Macroscopic Mechanical Response Research Articles

Shaft friction changes for cyclically loaded displacement piles: an X-ray investigation

The mechanisms occurring at the grain scale at sand–pile interface under axial cyclic loading are analysed quantitatively in a mini calibration chamber, using X-ray tomography and three-dimensional-digital image correlation. Grain kinematics and porosity evolution are followed along with the macroscopic mechanical response of the interface. The results show different phases in the evolution of shaft resistance during cyclic loading, with a non-negligible increase of shaft resistance in the latter phase. The test conditions are not representative of real engineering applications, where piles supporting bridges, tidal or wind turbines have to safely sustain severe load-controlled cycles. However, advanced image analysis sheds light on the mechanisms controlling the macroscopic behaviour of sand–pile interface. This study provides valuable data set against which theoretical or numerical approaches can be tested.

Crystal Plasticity Analysis of Multiple Slip and Macroscopic Mechanical Response in the Dispersed Particle Alloy

Crystal Plasticity Analysis of Multiple Slip and Macroscopic Mechanical Response in the Dispersed Particle Alloy

Multiscale Modeling of Polycrystalline NiTi Shape Memory Alloy under Various Plastic Deformation Conditions by Coupling Microstructure Evolution and Macroscopic Mechanical Response.

Numerical modeling of microstructure evolution in various regions during uniaxial compression and canning compression of NiTi shape memory alloy (SMA) are studied through combined macroscopic and microscopic finite element simulation in order to investigate plastic deformation of NiTi SMA at 400 °C. In this approach, the macroscale material behavior is modeled with a relatively coarse finite element mesh, and then the corresponding deformation history in some selected regions in this mesh is extracted by the sub-model technique of finite element code ABAQUS and subsequently used as boundary conditions for the microscale simulation by means of crystal plasticity finite element method (CPFEM). Simulation results show that NiTi SMA exhibits an inhomogeneous plastic deformation at the microscale. Moreover, regions that suffered canning compression sustain more homogeneous plastic deformation by comparison with the corresponding regions subjected to uniaxial compression. The mitigation of inhomogeneous plastic deformation contributes to reducing the statistically stored dislocation (SSD) density in polycrystalline aggregation and also to reducing the difference of stress level in various regions of deformed NiTi SMA sample, and therefore sustaining large plastic deformation in the canning compression process.

Numerical mesoscopic investigations of dynamic damage and failure mechanisms of polymer bonded explosives

A damage elasto-viscoplastic model has been developed for cyclotetramethylenetetranitramine (HMX) crystals, which considers the anisotropy nature of HMX crystals and dislocation-mediated plasticity as well as the cleavage damage. A damage viscoelastic model has been developed for the polymer binder and the interface, which captures rate dependent damage due to binder rupture and binder debonding during the loading process. The proposed models were implemented in the finite element code ABAQUS by the user subroutine VUMAT. Macroscopic mechanical responses of Polymer Bonded explosives (PBXs) 9501 homogenized across the microstructure is generally in agreement with Split Hopkinson Pressure Bar (SHPB) experimental stress-strain responses at the strain rate of 2000 s−1. Microstructural heterogeneity is responsible for the non-uniform stress, strain and damage fields. Crystal fracture is the dominant failure mechanism under dynamic compression while interfacial debonding plays a more important role under dynamic tension. Mesoscale modeling results along with macroscopic responses are significantly important to have a better understanding of deformation, damage and failure mechanisms of PBX samples under dynamic loading and to improve our predictive ability.

Thermo-mechanical coupling damage constitutive model of rock based on the Hoek–Brown strength criterion

Studying the thermal damage constitutive model of rock using statistical theory can better reflect the damage evolution process and the stress–strain relationship of rock under temperature and loading, which is one of the key problems especially in deep rock mechanics. The thermal-mechanical coupling damage constitutive model of rock is established using the Hoek–Brown strength criterion, based on the Weibull distribution and the continuous damage theory. The rationality of the model is also verified by experiments. The main conclusions are as follows. The stress–strain curves of rock can be divided into four stages according to the damage evolution characteristics, including the non-damage of loading, damage stability expansion, damage intensification expansion, and damage stability expansion to saturation, and the method of determining the demarcation points of each stage is given clearly. The initial damage point of the rock is about 25% of the peak stress, the damage value is about 0.3 when the rock reaches the peak stress and about 0.6 when reaches the residual stress. Both the damage value and the strain energy release rate of the rock corresponding to the peak stress show exponential growth with the increase in confining pressure. The maximum damage evolution rate of the rock shows exponential decay as the confining pressure rises, indicating that the confining pressure can delay the development of cumulative damage. The modified damage constitutive model considering compaction coefficient is in good agreement with the test curves in the stage of compaction, linear elasticity, yield, and pre-peak strength. It is hoped that through the research of this paper, it can provide references for studying the macroscopic mechanical response from the damage propagation characteristics of the rock in the future.

Numerical homogenization of the viscoplastic behavior of snow based on X-ray tomography images

Abstract. While the homogenization of snow elastic properties has been widely reported in the literature, homogeneous rate-dependent behavior responsible for the densification of the snowpack has hardly ever been upscaled from snow microstructure. We therefore adapt homogenization techniques developed within the framework of elasticity to the study of snow viscoplastic behavior. Based on the definition of kinematically uniform boundary conditions, homogenization problems are applied to 3-D images obtained from X-ray tomography, and the mechanical response of snow samples is explored for several densities. We propose an original post-processing approach in terms of viscous dissipated powers in order to formulate snow macroscopic behavior. Then, we show that Abouaf models are able to capture snow viscoplastic behavior and we formulate a homogenized constitutive equation based on a density parametrization. Eventually, we demonstrate the ability of the proposed models to account for the macroscopic mechanical response of snow for classical laboratory tests.

Evaluation of the performance of a breakage model for high porosity Haubourdin chalk

We examine a new continuum micromechanical approach to predicting the macroscopic mechanical responses of Haubourdin chalk under various load conditions. The approach is based on a simple breakage model that accounts for an evolving microstructural degradation through coccosphere crushing with only five physically meaningful parameters and one grading index. The model correlates the intrinsic failure mechanisms including the coccosphere crushing, pore collapse and plastic shearing that are identified by corresponding internal variables within thermodynamic framework. On this basis, numerical predictions of the stresses and strains are examined against their experimental counterparts as well as the results from an existing continuum model. Parametric studies are further conducted to investigate the effect of the model parameters. The favourable agreements in various conventional and complex compression tests indicate a satisfactory performance of the breakage model, highlighting the importance of capturing the microscopic degradation mechanisms when building a constitutive model.

Computational modelling of particulate-reinforced materials up to high volume fractions: Linear elastic homogenisation

This work focuses on the analysis of the micro and macroscopic mechanical response of particle-reinforced composites. A particular attention is paid to the influence of two fundamental design parameters, i.e. the particles shape and their volume fraction (up to very high values ranging from 0 to almost 0.8), on the overall mechanical response of the structure as well as on the resulting elastic symmetry of the material. The strain energy-based homogenisation technique of periodic media is here applied to a 2D finite element model of a representative volume element of the composite. Different algorithms are developed to generate, with a good level of accuracy, the real microstructure of the composite material characterised by circular as well as polygonal particles. Moreover, for each studied configuration, a link between the geometrical parameters of the microstructure (particles shape, size, distribution, and volume fraction) and the size of the representative volume element is also provided in order to properly describe the constitutive behaviour of the composite at the macroscopic scale. The numerical results are compared with analytical models taken from the literature to prove on the one hand the limitations of the analytical approaches and on the other hand the effectiveness of the proposed numerical models.

Macroscopic Simulation of Deformation in Soft Microporous Composites.

Soft microporous materials exhibit properties, such as gated adsorption and breathing, which are highly desirable for many applications. These properties are largely studied for single crystals; however, many potential applications expect to construct structured or composite systems, examples of which include monoliths and mixed-matrix membranes. Herein, we use finite element methods to predict the macroscopic mechanical response of composite microporous materials. This implementation connects the microscopic treatment of crystalline structures to the response of a macroscopic sample. Our simulations reveal the bulk modulus of an embedded adsorbent within a composite is affected by the thickness and properties of the encapsulating layer. Subsequently, we employ this methodology to examine mixed-matrix membranes and materials of negative linear compressibility. This application of finite element methods allows for unprecedented insight into the mechanical properties of real-world systems and supports the development of composites containing mechanically anomalous porous materials.

Intergranular Strain Evolution During Biaxial Loading: A Multiscale FE-FFT Approach

Predicting the macroscopic and microscopic mechanical response of metals and alloys subjected to complex loading conditions necessarily requires a synergistic combination of multiscale material models and characterization techniques. This article focuses on the use of a multiscale approach to study the difference between intergranular lattice strain evolution for various grain families measured during in situ neutron diffraction on dog bone and cruciform 316L samples. At the macroscale, finite element simulations capture the complex coupling between applied forces and gauge stresses in cruciform geometries. The predicted gauge stresses are used as macroscopic boundary conditions to drive a mesoscale full-field elasto-viscoplastic fast Fourier transform crystal plasticity model. The results highlight the role of grain neighborhood on the intergranular strain evolution under uniaxial and equibiaxial loading.

The turtle carapace as an optimized multi-scale biological composite armor – A review

The turtle carapace, the top dorsal part of the shell, is a remarkable multi-scale dermal armor that has evolved to withstand various types of high-stress events encountered in nature. This keratin-covered boney exoskeleton exhibits a number of structural motifs, including alternating rigid and flexible components, layering and functionally graded elements, designed to protect the reptile during predatory attacks, and smashing events. Here we review the multi-scale structural hierarchy of the turtle carapace and its corresponding mechanical properties. We show how the microscopic features of the carapace govern its various macroscopic mechanical responses relevant to protective functioning, including dynamic (impact and cyclic) compression and bending loading situations. In addition, the effect of hydration, a crucial factor for proper physiological-mechanical behavior of biological materials, is illustrated throughout. We also discuss carapace-inspired designs that could be advantageous over the traditional strategies adopted in impact-resistant materials, and could bring new mechanistic insights.

A nonlinear constitutive model for describing cyclic mechanical responses of $$\hbox {BaTiO}_{3}/\hbox {Ag}$$ composites

In this study, the macroscopic hysteretic response of \(\hbox {BaTiO}_{3}/\hbox {Ag}\) composites under uniaxial cyclic mechanical loading was characterized and described by formulating a thermodynamically consistent constitutive model. Cylindrical composite samples with varying silver composition (from 0 to 13 vol%) were fabricated by powder metallurgy technique. The stress–strain hysteretic response was characterized at room temperature under uniaxial compressive stress by cyclically loading and unloading samples to different stresses, until 200 MPa or failure of the sample. For each loading cycle, the tangent modulus was determined at the initiation of the unloading stage. The tangent modulus showed changes after each cycle with increasing loading magnitude in all samples. Permanent deformations were also observed after each unloading cycle, which were associated with changes in the microstructures of the specimens. In formulating the model to describe the above macroscopic mechanical responses of the composites, we assume that the body has two natural configurations, which are different stress-free configurations associated with the original and newly formed microstructures. The new microstructure is formed when the body is subjected to relatively large stress, leading to reorientation of the dipole moments in the crystalline structures and other possible microstructural changes such as cracking. The Gibbs potential was defined in terms of the stress and the volume fraction of the domain transformation, and the internal state variable and its corresponding driving force for domain transformation (dipole reorientations and microstructural changes) were identified. A Preisach operator was adopted to model the relation between the internal state variable and the driving force. The material parameter calibrations were discussed, and the model predictions of the hysteretic response were compared to the experiment results.

Predicting the elastic response of organic‐rich shale using nanoscale measurements and homogenisation methods

ABSTRACTDetermination of the mechanical response of shales through experimental procedures is a practical challenge due to their heterogeneity and the practical difficulties of retrieving good‐quality core samples. Here, we investigate the possibility of using multi‐scale homogenisation techniques to predict the macroscopic mechanical response of shales based on quantitative mineralogical descriptions. We use the novel PeakForce Quantitative Nanomechanical Mapping technique to generate high‐resolution mechanical images of shales, allowing the response of porous clay, organic matter, and mineral inclusions to be measured at the nanoscale. These observations support some of the assumptions previously made in the use of homogenisation methods to estimate the elastic properties of shale and also earlier estimates of the mechanical properties of organic matter. We evaluate the applicability of homogenisation techniques against measured elastic responses of organic‐rich shales, partly from published data and also from new indentation tests carried out in this work. Comparison of experimental values of the elastic constants of shale samples with those predicted by homogenisation methods showed that almost all predictions were within the standard deviation of experimental data. This suggests that the homogenisation approach is a useful way of estimating the elastic and mechanical properties of shales in situations where conventional rock mechanics test data cannot be measured.

Many-body interactions in soft jammed materials.

In jammed packings of soft frictionless particles such as foams or emulsions, stress is transmitted via a network of mechanical contacts between neighbors. In generic simplified models of such materials, particle interaction energies are assumed to be pairwise additive. We report ab initio simulations of foam microstructures, showing that in general, this fundamental assumption is not justified: the conservation of bubble volumes introduces a many-body coupling between all the contacts of a given particle. It strongly modifies the relation between forces and displacements at individual contacts, in a way that cannot be captured by an effective two-body interaction. We report the impact of this effect on the linear and nonlinear elastic response of ordered bubble packings with coordination numbers ranging from 6 to 12, used as simple model systems, and we present an analytical model without free parameters which is valid as long as bubbles have an approximately spherical shape. It predicts the many-body coupling of particle contact forces, as well as the macroscopic mechanical response. For packing fractions approaching the jamming transition where contact forces go to zero, we derive an asymptotic two-body interaction law. It contains a logarithmic term, yielding a critical scaling that cannot be approximated by a power law.

Crystal plasticity analysis of deformation in the vicinity of hard spherical inclusions and macroscopic mechanical response

Crystal plasticity analysis of deformation in the vicinity of hard spherical inclusions and macroscopic mechanical response

A Study on the Mechanical Properties of the Representative Volume Element in Fractal Porous Media

Natural porous structure is extremely complex, and it is of great significance to study the macroscopic mechanical response of the representative volume element (RVE) with the microstructure of porous media. The real porous media RVE is generated by an improved quartet structure generation set (QSGS), and the connectivity of the reconstructed porous media models is analyzed. The fractal dimension of the RVE is calculated by the box-counting method, which considers the different porosity, different fractal dimension, and different mechanical properties of the matrix. Thus, the stress-strain curves of the RVE in the elastoplastic stage under different conditions are obtained. The results show that when the matrix mechanics are consistent, the mechanical properties of the porous media RVE are negatively correlated with the porosity and fractal dimension; when the difference between the porosity and fractal dimension increases, the trend is more obvious. The mechanical properties of the RVE have a positive correlation with the modulus of elasticity of the matrix, though the correlation with Poisson’s ratio of the matrix is weak. The fractal dimension of complex porous media can better predict the RVE mechanical characteristics than the porosity.

Crystal Plasticity Analysis of Mechanical Response in Two Phase Alloys with Dispersion of Fine Particles

Macroscopic mechanical responses of alloy steels dispersed with fine vanadium carbide particles [1] were analyzed by crystal plasticity finite element method. Average distance of dispersed particles was used as a microscopic length scale and introduced to the models of the critical resolved shear stress and the mean free path of dislocations. Numerical result of yield stress agreed well with that of experimental result [1], but that of the work hardening rate was slightly higher than that of experimental one. When the dislocation mean free path was set to be 2 to 3 times the average spacing of dispersed particles, the work hardening rate fit better with the experimental one.

Deformation mechanisms in nanoporous metals: Effect of ligament shape and disorder

The current work presents a numerical modelling approach for investigating the effect of ligament shape and disorder on the macroscopic mechanical response of nanoporous gold (NPG). The approach starts from a ‘single ligament’ analysis with respect to three fundamental deformation modes, bending, torsion, and compression, that depend on the ligament shape. It can be shown that the predictive capability of the highly computationally efficient beam model is sufficient for a large variation in ligament shapes. Using a representative volume element (RVE) composed of such ligaments, different degrees of disorder are included. For both the single ligament and RVE models, the cylindrical beam serves as a common reference to compare the results when varying the ligament shape. From the comparison of the RVE elastic response with the single ligament results and the further analysis of statistical information from the elements in the RVE, it is found that bending is the major deformation mode for perfectly ordered RVEs, whereas torsion gains importance for increasing RVE disorder. The effect of compression of the ligaments can be neglected in general. It is concluded that the transition to torsion deformation due to disorder is the cause of the strongly reduced lateral expansion during compression deformation of NPG.

Low field depoling phenomena in soft lead zirconate titanate ferroelectrics

Reduction in polarisation of ferroelectric materials due to repeated electrical cycling is a major problem in ferroelectric non-volatile memory devices. There is a large amount of data addressing this issue at high electric field strengths under bipolar loading conditions, however the effect of field cycling at low electric field strengths (< Ec) has not been fully investigated. This paper addresses the effects of repeated cycling of soft lead zirconate titanate using electrical pulses at fields well below the coercive field strength of the material. It is shown that this mode of loading diminishes the macroscopic polarisation and mechanical response of the material. The origins of this behaviour are found to be a statistical non-non-reversible switching processes that does not result in classical fatigue related mechanical microstructural damage or defect agglomeration and domain pinning. Instead the process is fully recoverable and attributed to local changes in switching energy and clustering of switched ferroelectric cells.

Experimental and Numerical Investigation of Mechanical Behaviors of Cemented Soil–Rock Mixture

In order to reveal the macroscopic mechanical properties and mesoscopic failure mechanism of cemented soil–rock mixture (CSRM, for short) that widely exists in nature, a series of large-scale triaxial tests are carried out. Firstly, specimens of soil–rock mixture without cement and specimens mixed with small amounts of cement are compared to demonstrate that it is necessary to further divide soil–rock mixture into CSRM and uncemented soil–rock mixture. Then, laboratory large-scale triaxial tests on CSRM specimens with different rock block proportion (RBP, for short) are conducted to explore the effect of RBP on the macroscopic mechanical responses of CSRM. Finally, based on the developed three-dimensional discrete element modeling technology for irregularly shaped rock blocks and soil–rock mixture, a numerical simulation of laboratory tests is performed to analyze the mesoscopic failure mechanism of CSRM. The results indicate that CSRM specimen with 3 % cement exhibits strain softening and localization, whose strength and modulus increase dramatically compared with those of specimen without cement. Peak strength and brittleness index of CSRM specimen both are decreased with increasing RBP under the confining pressures of 0.1, 0.2 and 0.3 MPa. In CSRM specimens, microcracks initiate at the soil–rock interfaces, and then propagate in soil matrix bypassing the rock blocks with multiple tortuous failure bands coming into being throughout the specimen eventually. The effect of RBP on strength of CSRM depends on the combination of skeleton-effect of rock blocks and cementation-effect of the specimen.