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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]

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]

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 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]

• 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]

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]

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]

• 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]

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]