, displacement and rotational continuity and C0 and C1 continuity

This paper presents a novel framework for predicting computer-aided engineering (CAE) simulation results using machine learning (ML). The framework is applied to finite element (FE) simulations of dynamic axial crushing of rectangular crush tubes that are typically used in vehicle crashworthiness applications. A virtual design of experiments that varies the size and wall thickness of the FE model is

Numerous engineering applications employ composite materials due to the advantages that the combination of their components can provide. Fiber-reinforced composites are a particular group of composites which allows designing optimized structures by tailoring the orientation of the fiber. For this reason, new additive manufacturing technologies have been developed nowadays. These tools allow the manufacturing

We propose a high dimensional Bayesian inference framework for learning heterogeneous dynamics of a COVID-19 model, with a specific application to the dynamics and severity of COVID-19 inside and outside long-term care (LTC) facilities. We develop a heterogeneous compartmental model that accounts for the heterogeneity of the time-varying spread and severity of COVID-19 inside and outside LTC facilities

Considerable progress has been made during the last decade with respect to the development of discretization techniques that are based on the virtual element method. Here we construct a new scheme for large strain problems that include incompressible material behavior. The idea is to use a formulations analogous to the classical Taylor–Hood element, Taylor and Hood (1972) which is based on a mixed

Fracture is a ubiquitous phenomenon in most composite engineering structures, and is often the responsible mechanism for catastrophic failure. Over the past several decades, many approaches have emerged to model and predict crack failure. The phase field method for fracture uses a surrogate damage field to model crack propagation, eliminating the arduous need for explicit crack meshing. In this work

The computational modeling of thin-walled structures based on isogeometric analysis (IGA), non-uniform rational B-splines (NURBS), and Kirchhoff–Love (KL) shell formulations has attracted significant research attention in recent years. While these methods offer numerous benefits over the traditional finite element approach, including exact representation of the geometry, naturally satisfied high-order

Sensitivity analysis is a useful means to quantify the impact of a set of input variables on an output response. However, many traditional sensitivity analysis methods are applicable only to multi-input single-output (MISO) systems and are powerless for multi-input multi-output (MIMO) systems. This paper presents a global sensitivity analysis method based on variance and covariance decomposition (VCD-GSA)

An isogeometric finite element formulation for geometrically and materially nonlinear Timoshenko beams is presented, which incorporates in-plane deformation of the cross-section described by two extensible director vectors. Since those directors belong to the space R3, a configuration can be additively updated. The developed formulation allows direct application of nonlinear three-dimensional constitutive

Inferring arbitrary quantities of interest (QoI) using limited computational or, in realistic scenarios, financial budgets, is a challenging problem that requires sophisticated strategies for the optimal allocation of the available resources. Bayesian optimal experimental design identifies the optimal set of design locations for the purpose of solving a parameter inference problem and the optimality

A novel multi-objective topology optimization method is developed by simultaneously considering the diversity and uniformity of the optimum solutions in the objective and design variable spaces. To guarantee the diversity of the solutions, a configuration-based clustering scheme is developed and applied to avoid similar designs. By clustering Pareto optimal designs during the optimization process,

We present a two-level parameterized Model Order Reduction (pMOR) technique for the linear hyperbolic Partial Differential Equation (PDE) of time-domain elastodynamics. In order to approximate the frequency-domain PDE, we take advantage of the Port-Reduced Reduced-Basis Component (PR-RBC) method to develop (in the offline stage) reduced bases for subdomains; the latter are then assembled (in the online

The variational formulation of coupled mechanical problems has many advantages from the theoretical point of view and also guides the design of numerical methods that have attractive features such as symmetric tangents. In the current work we propose a novel variational principle for three-field, strongly coupled problems involving (inelastic, finite strain) mechanics, thermal transport, and mass diffusion

We present a stochastic modeling framework to represent and simulate spatially-dependent geometrical uncertainties on complex geometries. While the consideration of random geometrical perturbations has long been a subject of interest in computational engineering, most studies proposed so far have addressed the case of regular geometries such as cylinders and plates. Here, standard random field representations

A cohesive phase-field model of ductile fracture in a finite-deformation setting is presented. The model is based on a free-energy function in which both elastic and plastic work contributions are coupled to damage. Using a strictly variational framework, the field evolution equations, damage kinetics, and flow rule are jointly derived from a scalar least-action principle. Particular emphasis is placed

By employing a mortar-type contact algorithm, we develop a theoretical and numerical framework for elastoplastic interaction of unsaturated granular soils with a rigid cylindrical object in both static and dynamic analyses. The elastoplastic response is modelled with a constitutive model based on the effective stress concept for unsaturated soils. The constitutive model offers the ability to simulate

Earth system models are composed of coupled components that separately model systems such as the global atmosphere, ocean, and land surface. While these components are well developed, coupling them in a single system can be a significant challenge. Computational efficiency, accuracy, and stability are principal concerns. In this study we focus on these issues. In particular, implicit–explicit (IMEX)

The explicit semi-Lagrangian method for solution of Lagrangian transport equations as developed in Natarajan and Jacobs (2020) is adopted for the solution of stochastic differential equations that is consistent with Discontinuous Spectral Element Method (DSEM) approximations of Eulerian conservation laws. The method extends the favorable properties of DSEM that include its high-order accuracy, its

In this paper we investigate the iterative solution of enriched finite element methods for solving a frequency domain wave problem. The considered methods are partition of unity isogeometric analysis (PUIGA) and the partition of unity finite element method (PUFEM). We study the performance of an operator based preconditioner, namely, the shifted Laplace preconditioner against a complex shifted ILU

This paper presents a framework for the discrete design of optimal multimaterial structural topologies using integer design variables and mathematical programming. The structural optimization problems: compliance minimization subject to mass constraint, and mass minimization subject to compliance constraint are used to design the multimaterial topologies in this work. The extended SIMP interpolation

A novel domain-decomposition least-squares Petrov–Galerkin (DD-LSPG) model-reduction method applicable to parameterized systems of nonlinear algebraic equations (e.g., arising from discretizing a parameterized partial-differential-equations problem) is proposed. In contrast with previous works, we adopt an algebraically non-overlapping decomposition strategy rather than a spatial-decomposition strategy

An improved data-driven non-intrusive model order reduction (MOR) methodology capable of interpolating time-transient flow-fields and other types of data with respect to the parameters is proposed. The proposed MOR method comprises the following two stages: MOR and interpolation. For the MOR, modified proper orthogonal decomposition (POD) is used to collect the parametrically independent POD modes

Regularizing Finite-Element Digital Image Correlation (FE-DIC) problems is essential when using fine meshes, for instance to get a direct bridge with simulation tools or in view of performing data assimilation. Shape optimization brings comparable concerns so it is proposed to draw inspiration from this field of research. In this respect, a new general spline-based non-invasive regularization scheme

This work develops a continuum-based combined finite–discrete element method (FDEM) in the framework of the explicit finite element method in conjunction with fracture algorithms. To account for complex fracturing processes, both shear failure and tensile failure criteria are implemented. Furthermore, to investigate the effect of different fracture algorithms on the accuracy and computational efficiency

In this paper, a second-order temporal and spatial accurate, unconditionally energy stable scheme for the binary fluid flows model on arbitrarily curved surfaces is proposed. We construct a novel surface discrete finite volume method for the surface computation with second-order spatial accuracy. The discretization can be obtained based on the surface mesh consisting of triangular grids. In order to

In this work we present a computational framework for the parallel simulation of hydraulic fracturing processes. The simulation algorithm is built upon the staggered coupling of a fluid model that describes the viscous flow in the fractured domain and a model of the solid deformation and fracture response, driven by the pressure field induced by the fluid injection. The use of standard finite elements

A machine learning approach to accelerate convergence of the nonlinear solver in multiphase flow problems is presented here. The approach dynamically controls an acceleration method based on numerical relaxation. It is demonstrated in a Picard iterative solver but is applicable to other types of nonlinear solvers. The aim of the machine learning acceleration is to reduce the computational cost of the

In this work, we present a coupled 3D–1D model of solid tumor growth within a dynamically changing vascular network to facilitate realistic simulations of angiogenesis. Additionally, the model includes erosion of the extracellular matrix, interstitial flow, and coupled flow in blood vessels and tissue. We employ continuum mixture theory with stochastic Cahn–Hilliard type phase-field models of tumor

The scaled boundary finite element method (SBFEM) is known for its inherent ability to simulate unbounded domains and singular fields, and its flexibility in the meshing procedure. Keeping the analytical form of the field variables along one coordinate intact, it transforms the governing partial differential equations of the problem into a system of one-dimensional (initial–)boundary value problems

We consider the quasi-static Biot’s consolidation model in a three-field formulation with the three unknown physical quantities of interest being the displacement u of the solid matrix, the seepage velocity v of the fluid and the pore pressure p. As conservation of fluid mass is a leading physical principle in poromechanics, we preserve this property using an H(div)-conforming ansatz for u and v together

Approximately 1.6 million patients in the United States are affected by tricuspid valve regurgitation, which occurs when the tricuspid valve does not close properly to prevent backward blood flow into the right atrium. Despite its critical role in proper cardiac function, the tricuspid valve has received limited research attention compared to the mitral and aortic valves on the left side of the heart