Topology optimization of sandwich structures is attracting more interests due to its potential to balance mechanical performances and lightweight level, especially with the increasing application of additive manufacturing. This paper presents a topology optimization method to generate sandwich structures with solid-porous hybrid infill, in which this design feature of hybrid infill will improve the

We present a hybrid model/model-free data-driven approach to solve poroelasticity problems. Extending the data-driven modeling framework originated from Kirchdoerfer and Ortiz (2016), we introduce one model-free and two hybrid model-based/data-driven formulations capable of simulating the coupled diffusion-deformation of fluid-infiltrating porous media with different amounts of available data. To improve

We show that in the variational multiscale framework, the weak enforcement of essential boundary conditions via Nitsche’s method corresponds directly to a particular choice of projection operator. The consistency, symmetry and penalty terms of Nitsche’s method all originate from the fine-scale closure dictated by the corresponding scale decomposition. As a result of this formalism, we are able to determine

The data-driven computing paradigm initially introduced by Kirchdoerfer & Ortiz (2016) enables finite element computations in solid mechanics to be performed directly from material data sets, without an explicit material model. From a computational effort point of view, the most challenging task is the projection of admissible states at material points onto their closest states in the material data

The FE2 method is a very flexible but computationally expensive tool for multiscale simulations. In conventional implementations, the microscopic displacements are iteratively solved for within each macroscopic iteration loop, although the macroscopic strains imposed as boundary conditions at the micro-scale only represent estimates. In order to reduce the number of expensive micro-scale iterations

Advances in the computational modeling of fracture of solids have opened up new possibilities for structural design optimization to enhance fracture properties. Here, we investigate material optimization and design to improve fracture behavior of composite structures under quasi-static conditions. The rate-independent structural problem considering cohesive fracture is ill-posed in its original form

Incompressible flow problems with nonlinear viscosity, as they often appear in biomedical and industrial applications, impose several numerical challenges related to regularity requirements, boundary conditions, matrix preconditioning, among other aspects. In particular, standard split-step or projection schemes decoupling velocity and pressure are not as efficient for generalised Newtonian fluids

This paper presents a deep learning framework for epidemiology system identification from noisy and sparse observations with quantified uncertainty. The proposed approach employs an ensemble of deep neural networks to infer the time-dependent reproduction number of an infectious disease by formulating a tensor-based multi-step loss function that allows us to efficiently calibrate the model on multiple

One of the principal barriers in developing accurate and tractable predictive models in turbulent flows with a large number of species is to track every species by solving a separate transport equation, which can be computationally impracticable. In this paper, we present an on-the-fly reduced order modeling of reactive as well as passive transport equations to reduce the computational cost. The presented

An immersed enriched finite element method is proposed for the analysis of phononic crystals (PnCs) with finite element (FE) meshes that are completely decoupled from geometry. Particularly, a technique is proposed to prescribe Bloch–Floquet periodic boundary conditions strongly on non-matching edges of the periodic unit cell (PUC). The enriched finite element formulation effectively transforms a periodic

The present contribution is concerned with the incorporation of gradient-extended damage into a reduced integration-based solid-shell finite element formulation. To this end, a purely mechanical low-order solid-shell element based on the isoparametric concept is combined with a gradient-extended two-surface damage plasticity model. Due to a tailored combination of the assumed natural strain (ANS) as

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

In this paper, we extend the tangential-displacement normal–normal-stress continuous (TDNNS) method from Pechstein and Schöberl (2011) to nonlinear elasticity. By means of the Hu–Washizu principle, the distributional derivatives of the displacement vector are lifted to a regular strain tensor. We introduce three different methods, where either the deformation gradient, the Cauchy–Green strain tensor

In this paper, a Nitsche extended finite element method is presented to discretize the biharmonic interface problem with unfitted meshes. A new interface condition is proposed for the biharmonic interface problem, and the construction of the finite element space is based on the so-called modified Morley finite element for the interface elements and the Morley finite element for the others. By adding

We present a new class of fully-discrete one-step SPH schemes based on a mesh-free ADER (Arbitrary DERivatives in space and time) reconstruction on moving particles in multiple space dimensions. In particular, the new SPH scheme computes mesh-free and local high order accurate polynomials in space and time to evaluate numerical fluxes at the midpoint between two interaction particles with a proper

In this paper, we develop high-order nodal discontinuous Galerkin (DG) methods for hyperbolic conservation laws that satisfy invariant domain preserving properties using subcell flux corrections and convex limiting. These methods are based on a subcell flux corrected transport (FCT) methodology that involves blending a high-order target scheme with a robust, low-order invariant domain preserving method

Modeling and simulating interfacial shear load transfer in fiber-reinforced composites is crucial for characterizing fiber pullout behaviors. Addressing this complicated topic, this work presents a novel phase-field framework to simulate interfacial failure behaviors in fiber-reinforced cementitious composites. Specifically, a comprehensive constitutive model is proposed to describe both interfacial

A novel mathematical model for fiber-reinforced materials is proposed. It is based on a 1-dimensional beam model for the thin fiber structures, a flexible and general 3-dimensional elasticity model for the matrix and an overlapping domain decomposition approach. From a computational point of view, this is motivated by the fact that matrix and fibers can be easily meshed independently. Our main interest

In this paper we develop an isogeometric Bézier dual mortar method for coupling multi-patch Kirchhoff–Love shell structures. The proposed approach weakly enforces the continuity of the solution at patch interfaces through a dual mortar method and can be applied to both conforming and non-conforming discretizations. As the employed dual basis functions have local supports and satisfy the biorthogonality

A new fifth-order alternative finite difference multi-resolution weighted essentially non-oscillatory (WENO) scheme is designed to solve the hyperbolic conservation laws in this paper. With the application of the original finite difference multi-resolution WENO schemes (Zhu and Shu, 2018; Zhu and Shu, 2020), a series of unequal-sized central spatial stencils are adopted to perform the WENO procedures

In this paper, the collocation-based isogeometric boundary element method (IGABEM) is combined with the isogeometric Reissner–Mindlin shell elements to conduct the mixed dimensional solid–shell coupling analysis. On the basis of taking advantages of the geometric smoothness and exactness of isogeometric analysis (IGA), this method can reduce the computational scale of the solid part and eliminate the

It will be practically useful to know the mechanical properties of granular materials by only taking a photo of particles. This study attempts to deal with this challenge by developing a novel deep learning-based modelling strategy. In this strategy, the convolutional neural network (CNN) as image identification algorithm is first used to extract the particle information (particle size distribution

In this paper, we introduce a pressure-robust virtual element method for the Stokes problem on convex polygonal meshes. The method is based on the lowest order virtual element, in which the degrees of freedom for the velocity are simply given by the evaluations of velocity at the mesh vertices and the average values of normal velocity across the mesh edges, and the pressure is approximated by piecewise

This paper presents an extended polynomial chaos formalism for epistemic uncertainties and a new framework for evaluating sensitivities and variations of output probability density functions (PDF) to uncertainty in probabilistic models of input variables. An ”extended” polynomial chaos expansion (PCE) approach is developed that accounts for both aleatory and epistemic uncertainties, modeled as random

Multiscale models based on representative volume elements (RVEs) might help unraveling the ways in which macroscopic loadings affect the microstructure of tissues reinforced by collagen fibers, and vice versa. Tissues such as arteries, however, are characterized by a significant collagen dispersion. Therefore, many fibers have to be included in the RVE to achieve a representative geometrical model

The level set method can express smooth boundaries in structural topology optimization with the level set function’s zero-level contour. However, most applications still use rectangular/hexahedral mesh in finite element analysis, which results in zig-zag interfaces between the void and solid phases. We propose a reaction diffusion-based level set method using the adaptive triangular/tetrahedral mesh

In this paper, we propose a multiscale method for solving the Darcy flow of a single-phase fluid in two-dimensional fractured porous media. We consider a discrete fracture-matrix (DFM) model that treats fractures as one-dimensional objects, and flows in both the matrix and fractures respect the Darcy’s law. A multipoint flux mixed finite element (MFMFE) method with the broken Raviart–Thomas (RT12)

We propose a new approach for data-driven automated discovery of isotropic hyperelastic constitutive laws. The approach is unsupervised, i.e., it requires no stress data but only displacement and global force data, which are realistically available through mechanical testing and digital image correlation techniques; it delivers interpretable models, i.e., models that are embodied by parsimonious mathematical

The ultimate strength prediction of textile composite materials requires high-fidelity FE modeling with information-passing multiscale schemes and damage initiation and propagation algorithms. The numerical demand of this procedure together with the complexity of the observed response surface, hampers the quantification of uncertainties contributing to the scatter of strength values. This study proposes

The microstructural evolution in solids is driven by different factors, such as entropy density, the chemical potential and mechanical energy. The mechanical energy density propagates along with the propagation of the mechanical wave, which has a great influence on the rapid solid-state phase transformation, such as the martensitic transformation. In order to determine the mechanical contribution to

We present a class of high-order finite element methods that can conserve the linear and angular momenta as well as the energy for the equations of linear elastodynamics. These methods are devised by exploiting and preserving the Hamiltonian structure of the equations of linear elastodynamics. We show that several mixed finite element, discontinuous Galerkin, and hybridizable discontinuous Galerkin

With growing application of additive manufacturing (AM) in industry, simulation of transient heat conduction during the AM process has drawn increasing attention. However, detailed simulation with acceptable accuracy is extremely time consuming because of the large range of time scales involved in the problem. In this work, a multi-time stepping method using different timesteps in multiple subdomains

The capability to incorporate moving geometric features within models for complex simulations is a common requirement in many fields. Fluid mechanics within aeronautical applications, for example, routinely feature rotating (e.g. turbines, wheels and fan blades) or sliding components (e.g. in compressor or turbine cascade simulations). With an increasing trend towards the high-fidelity modelling of

In this work, we propose a two-way coupling technique between a total Lagrangian smoothed particle hydrodynamics (SPH) method for Solid Mechanics and the explicit incompressible SPH (EISPH) to simulate fluid–structure interaction problems. In the solid part, the total Lagrangian framework guarantees that the particle distribution keep stable to correctly calculate the deformation gradient and thus

This paper aims at developing an efficient preconditioned iterative domain decomposition (DD) method for the sampling of linear stochastic elliptic equations. To this end, we consider a non-overlapping DD method resulting in a Symmetric Positive Definite (SPD) Schur system for almost every sampled problem. To accelerate the iterative solution of the Schur system, we propose a new stochastic preconditioning

Laser-based metal processing including welding and three dimensional printing, involves localized melting of solid or granular raw material, surface tension-driven melt flow and significant evaporation of melt due to the applied very high energy densities. The present work proposes a weakly compressible smoothed particle hydrodynamics formulation for thermo-capillary phase change problems involving

In many contexts, it is of interest to assess the impact of selected parameters on the failure probability of a physical system. To this end, one can perform conditional reliability analysis, in which the probability of failure becomes a function of these parameters. Computing conditional reliability requires recomputing failure probabilities for a sample sequence of the parameters, which strongly

This paper presents an interpolation scheme applicable to meshless/mesh-based methods. The formulation is capable of generating ordinary as well as non-negative shape functions in a unified style. The flexibility of producing either strong Kronecker-delta in the domain or weak Kronecker-delta property at the boundaries is one of the method’s prominent features. Both convex and non-convex boundaries

Lattice-type structures can provide a combination of stiffness with light weight that is desirable in a variety of applications. Design optimization of these structures must rely on approximations of the governing physics to render solution of a mathematical model feasible. In this paper, we propose a topology optimization (TO) formulation that approximates the governing physics using component-wise

Mathematical modeling of cardiac function can provide augmented simulation-based diagnosis tools for complementing and extending human understanding of cardiac diseases, which represent the most common cause of worldwide death. As the realistic starting-point for developing a unified meshless approach for total heart modeling, in this paper we propose an integrative smoothed particle hydrodynamics

There is currently an increasing interest in developing efficient solvers for variational phase-field models of brittle fracture. The governing equations for this problem originate from a constrained minimization of a non-convex energy functional, and the most commonly used solver is a staggered solution scheme. This is known to be robust compared to the monolithic Newton method, however, the staggered

We consider the numerical approximations to simulate the active colloids dynamic process. One linear, decoupled, mass-preserving scheme is proposed, in which mass-preserving characteristic finite element method is utilized for the density equation of active colloids, and the traditional Galerkin finite element methods is used for the polarization dynamics equation and self-secreted chemical density

In the reproducing kernel particle method (RKPM), the approximation is achieved through construction of shape functions in the physical domain and the interaction of neighbouring nodes. When modelling large deformation problems, Lagrangian and semi-Lagrangian formulations have been proposed, where the RK functions are evaluated in the reference initial coordinates and in the current configuration,

A numerical approach based on the hidden physics model to estimate the model parameters of elastic wave equations with the sparse and noisy data is presented in this paper. Through discretizing the time derivatives of elastic wave equations and placing the priors of the state variables as Gaussian process, the model parameters and structure of elastic wave equations are encoded in the kernel function

We present a consistent and efficient approach to the formulation of geometric nonlinear finite elements for isogeometric analysis (IGA) and isogeometric B-Rep analysis (IBRA) based on the adjoint method. IGA elements are computationally expensive, especially for high polynomial degrees. Using the method presented here enables us to reduce this disadvantage and develop a methodical framework for the

The prediction of failure processes in polymer nanocomposites requires accurately capturing different factors such as damage mechanisms, and temperature- and rate-dependent material characteristics. This work presents the development of a finite deformation phase-field fracture model to analyze the thermo-viscoelastic behavior of boehmite nanoparticle/epoxy nanocomposites. To characterize the rate-dependent

We present a virtual element method (VEM) for the numerical approximation of the electromagnetics subsystem of the resistive magnetohydrodynamics (MHD) model in two spatial dimensions. The major advantages of the virtual element method include great flexibility of polygonal meshes and automatic divergence-free constraint on the magnetic flux field. In this work, we rigorously prove the well-posedness

A distinguishing feature of lipid (bilayer) membranes is their in-plane fluidity caused by free-flowing lipid molecules on the membrane surface. In continuum models for lipid membranes (e.g., the Helfrich–Canham model), fluidity manifests as invariance of the free energy to change in parametrization of the reference surface; a property termed reparametrization invariance. Two different parametric equations

Mechanical metamaterials that achieve ultimate anisotropic stiffness are highly desired in engineering practice. Particularly, the plate microstructures (PM) that are comprised of 6 sets of flat plates have been proved to attain any extreme stiffness in theory. In this paper, we solve two remaining issues for design of optimal PMs. On one hand, we investigate the stiffness optimality of three PMs that

Substitution of well-grounded theoretical models by data-driven predictions is not as simple in engineering and sciences as it is in social and economic fields. Scientific problems suffer many times from paucity of data, while they may involve a large number of variables and parameters that interact in complex and non-stationary ways, obeying certain physical laws. Moreover, a physically-based model

The paper presents a level set based topology optimization method for unidirectional phononic structures with finite layers of lattice cells. Boundary element method(BEM) is employed as the numerical approach to solve the acoustic problems governed by Helmholtz equation. A sized reduced coefficient matrix is derived due to the iteration forms for input and output quantities on the periodic boundary

We present a paradigm for developing thermodynamical consistent numerical algorithms for thermodynamically consistent partial differential equation (TCPDE) systems, called the supplementary variable method (SVM). We add a proper number of supplementary variables to the TCPDE system coupled with its energy equation and other deduced equations through perturbations to arrive at a consistent, well-determined

The estimation of the failure probability for complex systems is a crucial issue for sustainability. Reliability analysis methods are needed to be developed to provide accurate estimations of the safety levels for the complex systems and structures of today. In this paper, a novel hybrid framework for the reliability analysis of engineering systems and structures is extended to reduce the computational

This paper presents a new stochastic finite element method for computing structural stochastic responses of linear problems. The method provides a new expansion of stochastic response and decouples the stochastic response into a combination of a series of deterministic responses with random variable coefficients. A dedicated iterative algorithm is proposed to compute the deterministic responses and

Strong imposing Dirichlet boundary conditions remain a challenge for eXtended Finite Element Methods (XFEMs) or eXtended Isogeometric Analysis (XIGA) of discontinuous problems. Moreover, the physical meaning of the additional Degrees of Freedom (DOFs) in the displacement expression of XFEMs or XIGA is not clarified. To address these issues, we proposed a new method that combines XIGA and B++ splines

This paper presents a geometrically exact beam finite element for curved and twisted thin-walled bars undergoing large displacements and finite rotations, combined with cross-section in-plane and out-of-plane (warping) deformation. The underlying formulation is based on a previous work by the authors Gonçalves et al. (2010), which is now improved and extended for the pre-curved/twisted case. Cross-section

We use refined isogeometric analysis (rIGA) to solve generalized Hermitian eigenproblems (Ku=λMu). rIGA conserves the desirable properties of maximum-continuity isogeometric analysis (IGA) while it reduces the solution cost by adding zero-continuity basis functions, which decrease the matrix connectivity. As a result, rIGA enriches the approximation space and reduces the interconnection between degrees

The scaled boundary finite element method (SBFEM) is capable of generating polyhedral elements with an arbitrary number of surfaces. This salient feature significantly alleviates the meshing burden being a bottleneck in the analysis pipeline in the standard finite element method (FEM). In this paper, we implement polyhedral elements based on the SBFEM into the commercial finite element software ABAQUS

In the past few decades, the weighted essentially non-oscillatory (WENO) scheme has been widely used in mesh-based methods and has achieved great success, but its application to the smoothed particle hydrodynamics (SPH) is still limited. In this paper, a simple and accurate implementation of the WENO scheme to the SPH method is proposed for solving compressible flows with discontinuities and small-scale