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In this study, we present a method of numerical homogenization, combining asymptotic analysis and finite element modelling, to establish constitutive laws of heterogeneous materials with periodic microstructures tacking into account high-order strain gradients. By performing asymptotic analysis, the problem of local homogenization was split up into differential equations of different orders, which were solved using finite element modelling. This approach allows researcher to accurately calculate high-order stiffness tensors from representative volume elements (RVEs) with complicated microstructures and geometrical forms. The efficiency and accuracy of this approach were verified by means of numerical examples. The mechanical implications, consistency, and strain energy convexity of the strain gradient constitutive laws, obtained using the proposed approach, are analyzed on the basis of the numerical results. [ABSTRACT FROM AUTHOR]

The object of this article is to be able to simulate the behavior of reinforced and/or prestressed concrete beam's section in the shear loading through a model allowing the evaluation of nonlinear strains caused by shear, while taking into account the real behavior of the materials. In this approach, we are often confronted with problems of modeling uncertainties linked to some insufficiencies of the mechanical model allowing to describe the physical phenomena in a realistic way. For that, it is necessary to use a reliability model making it possible to evaluate their probability of failure, by establishing failure curves according to the different transition zones of the limit state curve of the nonlinear behavior in the shear loading up to at section failure of reinforced and/or prestressed concrete beams. In this work, we also propose a coupling of the reliability method by response surface to carry out the reliability optimization on complex mechanical models, where the mechanical and reliability models developed have been implemented on the Fortran. This allows the estimation in an efficient way of the different reliability characteristics according to each transition zone from the limit state curve to the real behavior until failure in the shear loading. [ABSTRACT FROM AUTHOR]

• A prefabricated crack growth of ceramic under thermal shock is studied in real-time. • A relation between the dynamic stress intensity factor and crack speed is identified. • A numerical model can reproduce the crack evolution process of the thermal shock. The prefabricated cracks propagation of ceramic under flame thermal shock was studied by real-time observation. The experimental results show that wing cracks are generated from both tips of the prefabricated crack, and the complete failure of the samples is a high-speed process. The crack propagation speed is fast at first and then gradually slows down. The maximum propagation speed of the near flame tip increases with the prefabricated crack distance to the heated surface, while an inverse trend is observed for the far flame tip. The effect of prefabricated crack angle on thermal shock crack propagation was also considered. In addition, numerical simulations based on dynamic fracture mechanics were carried out to reproduce the entire cracking process. To this end, the relation between the dynamic stress intensity factors and the crack growth speed in the speed range of 100 m/s to 2600 m/s was identified by combing experiments and numerical simulations. The simulation results and the above-mentioned relation are consistent with the experimental observations. The numerical model can faithfully reproduce the crack evolution process of the thermal shock, which is difficult to observe in an experiment due to the high speed of the cracking process. [ABSTRACT FROM AUTHOR]

Strain gradient theory is an accurate model for capturing the size effect and localization phenomena. However, the challenge in identification of corresponding constitutive parameters limits the practical application of the theory. We present and utilize asymptotic homogenization herein. All parameters in rank four, five, and six tensors are determined with the demonstrated computational approach. Examples for epoxy carbon fiber composite, metal matrix composite, and aluminum foam illustrate the effectiveness and versatility of the proposed method. The influences of volume fraction of matrix, the stack of RVEs, and the varying unit cell lengths on the identified parameters are investigated. The homogenization computational tool is applicable to a wide class materials and makes use of open-source codes in FEniCS. We make all of the codes publicly available in order to encourage a transparent scientific exchange. [Display omitted] • We exploit asymptotic homogenization for determining all the parameters in the strain gradient theory. • An FEM based computational approach determines all parameters in rank four, five, and six tensors in generalized elasticity. • The proposed homogenization method identifies the effective parameters of composite materials with periodic microstructures. • Verification of the identified parameters is conducted in the case of a 3-D beam bending problem by using open-source packages in FEniCS. • We make all of the codes publicly available in order to encourage a transparent scientific exchange. [ABSTRACT FROM AUTHOR]