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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]

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]

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]

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]