Multiple Characteristic Length Research Articles

The mechanical properties of TCP phase of rapidly cooled molybdenum

The rapidly-cooling of pure molybdenum (Mo) at 1010 Ks−1 and the uniaxial tensile of the solid at a strain rate of 2 × 10 s−1 were studied by molecular dynamics simulation; then the structure evolution was investigated in terms of pair distribution function and the largest standard cluster analysis. It is found that Mo melt was cooled into a complex crystal with multiple characteristic lengths. Further analysis revealed that it is a mixture topological close packing (TCP) crystal composed of the dominated A15 phase (Mo-A15) and the less Z phase, with H phase as twin grain boundary. The Phonon spectrum, potential energy, and cohesion energy revealed that Mo-A15 is stable slightly inferior to Mo-bcc. Compared to the prevailing bcc Mo, Mo-A15 holds much higher Young’s modulus, ultimate tensile strength, and Yield strength, being a representative material for barrier layer with high hardness.

Accounting for Small-Scale Heterogeneity and Variability of Clay Rock in Homogenised Numerical Micromechanical Response and Microcracking

Clayey rocks have a complex microstructure with multiple characteristic lengths. Deformation under mechanical loading generally induces damage by microcracking, which essentially concerns the scale of mineral inclusions embedded in the clay matrix. The modelling of these materials is considered within the framework of a double scale approach, by numerical homogenisation, of the squared finite element method type. This allows a heterogeneous microstructure of the material to be taken into account and a distribution of morphological properties to be introduced. Emphasis is placed on the generation of microstructures satisfying experimental observations, and keeping a certain simplicity to fit into the framework of double scale modelling. The material characteristics and behaviour are defined at the grain scale: the mineralogical properties include the mineral phase proportions and the grain morphology, while the material constituents are represented by elastic grains separated by damageable cohesive crack models. Then, the overall microscale behaviour of the material under solicitation is derived from equilibrated elementary area (EA) configuration and computational homogenisation. The variability of the material response is studied with regard to small-scale aspects as microstructure variability, microstructure size, grain angularity, and properties of grain contacts. Deformation analyses at grain contacts emphasise a dominant shear deformation mode and the development of decohesion between grains. The latter induces microfaulting processes across the entire EA and strain softening of the overall response. Moreover, the improvement of microscale behaviour modelling opens new possibilities for more realistic multi-scale modelling and upscaled behaviour of heterogeneous rocks.

Interpreting slip transmission through mechanically induced interface energies: a Fe–3%Si case study

Nanoindentation experiments are performed at the vicinity of grain boundaries, in Fe–Si tricrystals, to illustrate the existence of a critical stress at which slip transmission occurs across grain boundaries. Such a critical stress can be considered as a grain boundary yield stress and can be quantified within the framework of conventional gradient plasticity theory, enhanced by introducing a new mechanically induced “interface energy” term. The present study takes a first step in trying to provide a physical interpretation for this “far from thermodynamic equilibrium” interface energy term by conducting nanoindentation tests in three Fe–3wt%Si tricrystals, each of which had three distinct types of grain boundary misorientations, namely 22.5°, 42.0° and 44.6°. By relating the experimentally measured grain boundary yield stress to the predictions of interfacial gradient plasticity, it is possible to determine the interface parameter ( $$ \xi $$ ), which provides a measure of the resistance to slip transmission for each grain boundary examined. In particular, microscopic arguments from standard dislocation theory reveal that $$ \xi $$ depends on both the grain interior properties and the grain boundary structure. The internal length is shown to depend on multiple characteristic lengths of the microstructure, while a new expression is deduced for relating the Hall-Petch slope to both the interface parameter and internal length.

Mechanical characterization of glass-ceramic scaffolds at multiple characteristic lengths through nanoindentation

The mechanical behaviour of implantable scaffolds is of relevant interest in all applications which require load-bearing capability. This study aims at establishing a quantitative relationship between the mechanical properties of glass-ceramic scaffolds for bone repair and the nano/micro-scale properties of their constituent materials. A nanoindentation study is carried out spanning different penetration depth on bulk (pore-free) glass-ceramic samples and on the walls of porous scaffolds. Micro-tomographical investigations allow assessing small-scale porosity of the scaffold walls. A simple homogenization model is used to establish the relationship between the elastic modulus of the bulk material and that of the micro-porous walls of the scaffolds. The elastic modulus of scaffold walls was found to be approximately 50% lower than that of the bulk glass-ceramic. The properties estimated experimentally on the walls of the scaffolds are quantitatively consistent with the analytical predictions provided by the homogenization model and the micro-porosity measured through tomographical analyses.

Communication: Capturing protein multiscale thermal fluctuations.

Existing elastic network models are typically parametrized at a given cutoff distance and often fail to properly predict the thermal fluctuation of many macromolecules that involve multiple characteristic length scales. We introduce a multiscale flexibility-rigidity index (mFRI) method to resolve this problem. The proposed mFRI utilizes two or three correlation kernels parametrized at different length scales to capture protein interactions at corresponding scales. It is about 20% more accurate than the Gaussian network model (GNM) in the B-factor prediction of a set of 364 proteins. Additionally, the present method is able to deliver accurate predictions for some large macromolecules on which GNM fails to produce accurate predictions. Finally, for a protein of N residues, mFRI is of linear scaling (O(N)) in computational complexity, in contrast to the order of O(N(3)) for GNM.

High-Order Microplane Theory for Quasi-Brittle Materials with Multiple Characteristic Lengths

The heterogeneous internal structure of quasi-brittle materials governs several aspects of their behavior, especially in the nonlinear range. Size and spacing of weak spots (e.g., aggregate-matrix interfaces, flaws, and slip planes) where failure is likely to occur are two of the most important material characteristic lengths that can be used to characterize the micro- and meso-structure of these materials. Discrete (lattice and particle) models can be conveniently used to directly model these geometrical features, but they tend to be computationally expensive, and consequently, the derivation of macroscopic continuum-based approximations is often highly beneficial. The current study demonstrates that the continuum macroscale approximation of discrete fine-scale models leads naturally to a high-order microplane theory characterized by multiple characteristic lengths. The average weak spot spacing is shown to be associated with strain gradient effects; whereas the average weak spot size is shown to be associated with the Cosserat characteristics of the theory. The formulated microplane theory is compared with and contrasted to classical continuum theories available in the literature. Finally, for strain softening, known in the case of first-order local formulations to cause strain localization in an unrealistic vanishing size volume, a localization limiter capable of enforcing the minimum localization size to be of a finite value is formulated, exploiting the spectral wave propagation analysis approach.

Wavelet analysis of characteristic length scales and orientation of two-dimensional heterogeneous porous media

The global wavelet energy spectrum (GWES) has been used on one-dimensional transects of porous media to identify the characteristic length scale of a material property. The characteristic length scale is a measure of the distance over which property values are correlated. We extend the wavelet analysis technique to two-dimensional stationary porous media for identifying both the characteristic length scales and orientation of heterogeneity. We theoretically develop and evaluate the GWES for isotropic and anisotropic random fields using the two-dimensional Mexican hat wavelet. The relationship between the wavelet scale and the characteristic length scale of a two-dimensional random field is investigated for different covariance structures. The ability of the GWES to identify multiple characteristic length scales and orientations in a random field with nested covariance structures is also investigated. We use the technique to identify the characteristic length scales of a log hydraulic conductivity field used in a laboratory experiment.

On Solving the Ill-Conditioned System Ax=b: General-Purpose Conditioners Obtained From the Boundary-Collocation Solution of the Laplace Equation, Using Trefftz Expansions With Multiple Length Scales

Here we develop a general purpose pre/post conditioner T, to solve an ill-posed system of linear equations, Ax = b. The conditioner T is obtained in the course of the solution of the Laplace equation, through a boundary-collocation Trefftz method, leading to: Ty = x, where y is the vector of coefficients in the Tr- efftz expansion, and x is the boundary data at the discrete points on a unit circle. We show that the quality of the conditioner T is greatly enhanced by using multiple characteristic lengths (Multiple Length Scales) in the Trefftz expansion. We further show that T can be multiplicatively decomposed into a dilation TD and a rotation TR. For an odd-ordered A, we develop four conditioners based on the solution of the Laplace equation for Dirichlet boundary conditions, while for an even-ordered A we develop four conditioners employing the Neumann boundary conditions. All these conditioners are well-behaved and easily invertible. Several examples involv- ing ill-conditioned A, such as the Hilbert matrices, those arising from the Method of Fundamental Solutions, those arising from very-high order polynomial interpo- lations, and those resulting from the solution of the first-kind Fredholm integral equations, are presented. The results demonstrate that the presently proposed con- ditioners result in very high computational efficiency and accuracy, when Ax = b is highly ill-conditioned, and b is noisy.

Performance Evaluation for Multi-arm Manipulation of Hollow Suspended Organs

This paper presents a unified mathematical framework for modeling and evaluating the performance of multiple robotic arms that operate on hollow suspended organs. This framework is applied to a novel two-armed hybrid robotic system being developed for ophthalmic vitreous surgeries. Four cases are designated to capture the general movements required for any surgical procedure associated with hollow suspended organs. Dexterity measures, based on multiple characteristic lengths, are presented for procedures corresponding to these manipulation cases. Simulation results of the dual-arm robotic system for ophthalmic surgery are presented for all four manipulation cases. A comparison of this robotic system with current surgical tools shows a significant improvement in intraocular dexterity.

Wavelet analysis of dominant scales of heterogeneous porous media

Heterogeneity of aquifer permeability has a significant influence on the transport of solutes; therefore characterization of aquifer heterogeneity is needed to accurately predict the behavior of solutes. A critical characteristic of heterogeneity is a characteristic length scale that is a measure of the distance over which property values are correlated. We show that the characteristic length scale of a statistically homogeneous permeability field can be identified through wavelet analysis using the global wavelet energy spectrum (GWES). The relationship between the wavelet scale and the characteristic length scale of a random field is investigated for the Mexican hat and Morlet wavelets and different covariance structures. The ability of the GWES to identify multiple characteristic length scales in a random field with nested covariance structures is also investigated. We use the technique to identify the characteristic length scales of a laboratory‐collected permeability transect from Massillon sandstone.

COMPARTMENTAL MODELING OF MULTIDIMENSIONAL CRYSTALLIZATION

An approach that couples compartmental modeling with high resolution methods is developed to simulate spatial variations in the crystal size and shape distribution in solution crystallization processes. This is the first time that compartmental modeling has been applied to a crystal system with multiple characteristic length scales. The compartment model enables a more accurate modeling of the effect of secondary nucleation, which is key to accurately predicting the crystal size distribution of the final product. A parallel implementation of the numerical algorithm results in short computation times.