A microstructural elastoplastic model for unsaturated granular materials

The homogenization technique is used to obtain an elastoplastic stress–strain relationship for dry, saturated and unsaturated granular materials. Deformation of a representative volume of material is generated by mobilizing particle contacts in all orientations. In this way, the stress–strain relationship can be derived as an average of the mobilization behavior of these local contact planes. The local behavior is assumed to follow a Hertz–Mindlin’s elastic law and a Mohr–Coulomb’s plastic law. For the non-saturated state, capillary forces at the grain contacts are added to the contact forces created by an external load. They are calculated as a function of the degree of saturation, depending on the grain size distribution and on the void ratio of the granular assembly. Numerical simulations show that the model is capable of reproducing the major trends of a partially saturated granular assembly under various stress and water content conditions. The model predictions are compared to experimental results on saturated and unsaturated samples of silty sands under undrained triaxial loading condition. This comparison shows that the model is able to account for the influence of capillary forces on the stress–strain response of the granular materials and therefore, to reproduce the overall mechanical behavior of unsaturated granular materials.     

An elasto-plastic model for granular materials with microstructural consideration

In this paper, we have extended the granular mechanics approach to derive an elasto-plastic stress–strain relationship. The deformation of a representative volume of the material is generated by mobilizing particle contacts in all orientations. Thus, the stress–strain relationship can be derived as an average of the mobilization behavior of these local contact planes. The local behavior is assumed to follow a Hertz–Mindlin’s elastic law and a Mohr–Coulomb’s plastic law. Essential features such as continuous displacement field, inter-particle stiffness, and fabric tensor are discussed. The predictions of the derived stress–strain model are compared to experimental results for sand under both drained and undrained triaxial loading conditions. The comparisons demonstrate the ability of this model to reproduce accurately the overall mechanical behavior of granular media and to account for the influence of key parameters such as void ratio and mean stress. A part of this paper is devoted to the study of anisotropic specimens loaded in different directions, which shows the model capability of considering the influence of inherent anisotropy on the stress–strain response under a drained triaxial loading condition.     

Three-dimensional finite element simulations of ferroelectric polycrystals under electrical and mechanical loading

Complex, non-linear, irreversible, hysteretic behavior of polycrystalline ferroelectric materials under a combined electro-mechanical loading is a result of domain wall motion, causing simultaneous expansion and contraction of unlike domains, grain sub-divisions that have distinct spontaneous polarization and strain. In this paper, a 3-dimensional finite element method is used to simulate such a polycrystalline ferroelectric under electrical and mechanical loading. A constitutive law due to Huber et al. [1999. A constitutive model for ferroelectric polycrystals. J. Mech. Phys. Solids 47, 1663-1697] for switching by domain wall motion in multidomain ferroelectric single crystals is employed in our model to represent each grain, and the finite element method is used to solve the governing conditions of mechanical equilibrium and Gauss's law. The results provide the average behavior for the polycrystalline ceramic. We compare the outcomes predicted by this model with the available experimental data for various electromechanical loading conditions. The qualitative features of ferroelectric switching are predicted well, including hysteresis and butterfly loops, the effect on them of mechanical compression, and the response of the polycrystal to non-proportional electrical loading.     

An enriched damage-frictional cohesive-zone model incorporating stress multi-axiality

The paper presents an interphase cohesive zone model (CZM) incorporating stress multi-axiality devised to capture, by simplified micro-modeling, the influence of the in-plane strain and stress state in the mechanical response of the CZM. Moreover, the model is able to account for the Poisson-related effect in the interphase, which can play an important role in the modeling of heterogeneous masonry elements. From the constitutive point of view, the proposed formulation couples damage and friction by addressing a smooth transition from a quasi-brittle response to a residual frictional behavior described by a Coulomb law with unilateral contact. As in-plane stresses are accounted for, damage activation and evolution are governed by a Drucker–Prager law with linear softening. A predictor-corrector procedure based on a backward Euler scheme is detailed for integrating the nonlinear evolutive problem together with the related tangent operator which consistently linearizes the algorithmic strategy. This framework is embedded into a kinematically-enriched finite element interphase formulation incorporating stress multi-axiality. The modeling features of the resulting numerical tool are tested both at the local level, for the typical interphase point, and in meso-structural tests consisting of brick-mortar triplets, investigating the capability of the proposed model and numerical procedure to simulate the brick-mortar decohesion mechanism during confined slip tests.     

Effect of permanent indentation on the delamination threshold for small mass impact on plates

Small mass impacts on composite structures are common cases caused by hailstones and runway debris. Small mass impactors usually result in a wave controlled local response, which is independent of boundary conditions. This response occurs before the reflection of waves from the boundaries and cannot be modeled by large mass drop weight tests. An elasto-plastic contact law, which accounts for permanent indentation and damage effects, was used here to study small mass impact on laminated composite plates. By comparing with results from the Hertzian contact law, it was found that damage can change the dynamic response of the structure significantly with increasing impact velocity. Due to smaller contact force generated for the case of using elasto-plastic contact, the central displacement of the plate is also less than the one using Hertzian contact law. The linearized version of the contact law was then used to derive the closed-form approximations of the contact force, indentation and plate central displacement for the impact loading of composite laminates. The threshold velocity for delamination onset under small mass impact was predicted analytically based on the obtained peak contact forces by combining with an existing quasi-static delamination threshold load criterion. A good agreement was found between the predicted threshold values and published experimental results.     

Microstructural modeling of asphalt concrete using a coupled moisture–mechanical constitutive relationship

The coupled effect of moisture diffusion and mechanical loading on the microstructure of asphalt concrete is studied. The traditional Continuum Damage Mechanics (CDM) framework is modified to model detrimental effects of moisture and mechanical loading. Adhesive/cohesive moisture-induced damage constitutive relationships are proposed to describe the time-dependent degradation of material properties due to moisture. X-ray two-dimensional (2D) computed tomography-imaging technique is used to construct finite element (FE) microstructural representation of a typical dense-graded asphalt concrete. After being calibrated against pull-off experiments, the proposed moisture-induced damage constitutive relationship, which is coupled to thermo-viscoelastic–viscoplastic–viscodamage mechanisms, is used to simulate the microstructure of asphalt concrete. Simulation results demonstrate that the generated 2D FE microstructural representation along with the coupled moisture–mechanical constitutive relationship can be effectively used to model the overall thermo-hygro-mechanical response of asphalt concrete.     

Multi-grain analysis versus self-consistent estimates of ferroelectric polycrystals

Ferroelectrics are polycrystalline materials consisting of intragranular regions with different polarization directions, called domains. The domains can be switched into different states by the application of an electric field or mechanical stress. We study the influence of grain-to-grain interactions on the overall and local switching behavior. The behavior inside each grain is represented by the micromechanics model of Huber et al. [1999. A constitutive model for ferroelectric polycrystals. J. Mech. Phys. Solids 47 (8), 1663-1697]. The predictions of a self-consistent model of the polycrystal response are compared with those of a multi-grain model in which grains are represented individually. In one flavor of the multi-grain model, each grain is represented by a single finite element, while in the other the fields inside each grain are captured in more detail through a fine discretization. Different electrical and mechanical loading situations are investigated. It is found that the overall response is only mildly dependent on the accuracy with which grain-to-grain interactions are captured, while the distribution of grain-average stresses is quite sensitive to the resolution of the intragranular fields.     

幂律型浆液扩散压力环向分布模型

为研究幂律型浆液注浆时注浆压力的变化情况,考虑盾尾断面新注入浆液与已注入浆液间阻碍作用,假设壁后注浆时盾尾形成三维环形空隙,提出了幂律型浆液扩散压力环向分布模型,并利用流体力学理论推导了幂律型浆液扩散压力环向分布式,分析了公式适用范围以及各参数的实际意义。与实际工程数据对比,验证了模型和计算式的正确性。结果表明,计算式可以反映注浆时环向分布各个位置压力值的大小;当公式中稠度系数n=1时,该式即为牛顿流体计算式,环向压力扩散模型同样适用,且幂律型流体环向扩散压力小于牛顿流体;受浆液自重影响,注浆孔注浆时向上表现为减压,向下表现为加压;压力环向分布断面呈现出上窄下宽的不规则环形;同一注浆孔幂律型浆液水灰比越大,浆液扩散压力越小。     

A 3D Griffith peeling model to unify and generalize single and double peeling theories

It has been shown in recent years that many species in Nature employ hierarchy and contact splitting as a strategy to enhance the adhesive properties of their attachments. Maximizing the adhesive force is however not the only goal. Many animals can achieve a tunable adhesive force, which allows them to both strongly attach to a surface and easily detach when necessary. Here, we study the adhesive properties of 3D dendritic attachments, which are structures that are widely occurring in nature and which allow to achieve these goals. These structures exploit branching to provide high variability in the geometry, and thus tunability, and contact splitting, to increase the total peeling line and thus the adhesion force. By applying the same principles presented by A.A. Griffith 100 years ago, we derive an analytical model for the detachment forces as a function of their defining angles in 3D space, finding as limit cases 2D double peeling and 1D single peeling. We also develop a numerical model, including a nonlinear elastic constitutive law, for the validation of analytical calculations, allowing additionally to simulate the entire detachment phase, and discuss how geometrical variations influence the adhesive properties of the structure. Finally, we also realize a proof of concept experiment to further validate theoretical/numerical results. Overall, we show how this generalized attachment structure can achieve large variations in its adhesive and mechanical properties, exploiting variations of its geometrical parameters, and thus tunability. The in-depth study of similar basic structural units and their combination can in future lead to a better understanding of the mechanical properties of complex architectures found in Nature.

     

A nonlinear homogenization procedure for periodic masonry

The present paper deals with the problem of the determination of the in-plane behavior of masonry material. The masonry is considered as a composite material composed by a regular distribution of blocks connected by horizontal and vertical mortar joints. The overall constitutive relationships of the regular masonry are derived by a rational micromechanical and homogenization procedure. Linear elastic constitutive relationship is considered for the blocks, while a new special nonlinear constitutive law is proposed for the mortar joints. In particular, a mortar constitutive law, which accounts for the coupling of the damage and friction phenomena occurring during the loading history, is proposed; the developed model is based on an original micromechanical analysis of the damage process of the mortar joint. Then, an effective nonlinear homogenization procedure, representing the main novelty of the paper, is proposed; it is based on the transformation field analysis, using the technique of the superposition of the effects and the finite element method. The presented methodology is implemented in a numerical code. Finally, numerical applications are performed in order to assess the performances of the proposed procedure in reproducing the mechanical behavior of masonry material.     

DEM investigation of strain behaviour and force chain evolution of gravel–sand mixtures subjected to cyclic loading

The strain characteristic and load transmission of mixed granular matter are different from those of homogeneous granular matter. Cyclic loading renders the mechanical behaviours of mixed granular matter more complex. To investigate the dynamic responses of gravel–sand mixtures, the discrete element method (DEM) was used to simulate the cyclic loading of gravel–sand mixtures with low fines contents. Macroscopically, the evolution of the axial strain and volumetric strain was investigated. Mesoscopically, the coordination number and contact force anisotropy were studied, and the evolution of strong and weak contacts was explored from two dimensions of loading time and local space. The simulation results show that increasing fines content can accelerate the development of the axial strain and volumetric strain but has little effect on the evolution of contact forces. Strong contacts tend to develop along the loading boundary, presenting the spatial difference. Weak contacts are firstly controlled by confining pressure and then controlled by axial stress, while strong contacts are mainly controlled by axial stress throughout the whole cyclic loading. Once compression failure occurs, the release of axial stress causes the reduction of strong contact proportion in all local regions. These findings are helpful to understand the dynamic responses of gravel–sand mixtures, especially in deformation behaviours and the Spatio-temporal evolution of contact forces.     

Time and frequency domain nonlinear system characterization for mechanical fault identification

Mechanical systems are often nonlinear with nonlinear components and nonlinear connections, and mechanical damage frequently causes changes in the nonlinear characteristics of mechanical systems, e.g. loosening of bolts increases Coulomb friction nonlinearity. Consequently, methods which characterize the nonlinear behavior of mechanical systems are well-suited to detect such damage. This paper presents passive time and frequency domain methods that exploit the changes in the nonlinear behavior of a mechanical system to identify damage. In the time domain, fundamental mechanics models are used to generate restoring forces, which characterize the nonlinear nature of internal forces in system components under loading. The onset of nonlinear damage results in changes to the restoring forces, which can be used as indicators of damage. Analogously, in the frequency domain, transmissibility (output-only) versions of auto-regressive exogenous input (ARX) models are used to locate and characterize the degree to which faults change the nonlinear correlations present in the response data. First, it is shown that damage causes changes in the restoring force characteristics, which can be used to detect damage. Second, it is shown that damage also alters the nonlinear correlations in the data that can be used to locate and track the progress of damage. Both restoring forces and auto-regressive transmissibility methods utilize operational response data for damage identification. Mechanical faults in ground vehicle suspension systems, e.g. loosening of bolts, are identified using experimental data.     

Filtration Behaviour of Cement-Based Grout in Porous Media

Filtration behaviour of cement particles, especially under the high grouting pressure with a rapid grout flow velocity, has a significant effect on the grout injection. However, there have been few studies on this field where the governing equation of this behaviour remains unclear. In the present study, a novel experimental procedure for grout injection was adopted to acquire the spatial and temporal variations in porosity and viscosity of high-speed grout flow in coarse sand. Experimental observations showed that there were dramatic variations in viscosity and porosity during the grout penetration within the first 50 s, suggesting that the high velocity had a significant influence on the distribution of the filtration coefficient. A model based on the Stokes–Brinkman (S–B) equation and advection–filtration equations was established to describe the filtration of grout flow in porous media. Meanwhile, numerical solutions from both the proposed model and traditional Darcy’s law were compared with experimental results. The comparative results showed that the proposed approach can match the laboratory tests well; the analysis indicated that Darcy’s law was unable to properly describe high-speed grout flow in porous media due to the lack of a shear force and the inertial term. Nonuniform filtration behaviour of cement grout flowing in porous media was revealed. Due to the nonuniform distribution of the pore velocity isoline caused by Poiseuille flow, it led to a heterogenous distribution of porosity as well. Parametric studies on the applicability of Darcy’s law and S–B equation for grout flow were discussed, in which an error of less than 10% was calculated when the Reynolds number was less than 2.5.     

A combined experimental-numerical approach for elasto-plastic fracture of individual grain boundaries

The parameters for a crystal plasticity finite element constitutive law were calibrated for the aluminum–lithium alloy 2198 using micro-column compression testing on single crystalline volumes. The calibrated material model was applied to simulations of micro-cantilever deflection tests designed for micro-fracture experiments on single grain boundaries. It was shown that the load–displacement response and the local deformation of the grains, which was measured by digital image correlation, were predicted by the simulations. The fracture properties of individual grain boundaries were then determined in terms of a traction–separation-law associated with a cohesive zone. This combination of experiments and crystal plasticity finite element simulations allows the investigation of the fracture behavior of individual grain boundaries in plastically deforming metals.     

A simple nonlinear model to simulate the localized necking and neck propagation

This paper deals with the equilibrium problem in nonlinear dissipative inelasticity of damaged bodies subject to uniaxial loading and its main purpose is to show the interesting potentialities offered by the damage theory in modeling the necking and neck propagation phenomena in polymeric materials. In detail, the proposed mechanical model is a two-phase system, with the same constitutive law but with different levels of damage for each phase. Despite its simplicity, it is shown that the model can straightforwardly reproduce the overall load–elongation curve provided by experimental tensile tests by involving only five parameters of clear physical meaning.