This paper presents a general high-order kernel regularization technique applicable to all four integral operators of Calderón calculus associated with linear elliptic PDEs in two and three spatial dimensions. Like previous density interpolation methods, the proposed technique relies on interpolating the density function around the kernel singularity in terms of solutions of the underlying homogeneous

Fiber-reinforced soft materials have emerged as promising candidates in various applications such as soft robotics and soft fibrous tissues. To enable a systematic approach to design fiber-reinforced materials and structures, we propose a general topology optimization framework for the computational optimized design of hyperelastic structures with nonlinear and anisotropic fiber reinforcements under

Peridynamics is a nonlocal theory which can easily handle discontinuities such as cracks, while it is computationally more expensive compared with finite element method (FEM). Beams and shells, as the main units of structural idealization, can tremendously improve the computational efficiency for complex structures. This study presents new peridynamic (PD) beam and shell models with the effect of transverse

We introduce a deep learning framework designed to train smoothed elastoplasticity models with interpretable components, such as the stored elastic energy function, yield surface, and plastic flow that evolve based on a set of deep neural network predictions. By recasting the yield function as an evolving level set, we introduce a deep learning approach to deduce the solutions of the Hamilton–Jacobi

Peridynamics (PD) becomes increasingly promising in computational fracture mechanics for its powerful ability to capture complex crack problems. Nevertheless, the PD applications are mainly limited to brittle fracture, and a robust PD model for predicting mixed mode fracture of quasi-brittle materials is still lacking. In this work, a novel damage model is proposed in the PD-CZM to accurately predict

Phononic crystals (PnCs) have seen increasing popularity due to band gap property for sound wave propagation. As a natural bridge, topology optimization has been applied to the design of PnCs. However, thus far most of the existent works on topological design of PnCs have been focused on single micro-scale topology optimization of a periodical unit cell. Moreover, practical manufacturing of those designed

Multi-scale topology optimization (MTO) is exploited today in applications that require designs with large surface-to-volume ratio. Further, with the advent of additive manufacturing, MTO has gained significant prominence. However, a major drawback of MTO is that it is computationally expensive. As an alternate, graded MTO has been proposed where the design features at the smaller scale are graded

The random field theory is often utilized to characterize the inherent spatial variability of material properties. In order to incorporate sampled data from site investigations or experiments into simulations, a patching algorithm is developed to yield a conditional random field in this study. Comparison is conducted between the proposed algorithm and the conventional Kriging algorithm to underscore

In this paper, a novel density-based topology optimization method for cellular structures with quasi-periodic microstructures is proposed. Here, ‘quasi-periodic’ is developed from periodic microstructures composed with a base unit cell, through gradually changing one or multiple alterable microstructural sizing/shape parameters. However, it is a challenge and key issue to identify the explicit alterable

We present a semi-coupled resolved Computational Fluid Dynamics (CFD) and Discrete Element Method (DEM) to simulate a class of granular media problems that involve thermal-induced phase changes and particle–fluid interactions. We employ an immersed boundary (IB) method to model the viscous fluids surrounding solid particles in conjunction with a fictious CFD domain occupied by the actual positions

The geometric reinterpretation of the Finite Element Method (FEM) shows that Raviart–Thomas and Nédélec mass matrices map from degrees of freedoms (DoFs) attached to geometric elements of a tetrahedral grid to DoFs attached to the barycentric dual grid. The algebraic inverses of the mass matrices map DoFs attached to the barycentric dual grid back to DoFs attached to the corresponding primal tetrahedral

We construct a novel second-order time marching scheme with the full decoupling structure to solve a highly coupled nonlinear two-phase fluid flow system consisting of the nonlocal mass-conserved Allen–Cahn equation where two types of flow regimes are considered (Navier–Stokes and Darcy). We achieve the full decoupled structure by introducing a nonlocal variable and designing an additional ordinary

A new family of turbulence models, Large Eddy Simulation with Correction (LES-C) has been proposed in Labovsky (2020), that reduces the modeling error of LES models by using a predictor–corrector type method, known as defect correction. Here we propose to combine this approach with another predictor–corrector technique, known as deferred correction, to reduce the time discretization error of the LES-C

Recently, several approaches for multiscale simulations for problems with high contrast and no scale separation are introduced. Among them is nonlocal multicontinua (NLMC) method, which introduces multiple macroscopic variables in each computational grid. These approaches explore the entire coarse block resolution and one can obtain optimal convergence results independent of contrast and scales. However

This paper proposes a new level set based multi-material topology optimization method, where a difference-set-based multi-material level set (DS-MMLS) model is developed for topology description and an alternating active-phase algorithm is implemented. Based on the alternating active-phase algorithm, a multi-material topology optimization problem with N + 1 phases is split into N(N + 1)/2 binary-phase

This paper presents a novel multi-objective integrated optimization method for static shape control of piezoelectric functionally graded plates (FGPs). The new method combines isogeometric analysis (IGA) and an effective multi-objective non-gradient algorithm which has not been applied to the integrated design of piezoelectric FGPs. Mechanical behavior of the FGPs with surface bonded piezoelectric

This paper proposes an isogeometric formulation of the Reissner–Mindlin shell, using the Mixed Interpolation of Tensorial Components (MITC) technique to alleviate shear locking and membrane locking. Instead of over each Non-Uniform Rational B-Spline (NURBS) element, kinematics of the shell is directly formulated on the entire NURBS patch, with its displacements decoupled to the motions of control points

Pattern formation is a widely observed phenomenon in diverse fields including materials physics, developmental biology and ecology, among many others. The physics underlying the patterns is specific to the mechanisms, and is encoded by partial differential equations (PDEs). With the aim of discovering hidden physics, we have previously presented a variational approach to identifying such systems of

Isogeometric analysis (IGA) is an important mesh-free method that provides the technique for the integration of computer-aided design and analysis. However, its formulation is based on classical continuum mechanics and is not suitable for crack propagation problems. The peridynamics (PD) theory is based on the non-local integral equation, which avoids the discontinuous problem of classical continuum

Large-scale 3D martensitic microstructure evolution problems are studied using a finite-element discretization of a finite-strain phase-field model. The model admits an arbitrary crystallography of transformation and arbitrary elastic anisotropy of the phases, and incorporates Hencky-type elasticity, a penalty-regularized double-obstacle potential, and viscous dissipation. The finite-element discretization

The numerical simulation of wave propagation in heterogeneous unbounded media using domain discretization techniques requires truncation of the physical domain: at the truncation boundary, Perfectly Matched Layers (PMLs) – buffers wherein wave attenuation is imposed – are often used to mimic outgoing wave motion and prevent waves from re-entering the interior computational domain. The PML’s wave-dissipative

This paper presents an invariant isogeometric formulation for the geometric stiffness matrix of spatial curved Kirchhoff rods considering various end moments, i.e., the internal (member) moments and applied (conservative) moments. There are two levels of rigid-body qualification, one is on the buckling theory of the rod itself and the other on the isogeometric formulation for discretization. Both will

The simulation of structural problems involving the deformations of volumetric bodies is of paramount importance in many areas of engineering. Although the use of tetrahedral elements is extremely appealing, tetrahedral discretisations are generally known as very stiff and are hence often avoided in typical simulation workflows. The development of mixed displacement–pressure approaches has allowed

Pentamode metamaterials (PMMs) are a new class of three-dimensional (3D) mechanical metamaterials, engineered to have unusual elastic property of vanishing shear modulus. Here ‘penta’ denotes five, referring to only one non-zero but five vanishing eigenvalues in the elasticity tensor of isotropic materials. PMMs gain their properties from their rationally designed structural architecture rather than

This paper proposes a new methodology for computing boundary sensitivities in level set topology optimization using the discrete adjoint method. The adjoint equations are constructed using the discretized governing field equations. The objective function is differentiated with respect to the boundary point movement for computing boundary sensitivities using the discrete adjoint equations. For this

A superconvergent isogeometric collocation method that employs the conventional Greville abscissae as collocation points is proposed. Firstly, a basis transformation is presented for isogeometric basis functions, which preserves the exact geometry representation characterized by isogeometric analysis. More specifically, the geometry is exactly represented by the transformed isogeometric basis functions

Finding fast yet accurate numerical solutions to the Helmholtz equation remains a challenging task. The pollution error (i.e. the discrepancy between the numerical and analytical wave number k) requires the mesh resolution to be kept fine enough to obtain accurate solutions. A recent study showed that the use of Isogeometric Analysis (IgA) for the spatial discretization significantly reduces the pollution

We propose a goal-oriented mesh-adaptive algorithm for a finite element method stabilized via residual minimization on dual discontinuous-Galerkin norms. By solving a saddle-point problem, this residual minimization delivers a stable continuous approximation to the solution on each mesh instance and a residual projection onto a broken polynomial space, which is a robust error estimator to minimize

The penalty method has proven to be a well-suited approach for the application of coupling and boundary conditions on (trimmed) multi-patch NURBS shell structures within isogeometric analysis. Beside its favorable simplicity and efficiency, the main challenge is the appropriate choice of the underlying penalty factor — choosing the penalty factor too low yields a poor constraint accuracy, while choosing

This manuscript presents a multiscale reduced-order modeling framework for heterogeneous materials that accounts for both cohesive interface failure and continuum damage. The model builds on the eigendeformation-based reduced-order homogenization model (EHM), which relies on the pre-calculation of a set of coefficient tensors that account for the effects of linear and nonlinear material behavior between

A dispersive wave hydro-sediment-morphodynamic model developed by complementing the shallow water hydro-sediment-morphodynamic (SHSM) equations with the dispersive term from the Green–Naghdi equations is presented. A numerical solution algorithm for the model based on the second-order Strang operator splitting is presented. The model is partitioned into two parts, (1) the SHSM equations and (2) the

In this paper, we solve a constrained Willmore problem coupled with an electrical field using IsoGeometric Analysis (IGA) to simulate the morphological evolution of vesicles subjected to static electrical fields. The model consist of two phases, the lipid bilayer and the electrolyte. The two-phases problem is modeled using the phase-field method, a subclass of the diffusive interface models. The bending

In this paper, a new particle-based fluid–rigid-body interaction simulator for violent free-surface flow problems is developed. The incompressible Smoothed Particle Hydrodynamics (ISPH) method has been proven to produce a smooth and accurate pressure distribution of free-surface fluid flow with breaking and fragmentation. Computed hydrodynamic forces can be applied onto rigid bodies, which may simultaneously

Meshfree discretizations of state-based peridynamic models are attractive due to their ability to naturally describe fracture of general materials. However, two factors conspire to prevent meshfree discretizations of state-based peridynamics from converging to corresponding local solutions as resolution is increased: quadrature error prevents an accurate prediction of bulk mechanics, and the lack of

All material point method (MPM) codes approximate the full mass matrix with a lumped mass matrix. Because this approach causes dissipation, most MPM simulations rely on so-called FLIP methods to limit dissipation. Recent work to deal with noise caused by those FLIP methods derived the XPIC method (for extended particle in cell method) that filters null space noise from particle velocities using a projection

Extended finite element method (XFEM) achieves unprecedented success in crack growth simulations, in particular in 2D. However, challenges still remain for a 3D crack growth simulation. Among other issues like increased computational expense, one challenge is robust and efficient geometry representation of the non-planar surface and the usually curved front of the 3D crack, two unique features distinguished

Fiber-reinforced composite (FRC) structure design by topology optimization has become a hot spot in recent years. Nevertheless, the existing researches reveal several unfavorable issues including the fiber dis-continuity, the length scale separation, the decreased design freedom, as well as the complicated fiber orientation optimization. Thus, this paper proposes a full-scale fiber-reinforced structure

Reverse shape compensation is widely used in additive manufacturing to offset the displacement distortion caused by various sources, such as volumetric shrinkage, thermal cooling, etc. Also, reverse shape compensation is also an effective tool for the four-dimensional (4D) printing techniques, shape memory polymers (SMPs), or 3D self-assemble structures to achieve a desired geometry shape under environmental

This work proposes an iterative sparse-regularized regression method to recover governing equations of nonlinear dynamical systems from noisy state measurements. The method is inspired by the Sparse Identification of Nonlinear Dynamics (SINDy) approach of Brunton et al. (2016), which relies on two main assumptions: the state variables are known a priori and the governing equations lend themselves to

We propose a variational splitting technique for the generalized-α method to solve hyperbolic partial differential equations. We use tensor-product meshes to develop the splitting method, which has a computational cost that grows linearly with the total number of degrees of freedom for multi-dimensional problems. We use the generalized-α method for the temporal discretization while standard C0 finite

In this paper, an enhanced Virtual Element Method (VEM) formulation is proposed for plane elasticity. It is based on the improvement of the strain representation within the element, without altering the degree of the displacement interpolating functions on the element boundary. The idea is to fully exploit polygonal elements with a high number of sides, a peculiar VEM feature, characterized by many

Spaces of discrete differential forms can be applied to numerically solve the partial differential equations that govern phenomena such as electromagnetics and fluid mechanics. Robustness of the resulting numerical methods is complemented by pointwise satisfaction of conservation laws (e.g., mass conservation) in the discrete setting. Here we present the construction of isogeometric discrete differential

In this paper, a computational modeling tool is developed for fully coupled multiphase flow in deformable heterogeneous porous medium that consists of complex and non-uniform micro-structures using the dual continuum scales based on the computational homogenization approach. The first-order homogenization technique is employed to perform the multi-scale analysis. The governing equations of two-phase

Nondestructive damage identification is a central task, for example, in aeronautical, civil and naval engineering. The identification approaches based on (physical) models rely on the predictive accuracy of the forward model, and typically suffer from effects caused by ubiquitous modeling errors and uncertainties. The present paper considers the identification of defects in beams and plates under uncertain

Structural design optimization for additive manufacturing is primarily focused on planar layer-by-layer processes and design of composite cylindrical structures does not often accommodate manufacturing constraints. In this study, we propose to optimize the toolpath trajectory of additively manufactured composite cylinders comprised of multiple thin cylindrical annuli. Our printing process is based

We aim to test the performances of an incompressible turbulence Reynolds-Averaged Navier–Stokes one-closure equation model in a boundary layer (NSTKE model). We model a new boundary condition for the turbulent kinetic energy k (TKE), and we achieve the mathematical analysis of the resulting NSTKE model. A series of direct numerical simulation are performed, with flat and non trivial topographies, to

Thermally induced cracking occurs in many engineering problems such as drying shrinkage cracking of concrete, thermal shock induced fracture, micro cracking of two-phase composite materials etc. The computational simulation of such a fracture is complicated, but the use of phase-field models (PFMs) is promising as they can seamlessly model complex crack patterns like branching, merging, and fragmentation

In the framework of cardiac electrophysiology for the human heart, we apply multipatch NURBS-based Isogeometric Analysis for the space discretization of the Monodomain model. Isogeometric Analysis (IGA) is a technique for the solution of Partial Differential Equations (PDEs) that facilitates encapsulating the exact representation of the computational geometry by using basis functions with high-order

The concept of the partition of unity (PU) enabled the development of nodal enrichment strategies, such as the Extended Finite Element Method (XFEM) and Generalised Finite Element Method (GFEM), for realistic simulations of structural behaviour with applications to both static and dynamic problems. Nonetheless, the majority of existing methodologies still inherit instability issues for arbitrary discontinuity

Functionally graded materials have widespread applications for the practical engineering and industry of design and development. In the present work, free vibration and transient dynamic behaviors of functionally graded material (FGM) sandwich plates are semi-analytically investigated by the scaled boundary finite element method (SBFEM). A layerwise approach based on the three-dimensional (3D) theory

Integrated models for fluid-driven fracture propagation and general multiphase flow in porous media are valuable to the study and engineering of several systems, including hydraulic fracturing, underground disposal of waste, and geohazard mitigation across such applications. This work extends the coupled model multiphase flow and poromechanical model of Ren et al. (2018) to admit fracture propagation

This paper presents a windowed Green function (WGF) method for the numerical solution of problems of elastic scattering by “locally-rough surfaces” (i.e., local perturbations of a half space), under either Dirichlet or Neumann boundary conditions, and in both two and three spatial dimensions. The proposed WGF method relies on an integral-equation formulation based on the free-space Green function,

Auxetic materials have recently emerged as new types of advanced materials with unique material properties that conventional materials do not possess. In this paper, we examine the effect of in-plane negative Poisson’s ratio (NPR) on the thermal postbuckling behavior of graphene-reinforced metal matrix composite (GRMMC) laminated cylindrical shells. The shell consists of GRMMC layers arranged in a

We present a novel topology optimization (TO) method for the design of structures composed of bars that are made of an orthotropic, fiber-reinforced material. The designs generated under this framework tailor the layout of the fiber-reinforced bars to maximize the stiffness of the structure for a fixed amount of material. The proposed method extends the geometry projection method to represent the design

Robust optimization strategies typically aim at minimizing some statistics of the uncertain objective function and can be expensive to solve when the statistic is costly to estimate at each design point. Surrogate models of the uncertain objective function can be used to reduce this computational cost. However, such surrogate approaches classically require a low-dimensional parametrization of the uncertainties

Data assimilation in subsurface flow systems is challenging due to the large number of flow simulations often required, and by the need to preserve geological realism in the calibrated (posterior) models. In this work we present a deep-learning-based surrogate model for two-phase flow in 3D subsurface formations. This surrogate model, a 3D recurrent residual U-Net (referred to as recurrent R-U-Net)

This work proposes a new meta-heuristic method called Arithmetic Optimization Algorithm (AOA) that utilizes the distribution behavior of the main arithmetic operators in mathematics including (Multiplication (M), Division (D), Subtraction (S), and Addition (A)). AOA is mathematically modeled and implemented to perform the optimization processes in a wide range of search spaces. The performance of AOA

Virtual clustering analysis (VCA) has been developed for numerical homogenization of heterogeneous material. The integral form of the material system is the Lippmann–Schwinger equation, which imposes boundary condition at infinity for fictitious surrounding homogeneous reference material. The artificially chosen reference stiffness induces a distribution for traction on the material boundary. The deviation

In this work, a particle regeneration technique is developed for Smoothed Particle Hydrodynamics (SPH). In traditional SPH, the particle disorder phenomenon will occur when dealing with the strongly compressible flow problem. To solve this, in the present work, uniformly distributed background particles filled in the computational domain are adopted. The particle regeneration technique is that the

Cracking of rocks and rock-like materials exhibits a rich variety of patterns where tensile (mode I) and shear (mode II) fractures are often interwoven. These mixed-mode fractures are usually cohesive (quasi-brittle) and frictional. Although phase-field modeling is increasingly used for rock fracture simulation, no phase-field formulation is available for cohesive and frictional mixed-mode fracture