Analytical and numerical analysis of 3D grid-reinforced orthotropic composite structures

A comprehensive micromechanical investigation of 3D periodic composite structures reinforced with a grid of orthotropic reinforcements is undertaken. Two different modeling techniques are presented; one is based on the asymptotic homogenization method and the other is a numerical model based on the finite element technique. The asymptotic homogenization model transforms the original boundary value problem into a simpler one characterized by effective coefficients which are shown to depend only on the geometric and material parameters of a periodicity cell. The model is applied to various 3D grid-reinforced structures with generally orthotropic constituent materials. Analytical formula for the effective elastic coefficients are derived, and it is shown that they converge to earlier published results in much simpler case of 2D grid reinforced structures with isotropic constituent materials. A finite element model is subsequently developed and used to examine the aforementioned periodic grid-reinforced orthotropic structures. The deformations from the finite element simulations are used to extract the elastic and shear moduli of the structures. The results of the asymptotic homogenization analysis are compared to those pertaining to their finite element counterparts and a very good agreement is shown between these two approaches. A comparison of the two modeling techniques readily reveals that the asymptotic homogenization model is appreciably faster in its implementation (without a significant loss of accuracy) and thus is readily amenable to preliminary design of a given 3D grid-reinforced composite structure. The finite element model however, is more accurate and predicts all of the effective elastic coefficients. Thus, the engineer facing a particular design application, could perform a preliminary design (selection of type, number and spatial orientation of the reinforcements) and then fine tune the final structure by using the finite element model.     

Development and validation of a 3D computational tool to describe concrete behaviour at mesoscale. Application to the alkali-silica reaction

A finite element analysis of the large deformation of three-dimensional polycrystals is presented using pixel-based finite elements as well as finite elements conforming with grain boundaries. The macroscopic response is obtained through volume-averaging laws. A constitutive framework for elasto-viscoplastic response of single crystals is utilized along with a fully-implicit Lagrangian finite element algorithm for modeling microstructure evolution. The effect of grain size is included by considering a physically motivated measure of lattice incompatibility which provides an updated shearing resistance within grains. A domain decomposition approach is adopted for parallel computation to allow efficient large scale simulations. Conforming grids are adopted to simulate flexible and complex shapes of grains. The computed mechanical properties of polycrystals are shown to be consistent with experimental results for different grain sizes.     

Numerical simulation of plasticity-induced fatigue crack closure with emphasis on the crack growth scheme: 2D and 3D analyses

In this paper a numerical simulation of plasticity-induced fatigue crack closure is performed using the finite element method. Emphasis is placed on the crack growth scheme usually adopted for modelling fatigue crack growth in crack closure problems. The number of load cycles between node releases usually reported in the literature has been, in general, one or two. The present work shows that increasing the number of load cycles between node releases has a strong effect on the opening stresses, particularly, under plane strain conditions and 3D fatigue cracks, in contrast plane stress shows little variation with increasing number of load cycles. This investigation also suggests that ratchetting may take place close to the crack tip in both plane strain and 3D crack problems. The problem of discontinuous crack closure under plane strain conditions, often reported in the literature, is also addressed.     

Mechanical analysis of 3D braided composites: a finite element model

The analysis of 3D braided composites is more difficult due to its complex microstructure. A new type of finite element method is developed to predict the effective moduli and the local stress within 3D braided composites under the 3D mechanical loading. To verify the present method, the material properties of undamaged 3D braided composites predicted in this paper are compared with the previous work. To demonstrate this method, some examples are analyzed.     

Experimental study on the packing densification of mixtures of spherical and cylindrical particles subjected to 3D vibrations

To identify the dense packing of cylinder–sphere binary mixtures (spheres as filling objects), the densification process of such binary mixtures subjected to three-dimensional (3D) mechanical vibrations was experimentally studied. Various influential factors including vibration parameters (such as vibration time t, vibration amplitude A, frequency ω, vibration acceleration Γ) as well as particle size ratio r (small sphere vs. large cylinder), composition of the binary mixtures X_L (volume fraction of cylinders), and container size D (container diameter) on the packing density ρ were systematically investigated. The results show that the optimal vibration parameters for different binary cylinder–sphere mixtures are different. The smaller the size ratio, the less vibration acceleration is needed to form a stable dense packing. For each binary mixture, high packing density can be obtained when the volume fraction of large cylindrical particles is dominant. Meanwhile, increasing the container size can decrease the container wall effect and get higher packing density. The proposed analytical model has been proved to be valid in predicting the packing densification of current cylinder–sphere binary mixtures.     

Calculation of J-integrals using experimental and numerical data: Influences of ratio (a/W) and the 3D structure

Contrary to J-integral values calculated from the 2D numerical model, calculated J-integrals [1] from 3D specimen in the numerical and experimental cases are not very close with J-integral used in the literature and two distinct points are present. The first one is according to (a/W) and can be reduced, when this ratio is inferior to 0.2. The second is a structure problem and can be explain by local three-dimensional effects surrounding the crack tip. Two applications using polymer materials for large and minor deformations are experimented. A grid method is used to experimentally determine the in-plane displacement fields around a crack tip in a Single-Edge-Notch (SEN) tensile polyurethane and PMMA specimens. This indirect method composed of experimental in-plane displacement fields and of two theoretical formulations, allows the experimental J-integral to be determined and the results obtained by the numerical simulations to be confirmed.     

A combined experimental and numerical study of the behaviour of paperboard composites up to failure

Paperboard composites have been subjected to non-conventional inflation experiments using a novel instrumentation inspired by burst strength testers. The purpose is to understand the behaviour up to failure of strongly anisotropic and heterogeneous material samples under the loading condition more commonly experienced for instance by beverage packaging. The information collected by the exploited prototype equipment has been interpreted at the light of validated numerical models of the performed tests.     

Effect of surface slip on Stokes flow past a spherical particle in infinite fluid and near a plane wall

The motion of a spherical particle in infinite linear flow and near a plane wall, subject to the slip boundary condition on both the particle surface and the wall, is studied in the limit of zero Reynolds number. In the case of infinite flow, an exact solution is derived using the singularity representation, and analytical expressions for the force, torque, and stresslet are derived in terms of slip coefficients generalizing the Stokes–Basset–Einstein law. The slip velocity reduces the drag force, torque, and the effective viscosity of a dilute suspension. In the case of wall-bounded flow, advantage is taken of the axial symmetry of the boundaries of the flow with respect to the axis that is normal to the wall and passes through the particle center to formulate the problem in terms of a system of one-dimensional integral equations for the first sine and cosine Fourier coefficients of the unknown traction and velocity along the boundary contour in a meridional plane. Numerical solutions furnish accurate predictions for (a) the force and torque exerted on a particle translating parallel to the wall in a quiescent fluid, (b) the force and torque exerted on a particle rotating about an axis that is parallel to the wall in a quiescent fluid, and (c) the translational and angular velocities of a freely suspended particle in simple shear flow parallel to the wall. For certain combinations of the wall and particle slip coefficients, a particle moving under the influence of a tangential force translates parallel to the wall without rotation, and a particle moving under the influence of a tangential torque rotates about an axis that is parallel to the wall without translation. For a particle convected in simple shear flow, minimum translational velocity is observed for no-slip surfaces. However, allowing for slip may either increase or decrease the particle angular velocity, and the dependence on the wall and particle slip coefficients is not necessarily monotonic.     

Accuracy and limit of a least-squares method to calculate 3D notch SIFs

To evaluate the three-dimensional (3D) stress intensity factors (SIFs) of a sharp V-notch using the finite element result is limited in the literature. Thus, this study developed a least-squares method to solve this problem as well as study its restriction and accuracy. First, the William’s eigenfunction and complex stress function approach are deduced into a least-squares form, and then stress field from the finite element analysis is substituted into the least-squares equation to evaluate the 3D SIFs. Numerical simulations in this article show that the least-squares method can be used to calculate SIFs accurately if more than two stress terms are included. The calculated SIFs of this least-squares method are not sensitive to the maximum and minimum radiuses of the area from which data are included. The major advantage of the proposed method is that the procedure is simple and systematic, so it can be applied to any finite element code without difficulties.     

FE-investigations of a deterministic and statistical size effect in granular bodies within a micro-polar hypoplasticity

The paper deals with numerical investigations of a deterministic and statistical size effect in granular bodies during shearing of an infinite layer under plane strain conditions and free dilatancy. For a simulation of the mechanical behavior of a cohesionless granular material during a monotonous deformation path, a micro-polar hypoplastic constitutive was used which takes into account particle rotations, curvatures, non-symmetric stresses, couple stresses and the mean grain diameter as a characteristic length. The proposed model captures the essential mechanical features of granular bodies in a wide range of densities and pressures with a single set of constants. To describe a deterministic size effect, the calculations were carried out with an uniform distribution of the initial void ratio for four different heights of the granular layer: 5, 50, 500 and 2,000 mm. To investigate a statistical size effect, the distribution of the initial void ratio in infinite granular layers was assumed to be spatially correlated. As only primary stochastic calculations were performed, single examples of different random fields of the initial void ratio were generated. For this purpose a conditional rejection method was used.     

Development of a new software for adaptive crack growth simulations in 3D structures

A new software system called ADAPCRACK3D has been developed by the authors to predict fatigue crack growth in arbitrary 3D geometries under complex loading by the use of the finite element method. The main focus of ADAPCRACK3D is on the determination of 3D crack paths and surfaces as well as on the evaluation of components' lifetimes as a part of the damage tolerant assessment. Throughout the simulation of crack propagation an automatic adaptive mesh adaption is carried out in the vicinity of the crack front nodes. The fracture mechanical evaluation is based on a new criterion recently developed by the authors.     

Contribution to the understanding of the mechanical behaviour of CFRP-strengthened RC beams subjected to fire: Experimental and numerical assessment

Recent experimental tests and numerical simulations about the fire resistance behaviour of CFRP-strengthened RC beams proved that CFRP strengthening systems are able to attain considerable fire endurance, provided that adequate fire protection systems are used. In a fire event, even though a CFRP laminate may rapidly debond from the central part of the beam in which it is installed, if sufficiently thick insulation is applied in the anchorage zones, the laminate transforms into a “cable” fixed at the extremities, thus maintaining a considerable contribution to the mechanical response of the strengthened beam. This paper presents experimental and numerical investigations on CFRP-strengthened RC beams with the objective of understanding in further depth their fire resistance behaviour, namely the influence of the above mentioned “cable” mechanism on the mechanical response of the beams. The experimental campaign, performed at ambient temperature, comprised 4-point bending tests on RC beams strengthened with CFRP laminates according to either the EBR or the NSM techniques, in both cases fully or partially (only at the anchorages, thus simulating the cable mechanism) bonded to the soffit of the beams. For the test conditions used in this study, for both types of strengthening systems, partially bonding the CFRP laminates did not affect the stiffness of the beams and caused only a slight reduction of their strength (6–15%). The numerical study comprised the simulation of the structural response of all beams tested. Non-linear finite element models were developed in Atena commercial package, in which a smeared cracked model was adopted to simulate concrete and appropriate bond-slip constitutive relations were defined for the CFRP-concrete interfaces. A very good agreement was obtained between experimental data and numerical results, providing further validation to the “cable” mechanism and the possibility of taking it into account when designing fire protection systems for CFRP-strengthened RC beams.     

融合式引入三维几何建模的教学研究与实践

针对如何在工程图学课程中合理地引入三维几何建模,提出了基于Inventor建模流程的融合式引入方法;指出了在引入时应以教学体系完整性和建模软件辅助性为原则,重点在于建模思想的引入,强调徒手绘图、尺规绘图和三维几何建模并重,同时应注重将软件规则和制图国家标准相融合等要点,并辅以实例进行了说明;经过教学实践,提高了学生在构形、制图和建模等方面的能力。     

Regularized algorithms for the calculation of values on and near boundaries in 2D elastic BEM

It is verified that, under certain continuity conditions, the boundary integral equations (BIEs) of both displacement and displacement derivative can be expressed in a variety of regularized forms with at most weak singularities for any points within the domain or on its boundary. A series of algorithms embedded in the regularized formulations are presented to calculate the field variables within the domain or on its boundary. Detailed numerical results are given to check and compare the validities of the proposed algorithms and some practical effective algorithms are discovered. Due to the character of the at most weak singularities in the formulations, the algorithms require no special numerical treatments, but only the general Gauss quadrature to implement. To the end, the continuity requirements for the field variables and the validities of the algorithms are discussed.     

An implementation of the stiffness derivative method as a discrete analytical sensitivity analysis and its application to mixed mode in LEFM

In this work, an improvement in the stiffness derivative method based on a shape design sensitivity analysis is proposed, so that the error inherent in the finite difference procedure is avoided. For a global estimation of G from a given finite element solution, this approach is shown to be equivalent to the well-known J-integral when the latter is numerically implemented through its equivalent domain integral. However, it is verified that its direct application to 2D mixed mode problems of linear elastic fracture mechanics through the field decomposition technique yields estimates for G_I and G_II which are in general more accurate for the proposed method. The importance of the velocity field is also remarked and some suggestions for its choice are given.