A framework for damage modelling based on the fast Fourier transform (FFT) method is proposed to combine the variational phase-field approach with a cohesive zone model. This combination enables the application of the FFT methodology in composite materials with interfaces. The composite voxel technique with a laminate model is adopted for this purpose. A frictional cohesive zone model is incorporated

A numerical approach for modelling cavitating flows over moving hydrodynamic surfaces is presented. The operating fluid is modelled as an isothermal homogeneous mixture of water vapor and liquid phases. The flow field is governed by the Navier–Stokes equations along with a transport equation for the vapor volume fraction. The Arbitrary Lagrangian-Eulerian description of the continuum is adopted to

Several experimental investigations corroborate nanosized inclusions as being much more efficient reinforcements for strengthening polymers as compared to their microsized counterparts. The inadequacy of the standard first-order computational homogenization scheme, by virtue of lack of the requisite length scale to model such size effects, necessitates enhancements to the standard scheme. In this work

A correction to this paper has been published: https://doi.org10.1007/s00466-020-01970-7

In this paper, the dynamics of a 2D double emulsion under the combined effects of the electric field and shear flow are studied by using an incompressible smoothed particle hydrodynamics (ISPH) method. Six different systems are used, each corresponding to different electrical properties. The effects of capillary and electrical capillary numbers, and core to shell radius ratio on the deformation and

A novel phase-field model for ductile fracture is presented. The model is developed within a consistent variational framework in the context of finite-deformation kinematics. A novel coalescence dissipation introduces a new coupling mechanism between plasticity and fracture by degrading the fracture toughness as the equivalent plastic strain increases. The proposed model is compared with a recent alternative

A Correction to this paper has been published: https://doi.org/10.1007/s00466-019-01767-3

This paper presents an extended/generalized finite element method for bridging scales in linear elastodynamics in the absence of scale separation. More precisely, the GFEMgl framework is expanded to enable the numerical solution of multiscale problems through the automated construction of specially-tailored shape functions, thereby enabling high-fidelity finite element modeling on simple, fixed finite

For finite-strain plasticity with anisotropic yield functions and anisotropic hyperelasticity, we use the Kröner-Lee decomposition of the deformation gradient combined with a yield function written in terms of the Mandel stress. The source is here the right Cauchy-Green tensor provided by a FE discretization. For the integration of the flow law we adopt a scaled/squared series approximation of the

A Correction to this paper has been published: https://doi.org/10.1007/s00466-021-01990-x

This work develops a computational Digital-Twin framework to track and optimize the flow of solar power through complex, multipurpose, solar farm facilities, such as Agrophotovoltaic (APV) systems. APV systems symbiotically cohabitate power-generation facilities and agricultural production systems. In this work, solar power flow is rapidly computed with a reduced order model of Maxwell’s equations

This work presents a numerical study on the use of multi-resolution strategies for the computationally challenging problem of optimal design of high-resolution nonlinear electro-active shell-type devices using Topology Optimization methods. This paper puts forward the following novelties. First, it presents a tailor-made in-plane multi-resolution technique where a higher level of resolution for the

This paper describes the formulation and experimental testing of an estimation of submanifold models of animal motion. It is assumed that the animal motion is supported on a configuration manifold, Q, and that the manifold is homeomorphic to a known smooth, Riemannian manifold, S. Estimation of the configuration submanifold is achieved by finding an unknown mapping, \(\gamma \), from S to Q. The overall

The numerical assessment of the crack development in structures subjected to plastic deformations using a phase-field approach is investigated in the present study. By relying on distinctive features of phase-field diffusive crack concept, a recently-developed iterative staggered algorithm is employed for implementation of the overall system of equations, in which one can achieve results that are insensitive

A recently introduced representation by a set of Wang tiles—a generalization of the traditional Periodic Unit Cell-based approach—serves as a reduced geometrical model for materials with stochastic heterogeneous microstructure, enabling an efficient synthesis of microstructural realizations. To facilitate macroscopic analyses with a fully resolved microstructure generated with Wang tiles, we develop

Finite cell method is known as a combination of finite element method and fictitious domain approach in order to reduce the difficulties associated with mesh generation so that it can successfully handle complex geometries. This study proposes a stochastic extension of finite cell method, as a novel computational framework, for uncertainty quantification of structures. For this purpose, stochastic

Nesterov’s 1983 first-order minimization algorithm is equivalent to the numerical solution of a second-order ODE with non-constant damping. It is known that the algorithm can be obtained by time discretization with asynchronous damping, a long-standing technique in computational explicit dynamics. We extend the solution of the ODE to other time discretization algorithms, analyze their properties and

This paper deals with the presentation of a general, variational principle as theoretical support for the development of simple and efficient triangular elements having only one displacement and two rotations at the corner nodes to model thin to thick plates based on the first order Reissner- Mindlin plate theory. The functional is a modified Hellinger–Reissner mixed expression in terms of the kinematic

In this second part of a two-part article, we present extensive studies on spatial and temporal resolution in wind turbine wake computation with the computational framework presented in the first part. The framework, which is made of the Space–Time Variational Multiscale (ST-VMS) method, ST isogeometric discretization, and the Multidomain Method (MDM), enables accurate representation of the turbine

One approach for the simulation of metamaterials is to extend an associated continuum theory concerning its kinematic equations, and the relaxed micromorphic continuum represents such a model. It incorporates the Curl of the nonsymmetric microdistortion in the free energy function. This suggests the existence of solutions not belonging to \( H ^1\), such that standard nodal \( H ^1\)-finite elements

We propose a formulation for tracking general crack paths in elastodamaging materials without mesh adaptivity and broadening of the damage band. The idea is to treat in a unified way both the damaging process and the development of displacement discontinuities by means of the regularized finite element method. With respect to previous authors’ contributions, a novel damage evolution law and an original

The present study proposes an MPM (material point method)–FEM (finite element method) hybrid analysis method for simulating granular mass–water interaction problems, in which the granular mass causes dynamic motion of the surrounding water. While the MPM is applied to the solid (soil) phase whose motion is suitably represented by Lagrangian description, the FEM is applied to the fluid (water) phase

Motivated by the influence of (micro-)cracks on the effective electrical properties of material systems and components, this contribution deals with fundamental developments on electro-mechanically coupled cohesive zone formulations for electrical conductors. For the quasi-stationary problems considered, Maxwell’s equations of electromagnetism reduce to the continuity equation for the electric current

In this first part of a two-part article, we present a framework for wind turbine wake computation. The framework is made of the Space–Time Variational Multiscale (ST-VMS) method, ST isogeometric discretization, and the Multidomain Method (MDM). The ST context provides higher-order accuracy in general, and the VMS feature of the ST-VMS addresses the computational challenges associated with the multiscale

Mechanical modelling of poroelastic media under finite strain is usually carried out via phenomenological models neglecting complex micro-macro scales interdependency. One reason is that the mathematical two-scale analysis is only straightforward assuming infinitesimal strain theory. Exploiting the potential of ANNs for fast and reliable upscaling and localisation procedures, we propose an incremental

A novel numerical approach to analyze the mechanical behavior within composite materials including the inelastic regime up to final failure is presented. Therefore, a second-gradient theory is combined with phase-field methods to fracture. In particular, we assume that the polymeric matrix material undergoes ductile fracture, whereas continuously embedded fibers undergo brittle fracture as it is typical

This article addresses the simulation of non-smooth dynamics problems with unilateral contact constraints between rigid and deformable bodies. It proposes a modified CD-Lagrange scheme with a singular mass matrix. This scheme is explicit, and based on a contact condition on velocity. The formulation is designed for a 1D impact problem between deformable and rigid body with unilateral constraint. The

A modular pipeline for improving the constitutive modelling of composite materials is proposed.The method is leveraged here for the development of subject-specific spatially-varying brain white matter mechanical properties. For this application, white matter microstructural information is extracted from diffusion magnetic resonance imaging (dMRI) scans, and used to generate hundreds of representative

The explosive welding process is an extreme-deformation problem that involves shock waves, large plastic deformation, and fragmentation around the collision point, which are extremely challenging features to model for the traditional mesh-based methods. In this work, a particle-based Godunov shock algorithm under a semi-Lagrangian reproducing kernel particle method (SL-RKPM) is introduced into the

Forming of tires during production is a challenging process for Lagrangian solid mechanics due to large changes in the geometry and material properties of the rubber layers. This paper extends the Arbitrary Lagrangian–Eulerian (ALE) formulation to thermomechanical inelastic material models with special consideration of rubber. The ALE approach based on tracking the material and spatial meshes is used

In this article, we follow a thorough matrix presentation of material parameter identification using a least-square approach, where the model is given by non-linear finite elements, and the experimental data is provided by both force data as well as full-field strain measurement data based on digital image correlation. First, the rigorous concept of semi-discretization for the direct problem is chosen

The original article contained typographical errors that a number of double brackets.

In peridynamic models for fracture, the dissipated fracture energy is regularized over a non-local region denoted as the peridynamic horizon. This paper investigates the influence of this parameter on the dynamic fracture process in brittle solids, using two as well as three dimensional simulations of dynamic fracture propagation in a notched plate for two loading cases. The predicted crack speed for

This paper proposes and studies three methods for the identification of cracks in linear elastic bodies. They are based on the reciprocity gap principle which they extend to the case of partially redundant boundary data. The methods are all assessed on an academic 2D case, then the most appealing is more deeply analysed and illustrated on a 3D test-case.

Solid object water entry is a common problem in various natural, industrial and military applications, which involves large deformation of free surfaces and violent fluid–structure interactions. In computational fluid dynamics (CFD), this is a type of problem that tests the robustness and capacity of any CFD numerical algorithm. In this work, the newly-developed updated Lagrangian particle hydrodynamics

The efficient propagation of imprecise probabilities through expensive simulators has emerged to be one of the great challenges for mixed uncertainty quantification in computational mechanics. An active learning method, named Collaborative and Adaptive Bayesian Optimization (CABO), is developed for tackling this challenge by combining Bayesian Probabilistic Optimization and Bayesian Probabilistic Integration

The Taylor–Couette flow is a classical fluid mechanics problem that exhibits, depending on the Reynolds number, a range of flow patterns, with the interesting ones having small-scale structures, and sometimes even wavy nature. Accurate representation of these flow patterns in computational flow analysis requires methods that can, with a reasonable computational cost, represent the circular geometry

The virtual element method (VEM) for dynamic analyses of nonlinear elasto-plastic problems undergoing large deformations is outlined within this work. VEM has been applied to various problems in engineering, considering elasto-plasticity, multiphysics, damage, elastodynamics, contact- and fracture mechanics. This work focuses on the extension of VEM formulations towards dynamic elasto-plastic applications

Numerical artifacts in the form of spurious oscillations are among the critical issues of Fast Fourier Transfer (FFT) methods for solving multiphase elastic problems such as numerical homogenization, in spite of their computational simplicity and efficiency. In the first part of the present work, it is shown that the irregular discretization of the interface due to the use of a voxel-based discretization

This paper presents an extension of Direct \(\hbox {FE}^{2}\) method for the study of dynamic problems in heterogeneous materials. The proposed method can be formulated based on either the Hill–Mandel principle or the extended Hill–Mandel principle, the latter of which enforces the energy contributed by the internal force and the inertial force consistent at two scales. Unlike the traditional \(\hbox

We present a set of advanced analytical formulations that facilitates the accurate analysis and efficient implementation of finite deformable thin Kirchhoff–Love beams. This paper enhances the prevailing differential geometry based large deformation beam models by producing geometrically exact formulations for initial curvatures, non-zero force tangents and external stiffness matrix contributions of

The modeling of ductile damage in engineering metallic materials is an essential step in a design process. In this paper, a mixed finite element formulation is developed to predict ductile damage in thermoviscoplastic porous metals. The novel aspect of the model is the enhancement of Gurson’s plasticity formulation with a void shearing mechanism capable describing thermoviscoplastic flow stress and

The identification of nonhomogeneous elastic property distributions has been traditionally achieved with well acknowledged optimization based inverse approaches, but when full-field displacement measurements are available, the virtual fields method (VFM) can be computationally more efficient by converting the large-scale optimization problem into multiple small-scale optimization problems. A possible

This paper deals with the modelling and the prediction of the dynamic instabilities for a rubbing system. Two hybrid approaches are introduced for dynamic instability analysis and applied to a reduced disc brake system. The methods are based on stochastic algorithms coupled with the finite element method (FEM) using the complex eigenvalue analysis technique. By considering the input parameters as random

In this work, the phase-field approach to fracture is extended to model fatigue failure in high- and low-cycle regime. The fracture energy degradation due to the repeated externally applied loads is introduced as a function of a local energy accumulation variable, which takes the structural loading history into account. To this end, a novel definition of the energy accumulation variable is proposed

This work models spatially uncorrelated (independent) load uncertainty and develops a reduced-order Monte Carlo stochastic isogeometric method to quantify the effect of the load uncertainty on the structural response of thin shells and solid structures. The approach is tested on two demonstrative applications of uncertainty, namely, spatially uncorrelated loading, with (1) Scordelis–Lo Roof shell structure

Fiber optical strain sensors are used to measure the strain at a particular sensor position inside the fiber. In order to deduce the strain in the surrounding matrix material, one can employ the strain transfer principle. Its application is based on the assumption that the presence of the fiber does not impede the deformation of the matrix material in fiber direction. In fact, the strain transfer principle

In the present research, a numerical modeling approach of the initial stage of consolidation during spark plasma sintering on the microscopic scale is presented. The solution of a fully coupled thermo-electro-mechanical problem also accounting for grain boundary and surface diffusion is found by using a staggered way. The finite-element method is applied for solving the thermo-electro-mechanical problem

Direct representation of material microstructure in a macroscale simulation is prohibitively expensive, if even possible, with current methods. However, the information contained in such a representation is highly desirable for tasks such as material/alloy design and manufacturing process control. In this paper, a mechanistic machine learning framework is developed for fast multiscale analysis of material

In this contribution, we present a space-time formulation of the Newmark integration scheme for linear damped structures under both harmonic and transient excitations. The incremental set of equations of motion and the Newmark approximations are transformed into their corresponding space-time equivalents. The dynamic system is then represented by one algebraic space-time equation only. This equation

To respond to the ongoing pandemic of SARS-CoV-2, this contribution deals with recently highlighted COVID-19 transmission through respiratory droplets in form of aerosols. Unlike other recent studies that focused on airborne transmission routes, this work addresses aerosol transport and deposition in a human respiratory tract. The contribution therefore conducts a computational study of aerosol deposition

In this paper we present a fully-coupled, two-scale homogenization method for dynamic loading in the spirit of FE\(^2\) methods. The framework considers the balance of linear momentum including inertia at the microscale to capture possible dynamic effects arising from micro heterogeneities. A finite-strain formulation is adapted to account for geometrical nonlinearities enabling the study of e.g. plasticity

We introduce a goal-oriented strategy for multiscale computations performed using the Multiscale Finite Element Method (MsFEM). In a previous work, we have shown how to use, in the MsFEM framework, the concept of Constitutive Relation Error (CRE) to obtain a guaranteed and fully computable a posteriori error estimate in the energy norm (as well as error indicators on various error sources). Here, the

In this work, a consistent viscoplasticity formulation is derived from thermodynamical principles and employing the concept of continuum elastic corrector rate. The proposed model is developed based on the principle of maximum viscoplastic dissipation for determining the flow direction. The model uses both the equivalent viscoplastic strain and its rate as state variables. Power balance and energy

This study presents a robust method towards the computation of dispersion curves of surface waves in an anisotropic semi-infinite periodically layered structure (PLS) coated by a stack of layers. Using the properties of the symplectic transfer matrix to analyze the relationship between the eigenequations of surface waves in a semi-infinite PLS and of its corresponding finite PLS, the eigenfrequencies

The dynamics of the spread of epidemics, such as the recent outbreak of the SARS-CoV-2 virus, is highly nonlinear and therefore difficult to predict. As time evolves in the present pandemic, it appears more and more clearly that a clustered dynamics is a key element of the description. This means that the disease rapidly evolves within spatially localized networks, that diffuse and eventually create

In this study, the static bending behaviour of a size-dependent thick beam is considered including FGM (Functionally Graded Materials) effects. The presented theory is a further development and extension of the space-fractional (non-local) Euler–Bernoulli beam model (s-FEBB) to space-fractional Timoshenko beam (s-FTB) one by proper taking into account shear deformation. Furthermore, a detailed parametric

Discrete element method (DEM) has achieved considerable success on simulating complex granular material behaviours. One of the key challenges of DEM simulations is how to describe particles with realistic geometries. Many shape description methods have been developed including sphere-clustering, polyhedrons, sphero-polyhedrons, superquadric particles to name a few. However, to model general shaped

As a promising additive manufacturing method, direct energy deposition has been widely used to fabricate complex thin-walled parts. However, some defects such as uneven layer surface and excessive build-ups always occur in this process. In this study, a high-fidelity model adopting a novel laser/powder source is developed to simulate the detailed multi-layer deposition process. With layer surfaces

Simulation of additive manufacturing processes can provide essential insight into material behavior, residual stress, and ultimately, the performance of additively manufactured parts. In this work, we describe a new simulation based workflow utilizing both solid mechanics and fluid mechanics based formulations within the finite element software package SIERRA (Sierra Solid Mechanics Team in Sierra/SolidMechanics