A new specialised finite element for simulating the cracking and healing behaviour of quasi-brittle materials is presented. The element employs a strong discontinuity approach to represent displacement jumps associated with cracks. A particular feature of the work is the introduction of healing into the element formulation. The healing variables are introduced at the element level, which ensures consistency

Digital image correlation (DIC) is a full-field measurement technique. In instantaneous approaches (i.e., registering two images), DIC only gives access to displacement (or velocity) fields. Consequently, acceleration fields are not one of the primary measured variables. To evaluate acceleration fields, a regularization scheme has to be used. The latter may be either heuristic or mechanically motivated

One of the most important goals in civil engineering is to guarantee the safety of the construction. Standards prescribe a required failure probability in the order of $$10^{-4}$$ to $$10^{-6}$$. Generally, it is not possible to compute the failure probability analytically. Therefore, many approximation methods have been developed to estimate the failure probability. Nevertheless, these methods still

In this paper a robust and effective 4-node shell element for the structural analysis of thin structures is described. A Hu–Washizu functional with independent displacements, stress resultants and shell strains is the variational basis of the theory. Based on a previous paper an additional interpolation part using quadratic shape functions is introduced for the independent shell strains. Especially

We present and analyze a method for thin plates based on cut Bogner-Fox-Schmit elements, which are $$C^1$$ elements obtained by taking tensor products of Hermite splines. The formulation is based on Nitsche’s method for weak enforcement of essential boundary conditions together with addition of certain stabilization terms that enable us to establish coercivity and stability of the resulting system

This article presents an investigation about prediction accuracy of multi-parametric models derived from numerical data. Three different mechanical test-cases are used for the generation of the numerical data. From this data, models are derived for the prediction of characteristic variation to arbitrary changes of the input parameters. Different modeling approaches are evaluated regarding their prediction

Following publication of the original article [1], the authors reported the errors in the equations.

This work proposes an extension of phase change and latent heat models for the simulation of metal powder bed fusion additive manufacturing processes on the macroscale and compares different models with respect to accuracy and numerical efficiency. Specifically, a systematic formulation of phase fraction variables is proposed relying either on temperature- or enthalpy-based interpolation schemes. Moreover

This paper introduces a shape optimization of wire strands subjected to tensile loads. The structural analysis relies on a recently developed reduced helical finite element model characterized by an extreme computational efficacy while accounting for complex geometries of the wires. The model is extended to consider interactions between components and its applicability is demonstrated by comparison

In this work, we consider a transient thermal problem, with a nonlinear term coming from the radiation boundary condition and a nonparametrized variability in the form complex scenarios for the initial condition and the convection coefficients and external temperatures. We use a posteriori reduced order modeling by snapshot Proper Orthogonal Decomposition. To treat the nonlinearity, hyperreduction

In the present work, we propose a new approach, the so-called compressed adaptive integration scheme (C-AIS), for the computation of the stiffness and mass matrices in fictitious domain methods requiring the integration of discontinuous functions. The novel approach extends the conventional quadtree-decomposition-based adaptive integration scheme (AIS) by an additional step, in which established image-compression

A new in situ vibration mode measurement method within a tomograph is proposed based on Projection-based Digital Volume Correlation techniques. Several projection angles are selected and a large number of radiographs of the vibrating sample are acquired at random instants with a small exposure time in order to ‘freeze out’ the displacement and avoid motion blurring. Based on an initial reconstruction

Exotic behaviour of mechanical metamaterials often relies on an internal transformation of the underlying microstructure triggered by its local instabilities, rearrangements, and rotations. Depending on the presence and magnitude of such a transformation, effective properties of a metamaterial may change significantly. To capture this phenomenon accurately and efficiently, homogenization schemes are

We develop a novel unfitted finite element solver for composite materials with quasi-1D fibrous reinforcements. The method belongs to the class of mixed-dimensional non-conforming finite element solvers. The fibres are treated as 1D structural elements that may intersect the mesh of the embedding structure in an arbitrary manner. No meshing of the unidimensional elements is required. Instead, fibre

In the last years, the automotive engineering industry has been deeply influenced by the use of «machine learning» techniques for new design and innovation purposes. However, some specific engineering aspects like numerical optimization study still require the development of suitable high-performance machine learning approaches involving parametrized Finite Elements (FE) structural dynamics simulation

In this paper, we propose a general framework for projection-based model order reduction assisted by deep neural networks. The proposed methodology, called ROM-net, consists in using deep learning techniques to adapt the reduced-order model to a stochastic input tensor whose nonparametrized variabilities strongly influence the quantities of interest for a given physics problem. In particular, we introduce

We propose a hybrid interface preconditioner for the monolithic solution of surface-coupled problems. Powerful preconditioning techniques are crucial when it comes to solving large monolithic systems of linear equations efficiently, especially when arising from coupled multi-physics problems like in fluid–structure interaction. Existing physics-based block preconditioners have proven to be efficient

In this article, we present a computationally efficient homogenization technique for linear coupled diffusion–mechanics problems. It considers a linear chemo-mechanical material model at the fine scale, and relies on a full separation of scales between the time scales governing diffusion and mechanical phenomena, and a relaxed separation of scales for diffusion between the matrix and the inclusion

“When I use a word, it means whatever I want it to mean”: Humpty Dumpty in Alice’s Adventures Through The Looking Glass, Lewis Carroll. “Digital twin” is currently a term applied in a wide variety of ways. Some differences are variations from sector to sector, but definitions within a sector can also vary significantly. Within engineering, claims are made regarding the benefits of using digital twinning

Using a continuous representation of dislocations in elastoplastic polycrystals, we investigate slip transfer at grain boundaries by assessing the compatibility of the slip system shear rates with tangential continuity of the plastic distortion rate tensor at these interfaces. Fulfillment of this tangential continuity condition is needed for consistency of the continuous description of dislocations

Analysis benchmarking is used to evaluate new algorithms for automated VCCT-based delamination growth analysis. First, existing benchmark cases based on the Single Leg Bending (SLB) specimen for crack propagation prediction under quasi-static loading are summarized. Second, the development of new SLB-based benchmark cases to assess the static and fatigue growth prediction capabilities under mixed-mode

Formulating appropriate simulation models that capture the microstructure evolution at the mesoscale in metals undergoing thermomechanical treatments is a formidable task. In this work, an approach combining higher-order dislocation density based crystal plasticity with a phase-field model is used to predict microstructure evolution in deformed polycrystals. This approach allows to model the heterogeneous

Steering columns for column assist Electric Steering are one of the main elements of the passive safety restraint system in a passenger vehicle. It is designed to collapse applying an optimized ride down force to reduce chest and head injuries of the driver during a frontal crash event, making this requirement one of the most important ones for its development. The system crash response is generated

This paper presents an application to metal matrix composites (MMCs) of an enhanced elasto-viscoplastic Fast Fourier Transform (EVP-FFT) formulation coupled with a phenomenological continuum Mesoscale Field Dislocation Mechanics (MFDM) theory. Contrary to conventional crystal plasticity, which only accounts for plastic flow and hardening induced by statistically stored dislocations (SSDs), MFDM-EVP-FFT

By using a generalized, spatially resolved rate theory, we systematically studied the irradiation-induced diffusion and segregation of point defects near triple junctions. Our model captured not only the formation, growth, and recombination of point defects but also the interaction of these defects with pre-existing defects. We coupled the stress field of the triple junction with defect diffusion via

An enriched homogenized model is developed based on a proposed homogenization strategy, to describe the wave propagation behaviour through periodic layered composites. The intrinsic parameters characterising the micro-inertia effect and non-local interactions are defined transparently in terms of the constituent materials’ properties and volume fractions. The framework starts with the introduction

A novel thermo-elastoplastic self-consistent homogenization model for granular materials that exhibit inter-granular plasticity is presented. The model, TEPSCA, is made possible by identifying a new inter-granular plastic Eshelby-like tensor. A micromechanical model of interfacial yielding between grains of a Mohr–Coulomb type is provided, which is relatable to the description of imperfect interfaces

This paper proposes a new finite-element modelling of a recent layerwise model for multilayered plates. This layerwise model is built from a specific 3D stress-field expansion along the thickness direction and involves, in particular, interlaminar transverse shear and out-of-plane stresses as generalized stresses. Its main feature is that 3D equilibrium equations and free-edge boundary conditions are

The present work aims at the identification of the effective constitutive behavior of $$\Sigma 5$$ aluminum grain boundaries (GB) for proportional loading by using machine learning (ML) techniques. The input for the ML approach is high accuracy data gathered in challenging molecular dynamics (MD) simulations at the atomic scale for varying temperatures and loading conditions. The effective traction-separation

In our former works we proposed different Model Order Reduction strategies for alleviating the complexity of computational simulations. In fact we proved that separated representations are specially appealing for addressing many issues, in particular, the treatment of 3D models defined in degenerated domains (those involving very different characteristic dimensions, like beams, plate and shells) as

Aircraft structural analysis is a process that involves several engineers working concurrently to analyze in detail all structural elements of an airframe, as well as the behavior of the aircraft structure as a whole. The airframe has to be decomposed in its major components such as fuselage sections, wings and control surfaces to allow the distribution of the analyses among the engineers. Finite element

This paper aims at investigating the adoption of non-intrusive global/local approaches while modeling fracture by means of the phase-field framework. A successful extension of the non-intrusive global/local approach to this setting would pave the way for a wide adoption of phase-field modeling of fracture, already well established in the research community, within legacy codes for industrial applications

Recent advancements on the variational approach to fracture for the prediction of complex crack patterns in heterogeneous materials and composite structures is herein proposed, as a result of the frontier research activities undertaken in the FP7 ERC Starting Grant project CA2PVM which focuses on the development of computational methods for the durability and the reliability assessment of photovoltaic

BACKGROUND Cell adhesion is a process that involves the interaction between the cell membrane and another surface, either a cell or a substrate. Unlike experimental tests, computer models can simulate processes and study the result of experiments in a shorter time and lower costs. One of the tools used to simulate biological processes is the cellular automata, which is a dynamic system that is discrete

BACKGROUND Surrogate solutions and surrogate models for complex problems in many fields of science and engineering represent an important recent research line towards the construction of the best trade-off between modeling reliability and computational efficiency. Among surrogate models, hierarchical model (HiMod) reduction provides an effective approach for phenomena characterized by a dominant direction

Most of mechanical systems and complex structures exhibit plate and shell components. Therefore, 2D simulation, based on plate and shell theory, appears as an appealing choice in structural analysis as it allows reducing the computational complexity. Nevertheless, this 2D framework fails for capturing rich physics compromising the usual hypotheses considered when deriving standard plate and shell theories

This paper studies parametric reduced-order modeling via the interpolation of linear multiple-input multiple-output reduced-order, or, more general, surrogate models in the frequency domain. It shows that realization plays a central role and two methods based on different realizations are proposed. Interpolation of reduced-order models in the Loewner representation is equivalent to interpolating the

Assumed stress finite elements are known for their extraordinary good performance in the framework of linear elasticity. In this contribution we propose a mixed variational formulation of the Hellinger–Reissner type for hyperelasticity. A family of hexahedral shaped elements is considered with a classical trilinear interpolation of the displacements and different piecewise discontinuous interpolation

Shear and membrane locking phenomena are fundamental issues of shell finite element models. A family of refined shell elements for laminated structures has been developed in the framework of Carrera Unified Formulation, including hierarchical elements based on higher-order Legendre polynomial expansions. These hierarchical elements were reported to be relatively less prone to locking phenomena, yet

This work deals with the modeling of laminated composite and sandwich shells through a variable separation approach based on a Reissner’s Variational Mixed Theorem (RMVT). Both the displacement and transverse stress fields are approximated as a sum of products of separated functions of the in-plane coordinates and the transverse coordinate. This approach yields to a non-linear problem that is solved

Considering a large class of muscle contraction models accounting for actin–myosin interaction, we present a mathematical setting in which solution properties can be established, including fundamental thermodynamic balances. Moreover, we propose a complete discretization strategy for which we are also able to obtain discrete versions of the thermodynamic balances and other properties. Our major objective

This article reviews some integrators particularly suitable for the numerical resolution of differential equations on a large time interval. Symplectic integrators are presented. Their stability on exponentially large time is shown through numerical examples. Next, Dirac integrators for constrained systems are exposed. An application on chaotic dynamics is presented. Lastly, for systems having no exploitable

Composite structures are convenient structural solutions for many engineering fields, but their design is challenging and may lead to oversizing due to the significant amount of uncertainties concerning the current modeling capabilities. From a structural analysis standpoint, the finite element method is the most used approach and shell elements are of primary importance in the case of thin structures

This research work presents some comparisons and analyses of the time discontinuous space–time Galerkin method and the space discontinuous Galerkin method applied to elastic wave propagation in anisotropic and heterogeneous media. Mechanism of both methods to ensure their stability using time or space discontinuities of unknown fields is analyzed and compared. The most general case of anisotropic and

This article introduces benchmark cases for time integrators devoted to non-smooth impact dynamics. It focuses on numerical properties of explicit integrators. Each case tests one necessary numerical property in computational impact dynamics: energy behaviour at impact, angular momentum conservation, non-linear behaviour. The cases are easy to implement and analyse, providing a benchmark well-suited

Most of mechanical systems and complex structures exhibit plate and shell components. Therefore, 2D simulation, based on plate and shell theory, appears as an appealing choice in structural analysis as it allows reducing the computational complexity. Nevertheless, this 2D framework fails for capturing rich physics compromising the usual hypotheses considered when deriving standard plate and shell theories

The aim of the present paper is to study theoretically and numerically the Verlet scheme for the explicit time-integration of elastodynamic problems with a contact condition approximated by Nitsche’s method. This is a continuation of papers (Chouly et al. ESAIM Math Model Numer Anal 49(2), 481–502, 2015; Chouly et al. ESAIM Math Model Numer Anal 49(2), 503–528, 2015) where some implicit schemes (theta-scheme

The principal aim of this work is to provide an adapted numerical scheme for the approximation of elastic wave propagation in incompressible solids. We rely on high-order conforming finite element with mass lumping for space discretisation and implicit/explicit, second-order, energy-preserving time discretisation. The time step restriction only depends on the shear wave velocity and at each time step

In this contribution the multi-physics problem of fluid–structure–control interaction (FSCI) is solved by an iterative, partitioned approach utilizing Gauss–Seidel formulations. The aim is to conduct a fully coupled co-simulation of the FSCI problem, where the controller actively influences the dynamics of the structure. The purpose of this manuscript is twofold: In the first part, in order to get

In this paper we present a collection of techniques used to formulate a projection-based reduced order model (ROM) for zero Mach limit thermally coupled Navier–Stokes equations. The formulation derives from a standard proper orthogonal decomposition (POD) model reduction, and includes modifications to improve the drawbacks caused by the inherent non-linearity of the used Navier–Stokes equations: a

The original version of the article [1] unfortunately contained an error in the figure.

A new reduced order model (ROM) is proposed here for reconstructing super-critical flow past circular cylinder and lid driven cavity using time-scaling of vorticity data directly. The present approach is a significant improvement over instability-mode (developed from POD modes) based approach implemented in Sengupta et al. [Phys Rev E 91(4):043303, 2015], where governing Stuart–Landau–Eckhaus equations

We present the results of the first application in the naval architecture field of a methodology based on active subspaces properties for parameter space reduction. The physical problem considered is the one of the simulation of the hydrodynamic flow past the hull of a ship advancing in calm water. Such problem is extremely relevant at the preliminary stages of the ship design, when several flow simulations

A series of experiments has been performed to build a benchmark for the numerical modeling of mixed mode crack propagation in concrete. Two tests are selected so that the propagation is almost always stable although the material is quasi-fragile. Moreover the variation of mode mixity enables the study of the reorientation of the crack, as well as more complex phenomena such as branching or link-up

A coupled hydromechanical code based on a distributed brittle damage material model has been developed in order to simulate hydraulic fracturing processes. As specific feature, the code does not assume the development of a discrete number of sharp cracks but considers a diffused damage that takes place under overall confinement of the system. The code is validated against a laboratory test reproducing

We combine the asynchronous spacetime discontinuous Galerkin (aSDG) method, an interfacial-damage fracture model, and a dynamic contact model to simulate dynamic fracture and crack closure in brittle materials. The contact model enforces specialized Riemann solutions for bonded, separation, slip and stick conditions while preserving elastodynamic characteristic structure across fracture interfaces

The paper presents a robust algorithm, which allows to implicitly describe and track immersed geometries within a background mesh. The background mesh is assumed to be unstructured and discretized by tetrahedrons. The contained geometry is assumed to be given as triangulated surface. Within the background mesh, the immersed geometry is described implicitly using a discontinuous distance function based

In this paper the generation of random fields when the domain is much larger than the characteristic correlation length is made using an adaptation of the Karhunen–Loève expansion (KLE). The KLE requires the computation of the eigen-functions and the eigen-values of the covariance operator for its modal representation. This step can be very expensive if the domain is much larger than the correlation

An entire design-through-analysis workflow solution for isogeometric B-Rep analysis (IBRA), including both the interface to existing CADs and the analysis procedure, is presented. Possible approaches are elaborated for the full scope of structural analysis solvers ranging from low to high isogeometric simulation fidelity. This is based on a systematic investigation of solver designs suitable for IBRA

This work aims to present a complete full coupling eXtended finite element formulation of the thermo-mechanical problem of cracked bodies. The basic concept of the extended finite element method is discussed in the context of mechanical and thermal discontinuities. Benchmarks are presented to validate at the same time the implementation of stress intensity factors and numerical mechanical and thermal