Diffusion-type problems in (nearly) unbounded domains play important roles in various fields of fluid dynamics, biology, and materials science. The aim of this paper is to construct accurate absorbing boundary conditions (ABCs) suitable for classical (local) as well as nonlocal peridynamic (PD) diffusion models. The main focus of the present study is on the PD diffusion formulation. The majority of

The processes in which cardiac cells are reorganized for tissue regeneration is still unclear. It is a complicated process that is orchestrated by many factors such as mechanical, chemical, thermal, and/or electrical cues. Studying and optimizing these conditions in-vitro is complicated and time costly. In such cases, in-silico numerical simulations can offer a reliable solution to predict and optimize

The paper deals with the gradient based shape optimization of the biaxial X0-specimen, which has been introduced and examined in various papers, under producibility restrictions and the related experimental verification. The original, engineering based design of the X0-specimen has been applied successfully to different loading conditions persisting the question if relevant stress states could be reached

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

This paper presents a Lagrangian approach to simulating multibody dynamics in a tensegrity framework with an ability to tackle holonomic constraint violations in an energy-preserving scheme. Governing equations are described using non-minimum coordinates to simplify descriptions of the structure’s kinematics. To minimize constraint drift arising from this redundant system, the direct correction method

Magnetostrictive materials that couple mechanical and magnetic domains have been widely explored for use in sensors and actuators. These materials often exhibit a nonlinear material response under applied magnetic fields, which limits the use of linear constitutive models. Furthermore, the nonlinear constitutive relations tend to be implicit in nature. Hence, a finite element scheme that can handle

Phase-field models for brittle fracture in anisotropic materials result in a fourth-order partial differential equation for the damage evolution. This necessitates a \(\mathcal {C}^1\) continuity of the basis functions. Here, Powell-Sabin B-splines, which are based on triangles, are used for the approximation of the field variables as well as for the the description of the geometry. The use of triangles

In the original publication of the article, the sentence “If we assume that everyone in the beginning is susceptible (S(t = 0) = 1).

Fractional diffusion equations have been widely used to accurately describe anomalous solute transport in complex media. This paper proposes a local meshless method named the generalized finite difference method (GFDM), to solve a class of multidimensional space fractional diffusion equations (SFDEs) in a finite domain. In the GFDM, the spatial derivative terms are expressed as linear combinations

In this paper we alleviate limitations of the conventional embedded reinforcement formulation for applications with dense fiber contents. We demonstrate that by condensing the fiber degrees of freedom during the assembly stage, the condition number of the resultant stiffness matrix is effectively reduced and the use of iterative solvers is facilitated even without preconditioning. Numerical benchmarks

A large number of massive crystal-plasticity-finite-element (CPFE) simulations are performed and post-processed to reveal the effects of element type and mesh resolution on accuracy of predicted mechanical fields over explicit grain structures. A CPFE model coupled with Abaqus/Standard is used to simulate simple-tension and simple-shear deformations to facilitate such quantitative mesh sensitivity

In this paper layered shells subjected to static loading are considered. The displacements of the Reissner–Mindlin theory are enriched by a an additional part. These so-called fluctuation displacements include warping displacements and thickness changes. They lead to additional terms for the material deformation gradient and the Green–Lagrangian strain tensor. Within a nonlinear multi-field variational

In this work, a new thermo-mechanical formulation for the conventional and localizing gradient damage method is proposed. The proposed formulation is based on the generalized micromorphic theory, which accounts for the underlying fracture processes at the micro-level. The thermal and mechanical effects on the fracture response are incorporated in the formulation through three primary variables. These

The work is devoted to a coupling method for the finite element method (FEM) and the distance potential discrete element method. In this work, a well-defined distance potential function is developed. Meanwhile, a holonomic and precise algorithm for contact interaction is established, accounting for the influence of the tangential contact force. In addition, the measurement of deformation behaviors

We consider the numerical simulation of the left ventricle of the human heart by a hyperelastic fiber reinforced transversely isotropic model. This is an important model problem for the understanding of the mechanical properties of the human heart but its calculation is very time consuming because the lack of fast, scalable method that is also robust with respect to the model parameters. In this paper

We show that the logarithmic (Hencky) strain and its derivatives can be approximated, in a straightforward manner and with a high accuracy, using Padé approximants of the tensor (matrix) logarithm. Accuracy and computational efficiency of the Padé approximants are favourably compared to an alternative approximation method employing the truncated Taylor series. As an application, Hencky-type hyperelasticity

The article “The computational framework for continuum-kinematics-inspired peridynamics”.

Non-intrusive methods have been used since two decades to derive reduced-order models for geometrically nonlinear structures, with a particular emphasis on the so-called STiffness Evaluation Procedure (STEP), relying on the static application of prescribed displacements in a finite-element context. We show that a particularly slow convergence of the modal expansion is observed when applying the method

Selective laser melting (SLM) has gained large interest due to advanced manufacturing possibilities. However, the growing potential also necessitates reliable predictions of structures in particular regarding their long-term behaviour. The constitutive and structural response is thereby challenging to reproduce, due to the complex material behaviour. This motivates the aims of this contribution: To

We present computational flow analysis of a vertical-axis wind turbine (VAWT) that has been proposed to also serve as a tsunami shelter. In addition to the three-blade rotor, the turbine has four support columns at the periphery. The columns support the turbine rotor and the shelter. Computational challenges encountered in flow analysis of wind turbines in general include accurate representation of

X-ray tomography techniques give researchers the full access to material inner structures. With such ample information, employing numerical simulation on real material images becomes more and more common. Material behavior, especially, of heterogeneous materials, e.g. polycrystalline, composite, can be observed at the microscopic scale with the computed tomography (CT) techniques. In this work, an

A key strategy to prevent a local outbreak during the COVID-19 pandemic is to restrict incoming travel. Once a region has successfully contained the disease, it becomes critical to decide when and how to reopen the borders. Here we explore the impact of border reopening for the example of Newfoundland and Labrador, a Canadian province that has enjoyed no new cases since late April, 2020. We combine

The COVID-19 pandemic has captivated scientific activity since its early days. Particular attention has been dedicated to the identification of underlying dynamics and prediction of future trend. In this work, a switching Kalman filter formalism is applied on dynamics learning and forecasting of the daily new cases of COVID-19. The main feature of this dynamical system is its ability to switch between

A multiscale clustering-based topology optimization for thermo-elastic lattice structures is studied based on the extended multiscale finite element method (EMsFEM). The strain energy of thermo-elastic lattice structures is chosen as the objective function. The microstructural configuration and the macrostructural distribution of the thermo-elastic lattice material are designed through topology optimization

In this paper, we derive an analytical expression for reproducing kernel particle method (RKPM) shape functions. Based on this, we propose a necessary and sufficient stability condition for general RKPM in arbitrary function space, and illustrate with degenerate cases. By selecting proper basis vectors and the support of the kernel functions, we demonstrate that the RKPM framework allows generating

The article “Non-localised contact between beams with circular and elliptical cross-sections”, written by “Marco Magliulo, Jakub Lengiewicz, Andreas Zilian and Lars A. A. Beex”, was originally published Online First without open access. After publication in volume 65, issue 5, page 1247–1266 the authors decided to opt for Open Choice and to make the article an open access publication. Therefore, the

Marine gas hydrate is an important energy source while its extraction may induce environmental problems such as subsea landslide, which is usually challengeable for numerical simulation due to the marine environment with high pressure and the existence of gas hydrate. Smoothed particle hydrodynamics (SPH) is a Lagrangian particle method which is attractive in modeling problems with large deformations

The virtual element method is a lively field of research, in which considerable progress has been made during the last decade and applied to many problems in physics and engineering. The method allows ansatz function of arbitrary polynomial degree. However, one of the prerequisite of the formulation is that the element edges have to be straight. In the literature there are several new formulations

The outbreak of COVID-19 in 2020 has led to a surge in interest in the research of the mathematical modeling of epidemics. Many of the introduced models are so-called compartmental models, in which the total quantities characterizing a certain system may be decomposed into two (or more) species that are distributed into two (or more) homogeneous units called compartments. We propose herein a formulation

We extend the classical SIR model of infectious disease spread to account for time dependence in the parameters, which also include diffusivities. The temporal dependence accounts for the changing characteristics of testing, quarantine and treatment protocols, while diffusivity incorporates a mobile population. This model has been applied to data on the evolution of the COVID-19 pandemic in the US

A multiscale crack band model is proposed to alleviate spurious mesh size dependence in the solution for a strain softening constitutive model. A continuum damage mechanics-based material model for the constituent phases of a carbon fiber reinforced polymer (CFRP) based composite material is applied to the Eigenstrain based Reduced-order Homogenization framework for multiscale modeling. This paper

Phase-field methods for fracture have been integrated with plasticity for better describing constitutive behaviours. In most of the previous phase-field models, however, the length-scale parameter must be interpreted as a material property in order to match the material strength in experiments. This study presents a phase-field model for fracture coupled with plasticity for quasi-brittle materials

A summary is given of the mechanical characteristics of virus contaminants and the transmission via droplets and aerosols. The ordinary and partial differential equations describing the physics of these processes with high fidelity are presented, as well as appropriate numerical schemes to solve them. Several examples taken from recent evaluations of the built environment are shown, as well as the

The scaled boundary finite element method (SBFEM) has recently been employed as an efficient tool to model three-dimensional structures, in particular when the geometry is provided as a voxel-based image. To this end, an octree decomposition of the computational domain is deployed, and each cubic cell is treated as an SBFE subdomain. The surfaces of each subdomain are discretized in the finite element

The COVID-19 pandemic has led to an unprecedented world-wide effort to gather data, model, and understand the viral spread. Entire societies and economies are desperate to recover and get back to normality. However, to this end accurate models are of essence that capture both the viral spread and the courses of disease in space and time at reasonable resolution. Here, we combine a spatially resolved

The presence of uncertainty in material properties and geometry of a structure is ubiquitous. The design of robust engineering structures, therefore, needs to incorporate uncertainty in the optimization process. Stochastic gradient descent (SGD) method can alleviate the cost of optimization under uncertainty, which includes statistical moments of quantities of interest in the objective and constraints

Peridynamics (PD) is a non-local continuum formulation. The original version of PD was restricted to bond-based interactions. Bond-based PD is geometrically exact and its kinematics are similar to classical continuum mechanics (CCM). However, it cannot capture the Poisson effect correctly. This shortcoming was addressed via state-based PD, but the kinematics are not accurately preserved. Continuum

Throughout the past six months, no number has dominated the public media more persistently than the reproduction number of COVID-19. This powerful but simple concept is widely used by the public media, scientists, and political decision makers to explain and justify political strategies to control the COVID-19 pandemic. Here we explore the effectiveness of political interventions using the reproduction

In this paper we introduce a method to compare sets of full-field data using Alpert tree-wavelet transforms. The Alpert tree-wavelet methods transform the data into a spectral space allowing the comparison of all points in the fields by comparing spectral amplitudes. The methods are insensitive to translation, scale and discretization and can be applied to arbitrary geometries. This makes them especially

Surgical implants, known as Tissue Engineered Nerve Guides (TENGs) are often inserted to provide alignment and mechanical support to broken or damaged nerves. These implants are designed to be poroelastic and biodegradable, and the ideal rate of degradation would be that equal to the rate of regrowth of the recovering nerve. Inspired by the design of these TENGs, we develop a mixture theory based mathematical

An isogeometric approach for solving the Laplace–Beltrami equation on a two-dimensional manifold embedded in three-dimensional space using a Galerkin method based on Catmull–Clark subdivision surfaces is presented and assessed. The scalar-valued Laplace–Beltrami equation requires only \(C^0\) continuity and is adopted to elucidate key features and properties of the isogeometric method using Catmull–Clark

In this work, we propose a parameter estimation framework for fracture propagation problems. The fracture problem is described by a phase-field method. Parameter estimation is realized with a Bayesian approach. Here, the focus is on uncertainties arising in the solid material parameters and the critical energy release rate. A reference value (obtained on a sufficiently refined mesh) as the replacement

The pandemic of 2020 has led to a huge interest of modeling and simulation of infectious diseases. One of the central questions is the potential infection zone produced by a cough. In this paper, mathematical models are developed to simulate the progressive time-evolution of the distribution of locations of particles produced by a cough. Analytical and numerical studies are undertaken. The models ascertain

This paper develops a unified phase field model for simulating finite deformation crack evolution and interfacial decohesion in multi-phase elastic materials. Crack propagation is formulated using a phase field model, in which the order parameter \(s=1\) corresponds to the crack topology. The phase field model at the interface is enhanced with cohesive zone characteristics through a cohesive potential

This article is dedicated to the analysis of visco-plastic and damageable structures submitted to thermomechanical loadings embedding some uncertain parameters. In particular, complex time evolutions of the loadings are considered, at two different time scales. An homogenized-in-time model is used to provide kind of a surrogate model for damage evolution analysis. Then a stochastic analysis using polynomial

An adaptive relocation strategy for a coupled XFEM–Peridynamic (PD) model is introduced. The motivation is to enhance the efficiency of the coupled model and demonstrate its applicability to complex brittle fracture problems. The XFEM and PD approximation domains can be redefined during the simulation, to ensure that the computationally expensive PD model is applied only where needed. To this end a

The dynamic contact angle of a gas–liquid–solid system depends on the contact line velocity and ignoring this effect could lead to inaccurate estimations of the capillary pressures in microporous media. While most existing coarse-grained molecular dynamics (CGMD) models use one particle to represent a few molecules, we present a novel CGMD framework to model microscale CO2/water flows in silica with

Poisson Voronoi (PV) tessellations as artificial microstructures are widely used in investigations of material deformation behaviors. However, a PV structure usually describes a relative homogeneous field. This work presents a simple numerical method for generating 2D/3D artificial microstructures based on hierarchical PV tessellations. If grains/particles of a phase cover a large size span, the concept

Predictive analysis of poroelastic materials typically require expensive and time-consuming multiscale and multiphysics approaches, which demand either several simplifications or costly experimental tests for model parameter identification.This problem motivates us to develop a more efficient approach to address complex problems with an acceptable computational cost. In particular, we employ artificial

This work presents the development of the Particle Finite Element Method (PFEM) for the modelling of 3D solid mechanics problems under cutting conditions. The study and analysis of numerical models reproducing the cut of a material is a matter of interest in several areas; namely, the improvement of the material properties, the optimization of the process and tool geometries and the prediction of unexpected

Two mixed meshless collocation methods for solving problems by considering a linear gradient elasticity theory of the Helmholtz type are proposed. The solution process is facilitated by employing operator-split procedures, splitting the original 4th-order problem into two uncoupled second-order sub-problems, which are then solved in a staggered manner by applying the mixed meshless local Petrov–Galerkin

This paper extends the nonsmooth Relaxed Variational Approach (RVA) to topology optimization, proposed by the authors in a preceding work, to the solution of thermal optimization problems. First, the RVA topology optimization method is briefly discussed and, then, it is applied to a set of representative problems in which the thermal compliance, the deviation of the heat flux from a given field and

A goal-oriented a-posteriori error estimator is developed for transient coupled thermo-hydro-mechanical (THM) parametric problems solved with a reduced basis approximation. The estimator assesses the error in some specific Quantity of Interest (QoI). The goal-oriented error estimate is derived based on explicitly-computed weak residual of the primal problem and implicitly-computed adjoint solution

For wind turbines operating in cold weather conditions, ice accretion is an established issue that remains an obstacle in effective turbine operation. While the aerodynamic performance of wind turbine blades with ice accretion has received considerable research attention, few studies have investigated the structural impact of blade ice accretion. This work proposes an adaptable projection-based method

In this contribution, the phase change of unvulcanized to vulcanized rubber is described by a thermo-mechanical material model within the finite element method (FEM) framework. Before the vulcanization process (curing), rubber exhibits an elasto-visco-plastic behaviour with significant irreversible deformations without a distinct yield surface. After exposing rubber to high temperature, the molecular

In this study, we present a novel finite element approach to simulate crack propagation in shell structures. A local spider-web mesh is placed at the tip of a crack propagating through a global background mesh. Interface shell elements with assumed natural strains are used to connect a non-matching interface between the background mesh and the local spider-web mesh. Interface shell elements are also

In the framework of efficient partitioned numerical schemes for simulating multiphysics PDE problems, we propose using intergrid transfer operators based on radial basis functions to accurately exchange information among different PDEs defined in the same computational domain. Different (potentially non-nested) meshes can be used for the space discretization of the PDEs. The projection of the (primary)

Thin membranes are notoriously sensitive to instabilities under mechanical loading, and need sophisticated analysis methods. Although analytical results are available for several special cases and assumptions, numerical approaches are normally needed for general descriptions of non-linear response and stability. The paper uses the case of a thin spherical hyper-elastic membrane subjected to internal

In this work, we present a scalable and efficient parallel solver for the partitioned solution of fluid–structure interaction problems through multi-code coupling. Two instances of an in-house parallel software, TermoFluids, are used to solve the fluid and the structural sub-problems, coupled together on the interface via the preCICE coupling library. For fluid flow, the Arbitrary Lagrangian–Eulerian