Microstructure dependent dynamic fracture analyses of trabecular bone based on nascent bone atomistic simulations

Trabecular bone fracture is closely related to the trabecular architecture, microdamage accumulation, and bone tissue properties. Primary constituents of trabecular tissue are hydroxyapatite (HA) mineralized type-I collagen fibers. In this research, dynamic fracture in two dimensional (2-D) micrographs of ovine (sheep) trabecular bone is modeled using the mesoscale cohesive finite element method (CFEM). The bone tissue fracture properties are obtained based on the atomistic strength analyses of a type-I collagen + HA interfacial arrangement using molecular dynamics (MD). Analyses show that the presented framework is capable of analyzing the architecture dependent fracture in 2-D micrographs of trabecular bone.     

A computational strategy for multiscale systems with applications to Lorenz 96 model

Numerical schemes for systems with multiple spatio-temporal scales are investigated. The multiscale schemes use asymptotic results for this type of systems which guarantee the existence of an effective dynamics for some suitably defined modes varying slowly on the largest scales. The multiscale schemes are analyzed in general, then illustrated on a specific example of a moderately large deterministic system displaying chaotic behavior due to Lorenz. Issues like consistency, accuracy, and efficiency are discussed in detail. The role of possible hidden slow variables as well as additional effects arising on the diffusive time-scale are also investigated. As a byproduct we obtain a rather complete characterization of the effective dynamics in Lorenz model.     

A recursive-faulting model of distributed damage in confined brittle materials

We develop a model of distributed damage in brittle materials deforming in triaxial compression based on the explicit construction of special microstructures obtained by recursive faulting. The model aims to predict the effective or macroscopic behavior of the material from its elastic and fracture properties; and to predict the microstructures underlying the microscopic behavior. The model accounts for the elasticity of the matrix, fault nucleation and the cohesive and frictional behavior of the faults. We analyze the resulting quasistatic boundary value problem and determine the relaxation of the potential energy, which describes the macroscopic material behavior averaged over all possible fine-scale structures. Finally, we present numerical calculations of the dynamic multi-axial compression experiments on sintered aluminum nitride of Chen and Ravichandran [1994. Dynamic compressive behavior of ceramics under lateral confinement. J. Phys. IV 4, 177-182; 1996a. Static and dynamic compressive behavior of aluminum nitride under moderate confinement. J. Am. Soc. Ceramics 79(3), 579-584; 1996b. An experimental technique for imposing dynamic multiaxial compression with mechanical confinement. Exp. Mech. 36(2), 155-158; 2000. Failure mode transition in ceramics under dynamic multiaxial compression. Int. J. Fracture 101, 141-159]. The model correctly predicts the general trends regarding the observed damage patterns; and the brittle-to-ductile transition resulting under increasing confinement.     

Multiscale Finite Element Modeling of Arc Dynamics in a DC Plasma Torch

The dynamics of the electric arc inside a direct current non-transferred arc plasma torch are simulated using a three-dimensional, transient, equilibrium model. The fluid and electromagnetic equations are solved numerically in a fully coupled approach by a multiscale finite element method. Simulations of a torch operating with argon and argon–hydrogen under different operating conditions are presented. The model is able to predict the operation of the torch in steady and takeover modes without any further assumption on the reattachment process except for the use of an artificially high electrical conductivity near the electrodes, needed because of the equilibrium assumption. The results obtained indicate that the reattachment process in these operating modes may be driven by the movement of the arc rather than by a breakdown-like process. It is also found that, for a torch operating in these modes and using straight gas injection, the arc will tend to re-attach to the opposite side of its original attachment. This phenomenon seems to be produced by a net angular momentum on the arc due to the imbalance between magnetic and fluid drag forces.     

Enhanced mechanical properties of unidirectional basalt fiber/epoxy composites using silane-modified Na+-montmorillonite nanoclay

This study explores the effects of 3-glycidoxypropyltrimethoxysilane (3-GPTS) modified Na-montmorillonite (Na-Mt) nanoclay addition on mechanical response of unidirectional basalt fiber (UD-BF)/epoxy composite laminates under tensile, flexural and compressive loadings. Fourier transform infrared (FT-IR), X-ray diffraction (XRD) and simultaneous thermal analysis (STA) data confirmed the reaction mechanism between the silane compound and Mt. It was demonstrated that addition of 5 wt % 3-GPTS/Mt resulted in 28%, 11% and 35% increase in flexural, tensile and compressive strengths. Scanning electron microscopy (SEM) clarified the improvement in the adhesion between the basalt fibers and matrix in the case of Mt-enhanced epoxy specimens. Also, a theoretical route based on a Euler-Bernoulli beam-based approach was employed to estimate the compressive properties of the composites. The results demonstrated good agreement between theoretical and experimental approaches. Totally, the results of the study show that matrix modification is an effective strategy to improve the mechanical behavior of fibrous composites.     

Multi-scale magnetic resonance measurements and validation of Discrete Element Model simulations

This short review describes the capabilities of magnetic resonance (MR) to image opaque single- and two-phase granular systems, such as rotating cylinders and gas-fluidized beds operated in different fluidization regimes. The unique capability of MR to not only image the solids’ distribution (voidage) but also the velocity of the particulate phase is clearly shown. It is demonstrated that MR can provide measurements over different length and time scales. With the MR equipment used for the studies summarized here, temporal and spatial scales range from sub-millisecond to hours and from a few hundred micrometres to a few centimetres, respectively. Besides providing crucial data required for an improved understanding of the underlying physics of granular flows, multi-scale MR measurements were also used to validate numerical simulations of granular systems. It is shown that predictions of time-averaged properties, such as voidage and velocity of the particulate phase, made using the Discrete Element Model agree very well with MR measurements.     

Analysis of complex time series using refined composite multiscale entropy

Multiscale entropy (MSE) is an effective algorithm for measuring the complexity of a time series that has been applied in many fields successfully. However, MSE may yield an inaccurate estimation of entropy or induce undefined entropy because the coarse-graining procedure reduces the length of a time series considerably at large scales. Composite multiscale entropy (CMSE) was recently proposed to improve the accuracy of MSE, but it does not resolve undefined entropy. Here we propose a refined composite multiscale entropy (RCMSE) to improve CMSE. For short time series analyses, we demonstrate that RCMSE increases the accuracy of entropy estimation and reduces the probability of inducing undefined entropy.     

Analytical and numerical study of coupled atomistic-continuum methods for fluids

The stability and convergence rate of coupled atomistic-continuum methods are studied analytically and numerically. These methods couple a continuum model with molecular dynamics through the exchange of boundary conditions in the continuum-particle overlapping region. Different coupling schemes, including velocity–velocity, flux–velocity, velocity–flux and flux–flux, are studied. It is found that the velocity–velocity and flux–velocity schemes are stable. The flux–flux scheme is weakly unstable. The stability of the velocity–flux scheme depends on the parameter T_c which is the length of the time interval between successive exchange of boundary conditions. It is stable when T_c is small and unstable when T_c is large. For steady-state problems, the flux–velocity scheme converges faster than the other coupling schemes.     

Multiscale modeling of the effect of carbon nanotube orientation on the shear deformation properties of reinforced polymer-based composites

A combination of molecular dynamics (MD), continuum elasticity and FEM is used to predict the effect of CNT orientation on the shear modulus of SWCNT-polymer nanocomposites. We first develop a transverse-isotropic elastic model of SWCNTs based on the continuum elasticity and MD to compute the transverse-isotropic elastic constants of SWCNTs. These constants are then used in an FEM-based simulation to investigate the effect of SWCNT alignment on the shear modulus of nanocomposites. Furthermore, shear stress distributions along the nanotube axis and over its cross-sectional area are investigated to study the effect of CNT orientation on the shear load transfer.