Micro-scale modeling of interface-dominated mechanical behavior

A micro-scale interface dislocation dynamics approach to model the mechanical behavior of crystalline nanolaminates is presented. To circumvent the exhaustive atomistic modeling of interfaces and dislocations in nanolaminates, an atomistically informed dislocation dynamics model was developed in which interfaces are categorized using a geometrical interface classification scheme and the interface-dominated mechanical response is related to nucleation, glide, and reactions of lattice and interface dislocations at/within/across interfaces. We show that such a scheme is effective in mapping the structure–property relations of various types of interfaces.     

An assessment of plasticity theories for modeling the incrementally nonlinear behavior of granular soils

The objective of this paper is to assess the predictive capability of different classes of extended plasticity theories (bounding surface plasticity, generalized plasticity and generalized tangential plasticity) in the modeling of incremental nonlinearity, which is one of the most striking features of the mechanical behavior of granular soils, occurring as a natural consequence of the particular nature of grain interactions at the microscale. To this end, the predictions of the various constitutive models considered are compared to the results of a series of Distinct Element simulations performedad hoc. In the comparison, extensive use is made of the concept of incremental strain-response envelope in order to assess the directional properties of the material response for a given initial state and stress history.     

An assessment of plasticity theories for modeling the incrementally nonlinear behavior of granular soils

The objective of this paper is to assess the predictive capability of different classes of extended plasticity theories (bounding surface plasticity, generalized plasticity and generalized tangential plasticity) in the modeling of incremental nonlinearity, which is one of the most striking features of the mechanical behavior of granular soils, occurring as a natural consequence of the particular nature of grain interactions at the microscale. To this end, the predictions of the various constitutive models considered are compared to the results of a series of Distinct Element simulations performed ad hoc. In the comparison, extensive use is made of the concept of incremental strain-response envelope in order to assess the directional properties of the material response for a given initial state and stress history.     

Fatigue behavior and modeling of short fiber reinforced polymer composites including anisotropy and temperature effects

Effects of anisotropy and temperature on cyclic deformation and fatigue behavior of two short glass fiber reinforced polymer composites were investigated. Fatigue tests were conducted under fully-reversed (R = −1) and positive stress ratios (R = 0.1 and 0.3) with specimens of different thicknesses, different fiber orientations, and at temperatures of −40 °C, 23 °C, and 125 °C. In samples with 90° fiber orientation angle, considerable effect of thickness on fatigue strength was observed. Effect of mold flow direction was significant at all temperatures and stress ratios and the Tsai–Hill criterion was used to predict off-axis fatigue strengths. Temperature also greatly influenced fatigue strength and a shift factor of Arrhenius type was developed to correlate fatigue data at various temperatures, independent of the mold flow direction and stress ratio. Micromechanisms of fatigue failure at different temperatures were also investigated. Good correlations between fatigue strength and tensile strength were obtained and a method for obtaining strain–life curves from load-controlled fatigue test data is presented. A fatigue life estimation model is also presented which correlates data for different temperatures, fiber orientations, and stress ratios.     

Micromechanical behavior of granular materials with inherent anisotropy under cyclic loading using 2D DEM

This paper presents the micromechanical behavior of granular materials due to different initial inherent anisotropic conditions during cyclic loading using the discrete element method (DEM). Oval particles were used to model the samples. Three samples, with three different inherent anisotropic conditions based on the particle’s bedding direction, were prepared and subjected to biaxial cyclic loading. The differences in the inherent anisotropic conditions of the samples affect the stress–strain-dilative behavior of granular materials. The width of the stress–strain cyclic loops decreases as the preferred bedding angle changes from vertical to horizontal. Contact fabric evolution is found to be dependent on the inherent anisotropic fabric of the sample during loading and unloading. The fabric anisotropy is dominant for horizontal particle bedding at the end of loading and for vertical particle bedding at the end of unloading. A change in fabric anisotropy is observed only for the first few loading–unloading cycles for the given conditions depicted in the present study.     

DEM analysis of the size effects on the behavior of crushable granular materials

Four sets of individual-particle crushing tests were carried out on sandstone grains of different size with geometric similarity. The tensile strength was analyzed using Weibull statistics, and the size-hardening law was obtained. The experimental data also validated that the Weibull modulus is independent of the grain size. Considering both the shear and tensile fracture modes of the particle, the Mohr–Coulomb model with a tension cut-off was employed as the fracture criterion of a single particle. When the particle stresses satisfied the fracture criterion, three new fragments modeled by the ‘clump’ were generated to replace the broken particle. Nine spheres with four different sizes were released from the clump and allowed to continue crushing if the fragment stresses fulfilled the criterion again. Two polydisperse assemblies with different particle sizes but same initial fabrics were prepared. DEM simulations of triaxial shear tests with different grain sizes were carried out on the crushable granular material with varied confining pressures. The simulated stress–strain–dilation responses were in agreement with the experimental observations. The macro–micro responses of the two samples, including the stress–strain–dilation behavior, the particle crushing, and the normal contact force distribution, were discussed in detail. The cause of the size effect on the shear strength and deformation was thoroughly investigated through a variety of mechanism demonstrations and micromechanical analysis.     

Micro-scale modeling of axial flow through unidirectional disordered fiber arrays

The objective of this study is to develop a model for the axial hydraulic permeability (K_∥) of fibrous media, taking explicit account of the underlying microstructure and its variability. In this numerical study, a unidirectional fiber array is represented by a unit cell consisting of ∼600 randomly placed fiber cross-sections. Stokes flow through such a unidirectional fiber array in the axial direction is modeled by a two-dimensional Stokes equation and solved using a parallel implementation of the boundary element method. A large number of simulations in such geometries have been carried out. The results indicate that (K_∥) increases as the underlying microstructure progresses from a uniform distribution to a non-uniform one. To explain this relation between (K_∥) and microstructure, a microstructural parameter, namely the mean nearest inter-fiber spacing, is proposed to characterize the heterogeneity of the fiber distribution. Following this, an empirical model correlating the axial permeability and the mean nearest inter-fiber spacing is presented.     

Experimental evaluation and modeling of sulfur content and anisotropy of sulfide inclusions on fatigue behavior of steels

This paper presents and discusses experimental results on the effect of sulfur content and sulfide inclusions on fatigue behavior of steels with different sulfur and hardness levels under different loading directions. Ductility and toughness of the transverse samples were found to reduce considerably by the increase in sulfur content, while the differences in the yield and ultimate tensile strengths were not significant. High sulfur resulted in significant adverse effect of inclusions on fatigue behavior of the transverse samples, particularly in the long life regime. The difference between the high and low sulfur materials was larger at the higher hardness level. Both sub-surface and surface failure modes were observed at long lives, where the sub-surface failures exhibited much longer life. The √area parameter was used to estimate the fatigue limit of the materials used, resulting in reasonable estimations in most cases. Roessle–Fatemi equation, which is used to predict the strain-life curve of steels based on hardness, was modified in order to incorporate the effects of sulfur under transverse loading. It is shown that this modified equation results in relatively good predictions of fatigue lives.     

Discrete element modeling of first shear strain gradient effects on mechanical behaviors in granular materials

Granular Matter - We introduce an improved version of a computational algorithm that “clones”/generates an arbitrary number of new digital grains from a sample of real digitalized...     

Scan line void fabric anisotropy tensors of granular media

Soil fabric anisotropy tensors are related to the statistical distribution of orientation of different microstructural vector-like entities, most common being the contact normal vectors between particles, which are extremely difficult to determine for real granular materials. On the other hand, void fabric based tensors can be determined by image based quantification methods of voids (graphical approaches), which are well defined and easy to apply to both physical and numerical experiments. A promising void fabric characterization approach is based on the scan line method. Existing scan line based definitions of void fabric anisotropy tensors are shown analytically to inherit a shortcoming, since numerous small void segments in a sample have an inordinate contribution towards unwarranted isotropy. Discrete Element Method (DEM) of analysis subsequently confirms this analytical proof. The fact that such scan line void fabric tensor definitions yield acceptable results when used in conjunction with physical image-based measurements, is shown to be attributed to the natural “cut off” of smaller void segments that occurs during such measurements. This is the motivation to propose using the existing definition of void fabric tensors, with exclusion of void segments less than a “cut off” value associated with an internal length of the granular assembly. In addition, an entirely new void fabric tensor was introduced using the squared length, instead of the length of a void segment, as the weighting factor for the definition of the scan line void fabric tensor. It was found by means of DEM analysis that both alternative definitions are void of the aforementioned shortcoming and compatible with existing image quantification methods of void fabric anisotropy.     

Transient behavior of granular materials as result of tumbler shape and orientation effects

Granular flows are most often investigated at steady-state conditions. This allows time-averaged analysis to display results such as velocity profiles and convective accelerations within the thin flowing layer. Typically in rotating tumblers, constant rotation rates and circular shapes are used as they jointly produce a steady, uniform flowing layer at the free surface. Conversely, unsteady flowing layers can be generated through any combination of varying the rotation rate of a tumbler or using a non-circular cross-sectional shape to change the length of the flowing layer. The unsteady conditions, however, require the additional complexity of ensemble-averaged analysis of images in a sequence of multiple trials. The experiments of this paper examine the properties of unsteady flow produced by triangular-shaped rotating tumblers at constant rotation rates. The geometric shape naturally causes periodic changes in the flowing layer as a function of the instantaneous orientation of the triangle. Multiple experiments were conducted in which the parameters of tumbler dimension, particle size, fill level and rotation rate were varied in all combinations. The free surface properties of angle of repose and flowing layer length, position, and curvature are reported. Results show that the arithmetic difference between the angle of repose and the tumbler orientation has a functional relationship with the instantaneous flowing layer length in the form of a catenary indicating a minimization of energy in the granular flow. Furthermore, the oscillation of the flowing layer position appears to affect the free surface curvature in the upstream regions. This is likely due to the rapidly increasing and decreasing length of the free surface limiting the space where particles can enter or exit the flowing layer. Ultimately, the unsteady macroscopic properties of the free surface flowing layer in the triangular tumblers provide some indication of the complexities of granular velocity and acceleration that contribute to the mixing and segregation in this unique tumbler shape.     

Anisotropy of elasticity and fabric of granular soils

Anisotropy of elasticity is a very important feature of granular soils. In this paper, numerical experiments using discrete element method were performed to emulate drained triaxial tests and simple shear tests at different stress levels. From these numerical experiments the macroscopic elasticity parameters were determined. The results show that at isotropic stress states the stiffness of the numerical specimen increases, while the Poisson’s ratio decreases with increasing confining pressure. The small strain shear modulus of the numerical specimen agrees well with the laboratory experimental results on a specimen with similar conditions. At anisotropic stress states, there is a threshold stress ratio (\({ SR}_{\mathrm{th}}\)), which characterizes the degrees of stiffness change and fabric change during the shearing. When the stress ratio (SR) is less than \({ SR}_{\mathrm{th}}\), the microscopic contact number does not change and its distribution remains nearly isotropic, while the distribution of contact forces change and become anisotropic to resist the applied anisotropic stress. Therefore the stiffness anisotropy of the specimen mainly results from the anisotropy of contact forces. When SR is larger than \({ SR}_{\mathrm{th}}\), however, the contact number decreases significantly in the minor principal stress direction resulting in the fabric anisotropy, along with the adjustments of contact forces. The stiffness anisotropy of the specimen results from both the fabric anisotropy and the contact force anisotropy. It also indicates that the stress normalized stiffness may be used as an index of the degree of fabric anisotropy. Moreover, the Poisson’s ratio of the specimen increases continuously with increasing stress ratio and its anisotropy can be approximately related to the stiffness anisotropy.     

Use of CFD-DEM to evaluate the effect of intermediate stress ratio on the undrained behaviour of granular materials

This study investigates the effect of intermediate stress ratio (b) on the mechanical behaviour of granular soil in true triaxial tests. A CFD-DEM solver with the ability to model compressible fluid and moving mesh has been developed and calibrated based on existing experimental test results on Nevada sand. The effect of b on the undrained true triaxial test, which has been neglected in the literature, was investigated using a reasonable number of models. The effects of the initial confining stress and initial void ratio also have been studied. The developed model was used to calculate the hydrodynamic forces on the particles and evaluate the ratio of the particle–fluid interaction force to the resultant force on the particles. It has been demonstrated that, in numerical studies, the effect of these forces cannot be neglected.     

Multi-scale modeling of thermo-oxidation effects on the flexural behavior of cross-ply bismaleimide composites

Mechanics of Time-Dependent Materials - Mechanical properties of high-temperature polymer matrix composites deteriorate during their service. Oxidation plays a significant role in determining the...     

Viscoplastic modeling of asphalt mixes with the effects of anisotropy, damage and aggregate characteristics

This paper presents an approach for constitutive modeling of the viscoplastic behavior of asphalt mixes. This approach utilizes an anisotropic non-associated flow rule based on the Drucker–Prager yield surface. The selection of this yield surface is motivated by the field stress paths and material properties associated with permanent deformation at high temperatures. The efficacy of the model is demonstrated by analyzing data from compressive triaxial tests conducted at different confining pressures and strain rates for three different mixes. The model parameters are related to the experimental measurements of aggregate shape characteristics, aggregate surface energy, inherent anisotropic distribution of aggregates, and microstructure damage measured using X-ray computed tomography and image analysis techniques. Establishing the relationship between the model parameters and material properties is important in order to optimize the mix properties, and achieve desirable mix performance.     

The influence of rolling resistance on the stress-dilatancy and fabric anisotropy of granular materials

The effects of rolling resistance on the stress-dilatancy behavior and fabric anisotropy of granular materials were investigated through a three-dimensional discrete element method (DEM). A rolling resistance model was incorporated into the DEM code PFC3D and triaxial DEM simulations under simulated drained and undrained conditions were carried out. The results show that there existed a threshold value of the rolling friction. When the rolling friction was smaller than this value, the mechanical behavior of granular materials under both drained and undrained conditions were substantially influenced by the rolling friction, but the influence diminished when it was larger than the threshold value. A linear relationship has been observed between the dilatancy coefficient and the natural logarithm of the rolling-friction coefficient when it was smaller than the threshold value. An increase in the rolling friction led to an increase in the fabric anisotropy of all strong contacts under both testing conditions until the threshold value was attained. The investigation on the effect of rolling friction on the microstructure of granular materials revealed that the rolling friction enhanced the stability of force chains, which resulted in the difference in the stress-dilatancy behavior. Finally, the relationship between the stress ratio q/p\(^{\prime }\) and the fabric measure at strong contacts \(\hbox {H}_{\mathrm{d}}^{\mathrm{s}} /\hbox {H}_{\mathrm{m}}^{\mathrm{s}}\) was found independent of the inter-particle friction, rolling friction and testing conditions.