Constitutive modeling is a cornerstone for stress analysis of mechanical behaviors of biological soft tissues. Recently, it has been shown that machine learning (ML) techniques, trained by supervised learning, are powerful in building a direct linkage between input and output, which can be the strain and stress relation in constitutive modeling. In this study, we developed a novel generic physics-informed

In this paper, we propose a method that employs deep learning, an artificial intelligence technique, to generate stiffness matrices of finite elements. The proposed method is used to develop 4- and 8-node 2D solid finite elements. The deep learned finite elements practically pass the patch tests and the zero energy mode tests. Through various numerical examples, the performance of the developed elements

Understanding the outbreak dynamics of the COVID-19 pandemic has important implications for successful containment and mitigation strategies. Recent studies suggest that the population prevalence of SARS-CoV-2 antibodies, a proxy for the number of asymptomatic cases, could be an order of magnitude larger than expected from the number of reported symptomatic cases. Knowing the precise prevalence and

A generalized bond-based micropolar peridynamic model is proposed to simulate the nonlinear deformation and mixed-mode crack propagation of quasi-brittle materials under arbitrary dynamic loads. The mechanical behaviors of the material points are reformulated by incorporating the bond tension–rotation–shear coupling effects, which makes the model suitable for complex discontinuous problems in both

In this work, porosity-dependent nonlinear large-amplitude oscillation responses of rectangular microplates with and without a central square cutout made of a porous functionally graded material (PFGM) is explored using modified couple stress theory of elasticity (MCSTE). The associated nonlinear size-dependent modified couple stress-based differential motion equations are obtained based on third-order

A dual peridynamics (PD) for brittle fracture is implemented in the commercial software Abaqus by means of UEL/VUEL and UMAT/VUMAT subroutines, thereby, the peridynamic finite element method (PDFEM) will come into being. To this end, the concept of the peridynamic node and element is defined, subsequently, the peridynamic element internal force vector and mass matrix for the explicit PDFEM and the

The microstructural configuration of a material affects its macroscopic viscoelastic behavior, which suggests that materials can be engineered to achieve a desired viscoelastic behavior over a range of frequencies. To this end, we leverage topology optimization to find the optimized topology of a multi-phase viscoelastic composite to tailor its energy dissipation behavior as a function of frequency

In this paper, we perform non-linear minimization using the Hybridizable Discontinuous Galerkin method (HDG) for the discretization of the forward problem, and implement the adjoint-state method for the efficient computation of the functional derivatives. Compared to continuous and discontinuous Galerkin discretizations, HDG reduces the computational cost by using the numerical traces for the global

This paper proposes a novel computational framework for the solution of geometrically parametrised flow problems governed by the Stokes equation. The proposed method uses a high-order hybridisable discontinuous Galerkin formulation and the proper generalised decomposition rationale to construct an off-line solution for a given set of geometric parameters. The generalised solution contains the information

The virtual element method (VEM) for curved edges with applications to contact mechanics is outlined within this work. VEM allows the use of non-matching meshes at interfaces with the advantage that these can be mapped to a simple node-to-node contact formulation. To account for exact approximation of complex geometries at interfaces, we developed a VEM technology for contact that considers curved

A scheme for the solution of fluid–structure interaction (FSI) problems with weakly compressible flows is proposed in this work. A novel hybridizable discontinuous Galerkin (HDG) method is derived for the discretization of the fluid equations, while the standard continuous Galerkin (CG) approach is adopted for the structural problem. The chosen HDG solver combines robustness of discontinuous Galerkin

We present a new data-driven paradigm for variational brittle fracture mechanics. The fracture-related material modeling assumptions are removed and the governing equations stemming from variational principles are combined with a set of discrete data points, leading to a model-free data-driven method of solution. The solution at a given load step is identified as the point within the data set that

This paper presents an adjoint-based method for solving optimization problems involving pressurized membrane structures subject to external pressure loads. Shape optimization of pressurized membranes is complicated by the fact that, lacking bending stiffness, their three-dimensional shape must be sustained by the internal pressure of the inflation medium. The proposed method treats the membrane structure

Metamaterials are emerging as a new paradigmatic material system to render unprecedented and tailorable properties for a wide variety of engineering applications. However, the inverse design of metamaterial and its multiscale system is challenging due to high-dimensional topological design space, multiple local optima, and high computational cost. To address these hurdles, we propose a novel data-driven

In this paper, we develop the mixed variational formulation with independent displacement, rotation and stress fields based on the work of Hughes and Brezzi (1989). However, we further suppress rotation field to obtain element superior performance for classical continuum case with hybrid-stress interpolation. The lowest order Whitney’s interpolation or Raviart–Thomas vector space is employed to discretize

Topology optimization of dynamic acoustic–mechanical structures is challenging due to the interaction between the acoustic and structural domains and artificial localized vibration modes of structures. This paper presents a floating projection topology optimization (FPTO) method based on the mixed displacement/pressure (u/p) finite element formulation and the ersatz material model. The former is able

A data-driven framework is proposed towards the end of predictive modeling of complex spatio-temporal dynamics, leveraging nested non-linear manifolds. Three levels of neural networks are used, with the goal of predicting the future state of a system of interest in a parametric setting. A convolutional autoencoder is used as the top level to encode the high dimensional input data along spatial dimensions

In this paper, we consider the recently introduced EMAC formulation for the incompressible Navier–Stokes (NS) equations, which is the only known NS formulation that conserves energy, momentum and angular momentum when the divergence constraint is only weakly enforced. Since its introduction, the EMAC formulation has been successfully used for a wide variety of fluid dynamics problems. We prove that

We discuss two linearization and domain decomposition methods for mathematical models for two-phase flow in a porous medium. The medium consists of two adjacent regions with possibly different parameterizations. The model accounts for non-equilibrium effects like dynamic capillarity and hysteresis. The θ-scheme is adopted for the temporal discretization of the equations yielding nonlinear time-discrete

Mechanical metamaterials feature engineered microstructures designed to exhibit exotic, and often counter-intuitive, effective behaviour such as negative Poisson’s ratio or negative compressibility. Such a specific response is often achieved through instability-induced transformations of the underlying periodic microstructure into one or multiple patterning modes. Due to a strong kinematic coupling

In order to simulate the Kaufman-type discharge problems, a fully decoupled iterative method with anisotropic immersed finite elements on Cartesian meshes is proposed, especially for a three-dimensional (3D) non-axisymmetric anisotropic hybrid model which is more difficult than the axisymmetric or isotropic models. The classical hybrid model, which describes the important plasma distribution of the

In this paper, we propose and investigate a divergence-free reconstruction of the nonconforming virtual element for the Stokes problem. By constructing the computable Raviart–Thomas-like interpolation operator, we guarantee the independence between the velocity error estimation |u−uh|1,h and the continuous pressure p, as it happens for the divergence-free flow solver. Moreover, this modified scheme

This paper proposes a first-order Generalized/eXtended Finite Element Method (G/XFEM) for 2-D and 3-D linear elastic fracture mechanics problems. The conditioning of the method is of the same order as the standard FEM and it is robust with respect to the position of the mesh relative to 2-D or 3-D fractures. The method achieves an optimal rate of convergence in energy norm even when the solution of

Many quantities of interest (qois) arising from differential-equation-centric models can be resolved into functions of scalar fields. Examples of such qois include the lift over an airfoil or the displacement of a loaded structure; examples of corresponding fields are the static pressure field in a computational fluid dynamics solution, and the strain field in the finite element elasticity analysis

In this paper, a fully Lagrangian formulation for solving rigid–liquid coupling system with free surface is proposed, in which the spatial absolute nodal coordinates and the pressure of liquid are taken as the independent variables, combining the stabilized particle finite element method and multibody algorithms for unified modeling. The virtual contact elements generated in the remeshing process are

We propose a new algorithm to design lightweight and stiff structures exhibiting free-form features, with the aim of minimizing the compliance under a volume inequality constraint. The procedure is based on the coupling of geometric shape optimization with topology optimization. We start from a full-mass body corresponding to a given material occupying entirely the initial design domain. The first

Fatigue crack growth analysis using extended finite element method (XFEM) is an efficient way to predict the residual life of structures; however, when the structure parameters vary stochastically, it will be very hard to make accurate predictions. To bridge this research gap, this work proposed a data-driven learning algorithm to improve the prediction capacity of fatigue life by considering stochastic

Crack propagation is modelled in this contribution by combining different methods. The main idea is to use the newly developed virtual element method in combination with the phase-field methodology and a specific cutting technology. The idea is that the direction of a crack path can be easily predicted using the phase-field method. However this method needs a very fine mesh to resolve a real crack

This work presents the Griffith-type phase-field formation at large deformation in the framework of the adaptive edge-based smoothed finite element method (ES-FEM) for the first time. Therein the phase-field modeling of fractures has attracted widespread interest by virtue of its outstanding performance in dealing with complex cracks. The ES-FEM is an excellent member of the S-FEM family developed

We present novel H(div) and H1 liftings of given piecewise polynomials over a hierarchy of simplicial meshes, based on a global solve on the coarsest mesh and on local solves on patches of mesh elements around vertices on subsequent mesh levels. This in particular allows to lift a given algebraic residual. In connection with approaches lifting the total residual, we show how to obtain guaranteed, fully

The present work has been conducted in order to propose the extension of standard penalty and stabilization techniques to the improved element-free Galerkin (IEFG) method, for the numerical solution of incompressible fluid flow problems. In principle, the numerical procedures to be implemented in this communication have been conceived for finite element method (FEM)-based solutions, and these include

A pore scale numerical method dedicated to the simulation of heat transfer and associated thermo–hydro-mechanical couplings in granular media is described. The proposed thermo–hydro-mechanical approach builds on an existing hydro-mechanical model that employs the discrete element method for simulating the mechanical behavior of dense sphere packings and combines it with the finite volume method for

In this paper, an adaptive refinement technique using the scaled boundary finite element method (SBFEM) is proposed. The salient feature of this technique is that it is not required to regenerate the mesh for the whole model during the iterations. To this end, a local mesh refinement strategy is implemented based on a polytree algorithm in three dimensions, which can be applied to polyhedral elements

Porous infill structures have been widely studied and used in additive manufacturing because of their lightweight and excellent mechanical properties. However, without considering graded multi-material infill pattern, existed infill design methods have not yet fully tapped the potential of multiple materials in structural design. In this paper, a systematic multi-phase infill design method is proposed

In this paper, a mixed isogeometric analysis approach is developed to realize accurate and efficient simulations of the transient swelling of hydrogel strongly coupled with large deformation and fluid diffusion. In this method, the mixed isogeometric element is presented for the coupled multi-physics problems accompanied with the volumetric locking caused by the incompressibility of polymeric chains

Herein, we present a phase-field model and its efficient numerical method for incompressible single and binary fluid flows on arbitrarily curved surfaces in a three-dimensional (3D) space. An incompressible single fluid flow is governed by the Navier–Stokes (NS) equation and the binary fluid flow is governed by the two-phase Navier–Stokes–Cahn–Hilliard (NSCH) system. In the proposed method, we use

Uncertainty inadvertently exists in various stages of engineering system design, development, and operating conditions. During the system design and development stages, a design engineer encounters the reliability and robustness measures of a dynamic uncertain system. Due to the existence of dynamic uncertainties, incorporating the time-dependent reliability of an engineering system in reliability

This research work presents, within a unified and wave oriented variational framework, systematic development of upwind numerical fluxes for the space discontinuous Galerkin methods to model elastic wave propagation in multidimensional anisotropic media with discontinuous material properties. Both first-order velocity–stress and velocity–strain wave formulations are considered. The proposed approach

In this work, we present a novel Lagrange–Galerkin method for the resolution of the scalar pure-convection and convection-dominated diffusion equations in non-divergence-free velocity fields. The scheme has been formulated so that (i) time-integration is carried out by means of an arbitrary order backward differentiation formula, (ii) finite element space discretizations of any order can be employed

In variational phase-field modeling of brittle fracture, the functional to be minimized is not convex, so that the necessary stationarity conditions of the functional may admit multiple solutions. The solution obtained in an actual computation is typically one out of several local minimizers. Evidence of multiple solutions induced by small perturbations of numerical or physical parameters was occasionally

The propagation of cracks driven by a pressurized fluid emerges in several areas of engineering, including structural, geotechnical, and petroleum engineering. In this paper, we present a robust numerical framework to simulate fluid-driven fracture propagation that addresses the challenges emerging in the simulation of this complex coupled nonlinear hydro-mechanical response. We observe that the numerical

We present a machine learning approach that integrates geometric deep learning and Sobolev training to generate a family of finite strain anisotropic hyperelastic models that predict the homogenized responses of polycrystals previously unseen during the training. While hand-crafted hyperelasticity models often incorporate homogenized measures of microstructural attributes, such as the porosity or the

This research work introduces a novel phase-field thermo-hydro-mechanical (P-THM) modeling approach that allows to deeply understand and model the freezing–thawing cyclic process in a fluid-saturated porous medium. In this, a biphasic macroscopic, non-isothermal porous media model, augmented by the phase-field method (PFM), is applied to account for the temperature development, the interstitial pore-fluid

Shape-anisotropic granules and their surrounding interphase networks are significant constituents in granular materials. Structural and physical configurations of these constituents significantly affect the overall thermal performance of granular materials, specifically microstructure-dependent thermal conductive properties. It has been a key but unresolved issue how to quantitatively understand the

In this work, we modify a continuous Galerkin discretization of a scalar hyperbolic conservation law using new algebraic correction procedures. Discrete entropy conditions are used to determine the minimal amount of entropy stabilization and constrain antidiffusive corrections of a property-preserving low-order scheme. The addition of a second-order entropy dissipative component to the antidiffusive

Considering the high computation cost required in conventional computation fluid dynamic simulations, machine learning methods have been introduced to flow dynamic simulations in years, aiming on reducing CPU time. In this work, we propose a hybrid deep adversarial autoencoder (VAE-GAN) to integrate generative adversarial network (GAN) and variational autoencoder (VAE) for predicting parameterized

We propose a new ‘Bi-Reduced Space’ approach to solving 3D Variational Data Assimilation using Convolutional Autoencoders. We prove that our approach has the same solution as previous methods but has significantly lower computational complexity; in other words, we reduce the computational cost without affecting the data assimilation accuracy. We tested our proposal with data from a real-world application:

Additive manufacturing (AM) is an emerging technology that fuses deposited powder materials together layer-by-layer using a localized heat source to create an arbitrarily complex geometry. This technology is an inherently multiphysics problem, involving the simultaneous evolution of fluid flow, heat transfer, free surface, laser-material interaction and material phases including solid, liquid and gas

This article presents the first monolithic coupled numerical model for simulating proppant transport through a non-planar propagating hydraulic fracture. A fracture is propagated through a two-dimensional domain, driven by the flow of a proppant-laden slurry. Modeling of the slurry flow includes the effects of proppant bridging and the subsequent flow of fracturing fluid through the packed proppant

We present a computational framework for applying the phase-field approach to brittle fracture efficiently to complex shell structures. The momentum and phase-field equations are solved in a staggered scheme using isogeometric Kirchhoff–Love shell analysis for the structural part and isogeometric second- and fourth-order phase-field formulations for the brittle fracture part. For the application to

Reliability analysis for structural systems with multiple failure modes and expensive-to-evaluate simulations is challenging. In this paper, a new and efficient system reliability method is proposed based on the adaptive importance sampling and kriging models. The Metropolis–Hastings (M–H) algorithm is used to construct several Markov chains to fully explore complex failure regions. A number of Markov

It is known that spurious non-physical velocities can occur when one employs the finite element method for simulation of incompressible flows subjected to external forces. In presence of external body forces, the main reason for this is the incompressibility constraint that is satisfied only in a weak sense against test functions from the pressure function space. In case of the two-phase (incompressible)

A residual a-posteriori error estimate is used in conjunction with a q−adaptive procedure for selecting enrichment functions in the modelling of transient heat diffusion problems with the Generalized Finite Element Method (GFEM). The error estimate allows to assess local as well as global errors of the GFEM solutions and provides a tool to adaptively enrich the approximation space. With the proposed

Recently, the Shifted Boundary Method (SBM) was proposed within the class of unfitted (or immersed, or embedded) finite element methods. By reformulating the original boundary value problem over a surrogate (approximate) computational domain, the SBM avoids integration over cut cells and the associated problematic issues regarding numerical stability and matrix conditioning. Accuracy is maintained

Many important multi-component crystalline solids undergo mechanochemical spinodal decomposition: a phase transformation in which the compositional redistribution is coupled with structural changes of the crystal, resulting in dynamically evolving microstructures. The ability to rapidly compute the macroscopic behavior based on these detailed microstructures is of paramount importance for accelerating

In this paper, the virtual crack closure technique (VCCT), commonly used in the numerical finite element method (FEM), is for the first time reformulated in nonlocal peridynamic theory, and a new peridynamics-based virtual crack closure technique (PD_VCCT) is proposed for the energy release rate calculation in the framework of peridynamics. The mode I, mode II, and their mixed mode fracture cases are

In this paper, we formulate a time-dependent model for simulating surface plasmon polaritons (SPPs) in graphene. The stability for the governing equations of the model is established. Then we propose a time-domain finite element method for solving the system of the governing equations. The discrete stability similar to the continuous level is proved. Numerical results are presented to demonstrate the

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 representation of the strain rate, and, as a result, prevents

Over the years, Isogeometric Analysis has shown to be a successful alternative to the Finite Element Method (FEM). However, solving the resulting linear systems of equations efficiently remains a challenging task. In this paper, we consider a p-multigrid method, in which coarsening is applied in the spline degree p instead of the mesh width h, and compare it to h-multigrid methods. Since the use of

The free energy plays a fundamental role in theories of phase transformations and microstructure evolution. It encodes the thermodynamic coupling between different fields, such as mechanics and chemistry, within continuum descriptions of non-equilibrium materials phenomena. In mechano-chemically interacting materials systems, even consideration of only compositions, order parameters and strains results