Search

The Data-Driven Harmonic Analysis of Damage (DDHAD) has been proposed recently to construct arbitrarily anisotropic damage models in quasi-brittle heterogeneous materials from calculations on Representative Volume Elements. During preliminary off-line calculations, numerical crack propagations are simulated and the effective damaged elasticity tensor is computed by numerical homogenization. A macroscopic damage model with internal variables is defined using harmonic analysis of the elasticity tensor. The method, called DDHAD, is in this work improved by two key novelties. First, a numerical framework is proposed to evaluate efficiently the model during on-line calculations by computing all the integral terms during off-line calculations and expressing the damage model in a compact matrix form. Second, a reduced model is introduced to further reduce the number of internal variables which is in general large in 3D. It is shown in an application to the damage of 3D printed lattice that even for a complex 3D induced anisotropy, the number of internal variables can drop to a very small number (3 or 4) with the aid of the proposed strategy. [ABSTRACT FROM AUTHOR]

Solving nonlinear multiscale methods with history-dependent behaviors and fine macroscopic meshes is a well-known challenge. In this work, an unsupervised machine learning-based clustering approach is developed to reduce nonlinear Multilevel Finite Element-FE 2 calculations. In contrast with most available techniques which aim at developing Reduced Order Models (ROM) or AI-based surrogate models for the microscale nonlinear problems, the present technique reduces the problem from the macro scale by creating clusters of macro Gauss points which are assumed to be in close mechanical states. Then, a single micro nonlinear Representative Volume Element (RVE) calculation is performed for each cluster. A linear approximation of the macro stress is used in each cluster. Handling internal variables is carried out by using anelastic macro strains in the clustering vectors in addition to the macro strains components. Finally, some convergence issues related to the use of clusters at the macro scale are addressed through a cluster freezing algorithm. The technique is applied to nonlinear hyperelastic, viscoelastic and elastoplastic composites. In contrast to available ROM or machine-learning -based acceleration techniques, the present method does not require neither preliminary off-line calculations, nor training, nor data base, nor reduced basis at the macro scale, while maintaining typical speed-up factors about 20 as compared to classical FE 2. • An unsupervised machine learning-based clustering approach is developed to reduce nonlinear FE2 calculations. • A linear approximation of the macro stress is used in each cluster. • Handling internal variables is carried out by using anelastic macro strains in the clustering vectors. • Finally, some convergence issues related to the use of clusters at the macro scale are addressed. [ABSTRACT FROM AUTHOR]

In this work, a novel multiscale topology optimization method has been proposed for the design of electromechanical energy-harvesting systems converting mechanical vibrations into electric currents made of non-piezoelectric materials. At the microscopic scale, the material is assumed to be periodic, porous, and flexoelectric, although not piezoelectric. A first step of topology optimization is performed, in order to maximize the effective (homogenized) flexoelectric properties of the material, where a flexoelectric homogenization model is first formulated. As a result, the effective material, although made of a non-piezoelectric material, has apparent piezoelectric properties. In a second step, these properties are used to model the behavior of a dynamic electromechanical energy-harvesting system structure. A second topology optimization step, this time performed at the structural scale, aims to maximize the system electromechanical coupling factor (ECF) for a given forced vibration frequency, including the micro-inertial effect. At both scales, an isogeometric analysis method is employed to solve the strain-gradient problems numerically. We show that the optimized structure obtained offers significant gains in terms of ECF (by a factor of between 2 and 20) compared with non-optimized structures of the same volume, over a wide range of excitation frequencies. The procedure could open up new possibilities in the design of energy recovery systems without the use of piezoelectric materials. [ABSTRACT FROM AUTHOR]

Abstract In this work, a multiscale model for thermomechanical properties of composite structures containing phase change particles is developed. For the mechanical part, a classical linear computational homogenization procedure is employed. For the thermal part, due to the strong nonlinear, history-dependent thermal effects, a concurrent multiscale (FE2) method is extended to take into account the presence of Phase Change Materials particles (PCM) at the microscale. The PCM inclusions change from liquid to solid state in the range of room temperature. This phase change induces a modified macroscopic thermal behavior, which can be used e.g. to design materials with enhanced thermal inertia and reduce energy consumption in civil engineering constructions. The technique allows taking into account accurately the fully nonlinear, history-dependent thermal behavior through numerical calculations at the microscale based on a Representative Volume Element (RVE) and its effect at the macroscale. The method is applied to concrete material including paraffin wax PCM. The results show the benefits of the PCM on the thermal behavior, including shifted and smoothed temperature response as compared to materials without PCM particles. Highlights • First extension of FE2 method to nonlinear conduction with phase change (liquid/solid) at the microscale. • For stiff matrix, the mechanical effects can be decoupled in the multiscale nonlinear thermomechanical problem with PCM. • The results show the benefits of the PCM on the thermal behavior, including shifted and smoothed temperature response. [ABSTRACT FROM AUTHOR]

Highlights • First use of topology optimization of lattices structures taking into strain gradient. • Use of filter-based homogenization method with BESO to reduce computational time. • Considering strain gradient effects increases stiffness of the optimized structure. Abstract We present a topology optimization for lattice structures in the case of non-separated scales, i.e. when the characteristic dimensions of the periodic unit cells in the lattice are not much smaller than the dimensions of the whole structure. The present method uses a coarse mesh corresponding to a homogenized medium taking into strain gradient through a non-local numerical homogenization method. Then, the topological optimization procedure only uses the values at the nodes of the coarse mesh, reducing drastically the computational times. We show that taking into account the strain gradient within the topological optimization procedure brings significant increase in the resulting stiffness of the optimized lattice structure when scales are not separated, as compared to using a homogenized model based on the scale separation assumption. [ABSTRACT FROM AUTHOR]

A numerical model of graphene-reinforced nanocomposites taking into account the electric tunneling effect is employed to analyze the influence of microstructural parameters on the effective electric conductivity and the percolation thresholds of the composite. The generation procedure for the random microstructures of graphene-reinforced nanocomposites is described. Effects of the barrier height, of graphene aspect ratio and alignment of graphene sheets have been quantitatively evaluated. The results show that both higher graphene aspect ratio and lower barrier height can lead to smaller percolation threshold, and the alignment of graphene sheets results in anisotropic electrical behavior without affecting the percolation threshold. The numerical model also shows the importance of the tunneling effect to reproduce the nonlinear electric behavior and the low percolation thresholds reported in the literature. Finally, results are compared with available experimental data. [ABSTRACT FROM AUTHOR]

In this paper, we propose a numerical framework for optimizing the fracture resistance of quasi-brittle composites through a modification of the topology of the inclusion phase. The phase field method to fracturing is adopted within a regularized description of discontinuities, allowing to take into account cracking in regular meshes, which is highly advantageous for topology optimization purpose. Extended bi-directional evolutionary structural optimization (BESO) method is employed and formulated to find the optimal distribution of inclusion phase, given a target volume fraction of inclusion and seeking a maximal fracture resistance. A computationally efficient adjoint sensitivity formulation is derived to account for the whole fracturing process, involving crack initiation, propagation and complete failure of the specimen. The effectiveness of developed framework is illustrated through a series of 2D and 3D benchmark tests. [ABSTRACT FROM AUTHOR]

Tunnelling effect is a possible mechanism to explain the apparent large electric conductivity and nonlinear electric behavior of graphene-reinforced nanocomposites with polymer matrix. In this work, a numerical modeling framework is proposed to evaluate the effective electric conductivity in polymer composites reinforced with graphene sheets, taking into account the electrical tunnelling effect, which allows conduction between graphene sheets at nanometric distances. We introduce a nonlinear Finite Element formulation and a numerical methodology to model the nonlocal and nonlinear effects introduced by the tunnelling effect conduction model within the polymer matrix between close graphene sheets. In addition, to avoid meshing the thickness of the graphene sheets and in view of their very high aspect ratio, a highly conducting surface model is employed. The computed effective conductivity is evaluated over representative volume elements containing arbitrary distributed graphene sheets. The results exhibit tendencies and percolation thresholds which are in qualitative agreement with the available experimental results. [ABSTRACT FROM AUTHOR]

A topology optimization framework for improving the dynamic fracture resistance of structures is proposed. The phase field method for fracture is combined with Solid Isotropic Material with Penalization (SIMP) topology optimization. The topology optimization problem is defined as minimizing the fracture energy during the whole dynamic loading process, from initiation of cracks to full failure of the structure, under volume and compliance constraints. Semi analytical expressions of sensitivities in a dynamic context are provided to solve the topology optimization problem efficiently. Numerical examples involving structures subjected to impact loading are investigated. It is shown that the present framework allows a significant reduction of the fracture energy as compared to designs obtained by static optimization. [ABSTRACT FROM AUTHOR]

Numerical methods motivated by rapid advances in image processing techniques have been intensively developed during recent years and increasingly applied to simulate heterogeneous materials with complex microstructure. The present work aims at elaborating an incremental-iterative numerical method for voxel-based modeling of damage evolution in quasi-brittle microstructures. The iterative scheme based on the Lippmann-Schwinger equation in the real space domain (Yvonnet, in Int J Numer Methods Eng 92:178-205, ) is first cast into an incremental form so as to implement nonlinear material models efficiently. In the proposed scheme, local strain increments at material grid points are computed iteratively by a mapping operation through a transformation array, while local stresses are determined using a constitutive model that accounts for material degradation by damage. For validation, benchmark studies and numerical simulations using microtomographic data of concrete are performed. For each test, numerical predictions by the incremental-iterative scheme and the finite element method, respectively, are presented and compared for both global responses and local damage distributions. It is emphasized that the proposed incremental-iterative formulation can be straightforwardly applied in the framework of other Lippmann-Schwinger equation-based schemes, like the fast Fourier transform method. [ABSTRACT FROM AUTHOR]

3D-printed structures may be characterized by anisotropic fracture behavior because of their layered nature. Depending on the orientation of the sample during the layer deposition, a completely different mechanical response can be obtained, ranging from quasi-brittle to elastoplastic, and with large variations in the maximum stress to failure. In this study, an optimization framework is proposed for 3D-printed samples to maximize their resistance to fracture with respect to both the orientation of the deposited layers during the process and the topology of the sample. To achieve this, a phase-field anisotropic elastoplastic fracture model is combined with a Bidirectional Evolutionary Structural Optimization topology optimization. The model makes it possible to predict the response of the structure until failure with respect to the orientation of the deposited layers in the 3D-printing process and then optimize this orientation to maximize the mechanical response. A large increase in fracture resistance can be obtained by optimizing the orientation, and a significant increase in fracture resistance can be achieved using the present nonlinear anisotropic topology optimization compared with the use of linear topology optimization. [Display omitted] • Optimization of 3D printed materials to maximize their fracture resistance. • Optimization is made both regarding the layers orientation and the topology. • A phase-field anisotropic elastoplastic model is combined with BESO method. • A large increase in fracture resistance is obtained by optimizing the layers angle. • Additional increase in fracture resistance can be achieved by optimizing the topology. [ABSTRACT FROM AUTHOR]

A numerical procedure based on isogeometric analysis (IGA) is developed to analyze the dynamic response of flexoelectric systems in the frequency domain. In materials or composites with an effective flexoelectric response, a polarization can be induced by local strain gradients. In general, these effects are small in the static regime. However, larger effects may be induced by dynamic loads, and can be used in energy harvesters converting mechanical vibrations into electrical energy. In this work, the equations describing frequency response of flexoelectric systems under dynamic loads are first described. Then, an IGA discretization procedure is employed to handle the C 1 continuity of the displacement fields. The conditions of both open and close-circuits are formulated. The numerical methodology is used to evaluate the sensitivity of different parameters such as load resistors, dynamic scale parameter, and the use of flexoelectric or non-flexoelectric materials on the frequency response of output voltage, power and displacements of beam-like structures, possibly incorporating structural geometrical features. The potential of IGA with respect to mesh refinement (h-refinement) and higher order approximation (p-refinement) for modeling complex geometries within the present framework is invetigated. [ABSTRACT FROM AUTHOR]

A phase field model for anisotropic, elastoplastic fracture model in layered structures obtained by 3D printing processes is proposed. An extension of anisotropic phase field to elastoplasticity model is developed. The model is able to describe a transition from quasi-brittle to elastoplastic fracture behaviors depending on the angle of layers in the microstructure with respect to the external loading. Such feature is of special interest to describe the anisotropic fracture behavior in layered 3D printed materials. The present model introduces two phase field variables, one bulk fracture damage and one micro interfacial damage variables, describing two different micro damage mechanisms. Finally, we have proposed an original methodology to identify the macroscopic strain density as a function of the micro interfacial damage variable using numerical homogenization on Representative Volume Elements. Numerical investigations show that the present model is convergent with respect to mesh refinement, and allows to describe complex crack initiation and propagation in layered elastoplastic structures. An experimental comparison is provided to validate the use of such model for 3D printed polymer materials. [ABSTRACT FROM AUTHOR]

Experimental results for the cracking of heterogeneous clay samples during desiccation are reported, and an associated numerical model is developed for comparison. The clay samples contain embedded rigid inclusions to induce heterogeneous strain fields during drying. The crack paths and local strain fields are monitored during the desiccation process using digital image correlation. A numerical phase field model for crack initiation and propagation is introduced and compared with the experimental results. A qualitative agreement is found for the obtained crack paths, whereas discrepancies remain for the local strain fields. A discussion regarding the comparison between the experimental results and model is provided. • Original experimental results of desiccation cracks in heterogeneous clay samples including macro inclusions. • Cracks evolution in heterogeneous samples is measured using optical experimental techniques. • Strain fields are evaluated experimentally using digital image correlation. • A phase field crack model is developed to reproduce the experiments. • A comparison and critical discussion on the agreement between experiments and numerical simulations is provided. [ABSTRACT FROM AUTHOR]

A stochastic data-driven multilevel finite-element (FE 2 ) method is introduced for random nonlinear multiscale calculations. A hybrid neural-network–interpolation (NN–I) scheme is proposed to construct a surrogate model of the macroscopic nonlinear constitutive law from representative-volume-element calculations, whose results are used as input data. Then, a FE 2 method replacing the nonlinear multiscale calculations by the NN–I is developed. The NN–I scheme improved the accuracy of the neural-network surrogate model when insufficient data were available. Due to the achieved reduction in computational time, which was several orders of magnitude less than that to direct FE 2 , the use of such a machine-learning method is demonstrated for performing Monte Carlo simulations in nonlinear heterogeneous structures and propagating uncertainties in this context, and the identification of probabilistic models at the macroscale on some quantities of interest. Applications to nonlinear electric conduction in graphene–polymer composites are presented. [ABSTRACT FROM AUTHOR]

We propose a novel nonlinear topology optimization framework tailored for flexoelectric soft dielectrics undergoing large deformation. A numerical method based on Isogeometric analysis (IGA) is introduced to nonlinear soft dielectrics at finite strain, ensuring the C 1 -continuity for flexoelectric problems. We outline the process of consistent linearizations and IGA discretizations. Additionally, we introduce an innovative and efficient Strain Density Function (SDF) interpolation scheme for optimizing electromechanical coupling factors (ECFs). In this scheme, the interpolation of electromechanical and hyper-elastic energy terms is grounded in the SIMP model, while a linear material interpolation model is employed for the dielectric energy. Our numerical analysis highlights the remarkable performance of the proposed SDF interpolation scheme in nonlinear electromechanical optimization scenarios. An energy remedy scheme is applied to void regions to eliminate the instability of nonlinear optimization, effectively preventing distortion deformations in low-stiffness elements. Furthermore, we investigate the influence of size effect and larger deformation on the optimization of flexoelectric soft materials. The proposed topology optimization framework adeptly leverages the interplay between size effect and larger deformation, resulting in a notable improvement in ECFs within the optimized structures. Finally, the electromechanical coupling factors (ECFs) of the optimized structures in all the examined cases exhibit enhancements up to 9 times as compared to the reference guess designs. [ABSTRACT FROM AUTHOR]

Topology optimization for maximizing the fracture resistance of particle-matrix composites is investigated. The methodology developed in our previous works, combining evolutionary topology optimization and phase field method to fracture embedding interfacial damage, is applied and extended to periodic composites and multiple objectives. On one hand, we constrain the periodicity of unit cells geometry and conduct their topology optimization for one given load prescribed over the whole structure. On the other hand, we consider a single unit cell whose topology is optimized with respect to the fracture energy criterion when subjected to multiple loads. Size effects are investigated. We show that significant enhancement of the fracture resistance can be achieved for the studied composite structures by the present method. In addition, a first attempt to fracture resistance enhancement of a unit cell associated with a material is investigated for multiple loads, exhibiting a complex optimized microstructure. [ABSTRACT FROM AUTHOR]

• A numerical framework for crack propagation in elastoplastic microstructures interacting with interfacial damage. • An associated phase field framework is developed. • Convergence with respect to the mesh is verified. • The framework is applicable to image-based microtomograpy images in regular meshes. An extension of the phase field method to model interfacial damage in elastoplastic composites is proposed. In the matrix, an elastoplastic phase field is employed to model the fracture process. To introduce interfacial damage between inclusions and the matrix, a strain density function depending on the jump due to decohesion is added to the total energy. Smooth indicator functions are used to maintain the regularized character of the approximation. They weight the different terms in the energy with respect to the vicinity of interfaces. Then, the different problems (mechanical and phase field problems) are derived and an algorithmic procedure is described. Numerical examples show the capabilities of the method to handle initiation, propagation and interactions between both elastoplastic fracture and interfacial cracks in complex elastoplastic composite microstructures. It is also shown that the solutions are convergent with respect to the mesh refinement. [ABSTRACT FROM AUTHOR]

A Coarse Mesh Condensation Multiscale Method (CMCM) is proposed to solve large heterogeneous linear structures without scale separation assumption. The technique aims to approximate the full field solution in heterogeneous structures by performing parallel calculations on subdomains. In the linear case, treated in this paper, direct linear relationships can be established between a reduced number of parameters describing Dirichlet boundary conditions on the subdomains boundaries and the degrees of freedom of a coarse mesh. The problem associated with the coarse mesh can be solved in one iteration and allows reconstructing the fine mesh solution in all subdomains. The accuracy of the method is analyzed through benchmarks involving subdomains crossed by the interfaces. Applications to large industrial finite element applications are presented, including one involving around 1.3 billion degrees of freedom. [ABSTRACT FROM AUTHOR]

• Propose a new interfacial cracking model in the phase field framework. • Consider the effects of both stiff and soft interphases on the fracture behavior of heterogeneous materials. • Simulate the material degradation both on the interface and in bulk within the context of the phase field method for fracture. • Model the competition between the interface and bulk cracking. • Capture the complex cracking phenomena on interfaces such as initiation, delamination, coalescence, deflection. A new interfacial cracking model in the phase field framework is proposed. The developed method is able to capture the effects of both stiff and soft interphases on the fracture behavior of heterogeneous materials. A dimensional-reduced model based on a rigorous asymptotic analysis is adapted to derive the zero thickness imperfect interface models from an original configuration containing thin interphase. Then, the energetic approach is used to describe the material degradation both on the interface and in bulk within the context of the phase field method for fracture. This technique allows to effectively model the competition between the interface and bulk cracking. Furthermore, a unilateral contact condition is also proposed to ensure the physical crack propagation patterns in the case of spring imperfect interface. The complex cracking phenomena on interfaces such as initiation, delamination, coalescence, deflection are successfully predicted by the present method. The numerical implementation using a staggered algorithm provides an extremely robust approach. The performance of the proposed framework is demonstrated through numerical examples involving complex microcracking of both stiff and soft interfaces in complex microstructures. [ABSTRACT FROM AUTHOR]

In this work, we extend a phase field formulation for dynamic ductile fracture to consider interfacial debonding in elastoplastic composites. The interfacial weak zone is created through a regularization of the sharp interfaces, and the singular strain part along the interfaces is approximated by using a Taylor expansion. Then, a strain density depending on the displacement jump related to matrix/inclusions decohesion is added to the total energy to take into account interfacial debonding. The coupling problems (displacement, plasticity and damage problems) are derived within the variational framework and a staggered iterative algorithmic procedure is described to solve the coupling problems. Numerical examples demonstrate that this method can handle the initiation, propagation, and interaction between bulk dynamic fracture and interface cracks, as well as the anisotropic behavior in the complex microstructure of elastic–plastic composite materials. It also indicates that this model is convergent in terms of mesh refinement. • A numerical framework for dynamic crack propagation in elastoplastic composites interacting with interfacial debonding is proposed. • An associated phase field framework is developed, and the convergence with respect to the mesh is verified. • The framework is applicable to 3D elastoplastic composite microstructures obtained from X-ray computed tomography (XRCT) technique. [ABSTRACT FROM AUTHOR]

In this paper, a data-driven-based computational homogenization method based on neural networks is proposed to describe the nonlinear electric conduction in random graphene-polymer nanocomposites. In the proposed technique, the nonlinear effective electric constitutive law is provided by a neural network surrogate model constructed through a learning phase on a set of RVE nonlinear computations. In contrast to multilevel (FE 2 ) methods where each integration point is associated with a full nonlinear RVE calculation, the nonlinear macroscopic electric field-electric flux relationship is efficiently evaluated by the surrogate neural network model, reducing drastically (by several order of magnitudes) the computational times in multilevel calculations. Several examples are presented, where the RVE contains aligned graphene sheets embedded in a polymer matrix. The nonlinear behavior is due to the modeling of the tunelling effect at the scale of graphene sheets. [ABSTRACT FROM AUTHOR]

A new multi-phase-field method is developed for modeling the fracture of polycrystals at the microstructural level. Inter and transgranular cracking, as well as anisotropic effects of both elasticity and preferential cleavage directions within each randomly oriented crystal are taken into account. For this purpose, the proposed phase field formulation includes: (a) a smeared description of grain boundaries as cohesive zones avoiding defining an additional phase for grains; (b) an anisotropic phase field model; (c) a multi-phase field formulation where each preferential cleavage direction is associated with a damage (phase field) variable. The obtained framework allows modeling interactions and competition between grains and grain boundary cracks, as well as their effects on the effective response of the material. The proposed model is illustrated through several numerical examples involving a full description of complex crack initiation and propagation within 2D and 3D models of polycrystals. [ABSTRACT FROM AUTHOR]

In this study, we explore the use of SIMP topology optimization and the phase field approach to fracture to maximize fracture resistance in functionally graded materials (FGMs) in the presence of a second phase. We derive a mathematical formulation using a consistent derivation of the second law of thermodynamics to maximize the external work under the constraints of volume fraction. We also demonstrate that, for every distribution of the density function, the topology optimization problem Γ − Converges. We highlight the significant difference between the fracture resistance in FGMs and homogeneous materials. We investigate the crack propagation path along with the optimum topology for the FGM under different grading profiles, elastic mismatch ratio, strength mismatch ratio, and inclusion mismatch ratio. We present several numerical examples to demonstrate the predictive capability of the presented model. A comparison between the initial design guess and the final optimized design is also provided for each example, to further assess the model capability. • Minimization of compliance and maximization of the fracture resistance in FGMs. • Proof of Γ -Convergence for every distribution of optimisation density function. • Effect of elastic mismatch, strength mismatch, and inclusion mismatch with comparison to homogenous materials on optimum topology. • Comparison between initial design guess and optimum design. • Convergence properties of the design. [ABSTRACT FROM AUTHOR]

This paper presents a numerical algorithm based on a perturbation technique named asymptotic numerical method (ANM) to solve nonlinear problems with hyperelastic constitutive behaviors. The main advantages of this technique compared to Newton-Raphson are: (a) a large reduction of the number of tangent matrix decompositions; (b) in presence of instabilities or limit points no special treatment such as arc-length algorithms is necessary. The ANM uses high order series approximation with auto-adaptive step length and without need of any iteration. Introduction of this expansion into the set of nonlinear equations results into a sequence of linear problems with the same linear operator. The present work aims at providing algorithms for applying the ANM to the special case of compressible and incompressible hyperelastic materials. The efficiency and accuracy of the method are examined by comparing this algorithm with Newton-Raphson method for problems involving hyperelastic structures with large strains and instabilities. [ABSTRACT FROM AUTHOR]

This article tackles the problem of identification of elastic continuum model by atomistic simulations for graphene polymer nanocomposite. The Atomistic Local IdentificAtion of Stiffness method, so-called ALIAS method, is developed to estimate the local stiffness tensor at all points of polymer graphene laminate nanocomposite. Results suggest that the graphene can be modeled at continuum scale by a general imperfect interface with zero thickness. Moreover, the identification procedure reveals the existence of interphase on either side of the graphene with a thickness of 1 nm, which is one and a half times stiffer than the polymer bulk matrix. The identified continuum model is used to study the effective elastic properties of nanocomposites with sandwich microstructure. This study at continuum scale reveals a softening effect due the very low stiffness of slip along graphene plane. The softening due to the interfaces is preponderant in relation to the interphase stiffening. Finally, the continuum model also suggests that the wrinkling of graphene increases the stiffness of nanocomposites. [Display omitted] • Identification of a continuum elastic model of nanocomposite by atomistic simulations. • Existence of interphase one and a half times stiffer with a thickness of 1 nm. • The interface between graphene and polymer has a softening effect. • The interface softening is preponderant in relation to the interphase stiffening. • Wrinkling of graphene increases the stiffness of graphene polymer nanocomposite. [ABSTRACT FROM AUTHOR]

• Phase field - SIMP topology optimization for fracture resistance of bi-materials. • An original comparison between BESO and SIMP is conducted. • Fracture resistance can be improved in 2D and 3D composite structures. We investigate the use of combining SIMP topology optimization and phase field method to fracture for maximizing the fracture resistance of a structure composed of two materials. The optimization problem is formulated with respect to maximizing the external work under the constraint of inclusion volume fraction. The performance and convergence of the proposed algorithm are investigated. It is shown that the fracture resistance can be improved as compared to several guess designs with the same volume fraction of reinforcement (inclusion material). A comparison between the present SIMP and BESO methods is performed, showing a better convergence of the SIMP method, more specifically when a homogeneous initial guess design is used. Applications to 2D and 3D composite structure are presented to show the potential and robustness of the approach. [ABSTRACT FROM AUTHOR]

• A homogenization approach is provided to compute the strain gradient elasticity coefficients. • We modify the method based on quadratic boundary conditions to eliminate the persistence of strain gradient elasticity effects for a homogeneous solid. • The principle of the approach consists to establish a bridge with the method based on asymptotic series expansion. • The case of a composite with fibers is considered as an illustration in order to show the improvement of the corrected method. In this paper we deal with the determination of the strain gradient elasticity coefficients of composite material in the framework of the homogenization methods. Particularly we aim to eliminate the persistence of the strain gradient effects when the method based on quadratic boundary conditions is considered. Such type of boundary conditions is often used to determine the macroscopic strain gradient elastic coefficients but leads to contradictory results, particularly when a RVE is made up of a homogeneous material. The resulting macroscopic equivalent material exhibits strain gradient effects while it should be expected of Cauchy type. The present contribution is to provides new relationship to correct the approach based on the quadratic boundary condition. To this purpose, we start from the asymptotic homogenization approach, we establish a connection with the method based on quadratic boundary conditions and we highlight the correction required to eliminate the persistence of the strain gradient effects. An application to a composite with fibers is provided to illustrate the method. [ABSTRACT FROM AUTHOR]

Highlights from the article: However, purely data-driven approaches for machine learning present difficulties when the data is I scarce i and of I variable fidelity i relative to the complexity of the system. Laurent Stainier, et al., proposed model-free data-driven methods in mechanics material data identification and solvers. Model-free data-driven methods in mechanics: material data identification and solvers.

This paper revisits the modeling of compressive failure of long fiber composite materials by considering a multiscale finite element approach. It is well known that this failure follows from a fiber microbuckling phenomenon. Fiber microbuckling is governed by both material and geometrical quantities: the elastoplastic shear behavior of the matrix and the fiber misalignment. Although all these parameters are easily accounted by a finite element analysis at the local level, the failure is also influenced by macrostructural quantities. That is why a multilevel finite element model (FE 2 ) is relevant to describe the compressive failure of composite. Furthermore, fiber local buckling leads to a loss of ellipticity of the macroscopic model, which can be a criterion of failure. [ABSTRACT FROM AUTHOR]

Abstract: Modelling transport and long-term creep in concrete materials is a difficult problem when the complexity of the microstructure is taken into account, because it is hard to predict instantaneous elastic responses. In this work, several numerical methods are compared to assess their properties and suitability to model concrete-like microstructures with large phase properties contrast. The methods are classical finite elements, a novel extended finite element method (μ-xfem), an unconstrained heuristic meshing technique (amie), and a locally homogenising preprocessor in combination with various solvers (benhur). The benchmark itself consists of a number of simple and complex microstructures, which are tested with a range of phase contrasts designed to cover the needs of creep and transport modelling in concrete. The calculations are performed assuming linear elasticity and thermal conduction. The methods are compared in term of precision, ease of implementation and appropriateness to the problem type. We find that xfem is the most suitable when the mesh if coarse, and methods based on Cartesian grids are best when a very fine mesh can be used. Finite element methods are good compromises with high flexibility. [Copyright &y& Elsevier]

In the original publication of the article, second author's name was misspelt. [ABSTRACT FROM AUTHOR]