The configuration evolution and macroscopic elasticity of fluid-filled closed cell composites : micromechanics and multiscale homogenization modelling

For fluid-filled closed cell composites widely distributed in nature, the configuration evolution and effective elastic properties are investigated using a micromechanical model and a multiscale homogenization theory, in which the effect of initial fluid pressure is considered. Based on the configuration evolution of the composite, we present a novel micromechanics model to examine the interactions between the initial fluid pressure and the macroscopic elasticity of the material. In this model, the initial fluid pressure of the closed cells and the corresponding configuration can be produced by applying an eigenstrain at the introduced fictitious stress-free configuration, and the pressure-induced initial microscopic strain is derived. Through a configuration analysis, we find the initial fluid pressure has a prominent effect on the effective elastic properties of freestanding materials containing pressurized fluid pores, and a new explicit expression of effective moduli is then given in terms of the initial fluid pressure. Meanwhile, the classical multiscale homogenization theory for calculating the effective moduli of a periodical heterogeneous material is generalized to include the pressurized fluid "inclusion" effect. Considering the coupling between matrix deformation and fluid pressure in closed cells, the multiscale homogenization method is utilized to numerically determine the macroscopic elastic properties of such composites at the unit cell level with specific boundary conditions. The present micromechanical model and multiscale homogenization method are illustrated by several numerical examples for validation purposes, and good agreements are achieved. The results show that the initial pressure of the fluid phase can strengthen overall effective bulk modulus but has no contribution to the shear modulus of fluid-filled closed cell composites.

Assessing the homogenization of urban land management with an application to US residential lawn care.

Changes in land use, land cover, and land management present some of the greatest potential global environmental challenges of the 21st century. Urbanization, one of the principal drivers of these transformations, is commonly thought to be generating land changes that are increasingly similar. An implication of this multiscale homogenization hypothesis is that the ecosystem structure and function and human behaviors associated with urbanization should be more similar in certain kinds of urbanized locations across biogeophysical gradients than across urbanization gradients in places with similar biogeophysical characteristics. This paper introduces an analytical framework for testing this hypothesis, and applies the framework to the case of residential lawn care. This set of land management behaviors are often assumed--not demonstrated--to exhibit homogeneity. Multivariate analyses are conducted on telephone survey responses from a geographically stratified random sample of homeowners (n = 9,480), equally distributed across six US metropolitan areas. Two behaviors are examined: lawn fertilizing and irrigating. Limited support for strong homogenization is found at two scales (i.e., multi- and single-city; 2 of 36 cases), but significant support is found for homogenization at only one scale (22 cases) or at neither scale (12 cases). These results suggest that US lawn care behaviors are more differentiated in practice than in theory. Thus, even if the biophysical outcomes of urbanization are homogenizing, managing the associated sustainability implications may require a multiscale, differentiated approach because the underlying social practices appear relatively varied. The analytical approach introduced here should also be productive for other facets of urban-ecological homogenization.

A new solution method for homogenization of effective properties of electromagnetic honeycombs

In this paper, an analytical model and its new numerical solution using the homogenization method are developed to determine the effective electromagnetic characteristics of honeycombs. Based on the proposed solution method, the electromagnetic properties are obtained by employing the multi-scale homogenization theory and periodical electric (magnetic) potential boundary conditions. Further, the effect of geometry of honeycomb's unit cell on effective electromagnetic properties is investigated with the use of the proposed method. The numerical results are compared with analytic results using the Smith-Scarpa's semi-empirical formula.

An anisotropic elastic-viscoplastic damage model for bone tissue

A new anisotropic elastic-viscoplastic damage constitutive model for bone is proposed using an eccentric elliptical yield criterion and nonlinear isotropic hardening. A micromechanics-based multiscale homogenization scheme proposed by Reisinger et al. is used to obtain the effective elastic properties of lamellar bone. The dissipative process in bone is modeled as viscoplastic deformation coupled to damage. The model is based on an orthotropic ecuntric elliptical criterion in stress space. In order to simplify material identification, an eccentric elliptical isotropic yield surface was defined in strain space, which is transformed to a stress-based criterion by means of the damaged compliance tensor. Viscoplasticity is implemented by means of the continuous Perzyna formulation. Damage is modeled by a scalar function of the accumulated plastic strain D(κ) , reducing all element s of the stiffness matrix. A polynomial flow rule is proposed in order to capture the rate-dependent post-yield behavior of lamellar bone. A numerical algorithm to perform the back projection on the rate-dependent yield surface has been developed and implemented in the commercial finite element solver Abaqus/Standard as a user subroutine UMAT. A consistent tangent operator has been derived and implemented in order to ensure quadratic convergence. Correct implementation of the algorithm, convergence, and accuracy of the tangent operator was tested by means of strain- and stress-based single element tests. A finite element simulation of nano- indentation in lamellar bone was finally performed in order to show the abilities of the newly developed constitutive model.

A Note on Iterations-based Derivations of High-order Homogenization Correctors for Multiscale Semi-linear Elliptic Equations

This Note aims at presenting a simple and efficient procedure to derive the structure of high-order corrector estimates for the homogenization limit applied to a semi-linear elliptic equation posed in perforated domains. Our working technique relies on monotone iterations combined with formal two-scale homogenization asymptotics. It can be adapted to handle more complex scenarios including for instance nonlinearities posed at the boundary of perforations and the vectorial case, when the model equations are coupled only through the nonlinear production terms.

Multiscale Analysis of Topographic Surface Roughness in the Midland Valley, Scotland

Surface roughness is an important geomorphological variable which has been used in the Earth and planetary sciences to infer material properties, current/past processes, and the time elapsed since formation. No single definition exists; however, within the context of geomorphometry, we use surface roughness as an expression of the variability of a topographic surface at a given scale, where the scale of analysis is determined by the size of the landforms or geomorphic features of interest. Six techniques for the calculation of surface roughness were selected for an assessment of the parameter`s behavior at different spatial scales and data-set resolutions. Area ratio operated independently of scale, providing consistent results across spatial resolutions. Vector dispersion produced results with increasing roughness and homogenization of terrain at coarser resolutions and larger window sizes. Standard deviation of residual topography highlighted local features and did not detect regional relief. Standard deviation of elevation correctly identified breaks of slope and was good at detecting regional relief. Standard deviation of slope (SD(slope)) also correctly identified smooth sloping areas and breaks of slope, providing the best results for geomorphological analysis. Standard deviation of profile curvature identified the breaks of slope, although not as strongly as SD(slope), and it is sensitive to noise and spurious data. In general, SD(slope) offered good performance at a variety of scales, while the simplicity of calculation is perhaps its single greatest benefit.

Multiphase material modelling by multiscale particle-in-cell method

A particle-based method for multiscale modeling of multiphase materials such as Dual Phase (DP) and Transformation Induced Plasticity (TRIP) steels has been developed. The multiscale Particle-In-Cell (PIC) method benefits from the many advantages of the FEM and mesh-free methods, and to bridge the micro and macro scales through homogenization. The conventional mesh-based modeling methods fail to give reasonable and accurate predictions for materials with complex microstructures. Alternatively in the multiscale PIC method, the Lagrangian particles moving in an Eulerian grid represent the material deformation at both the micro and macro scales. The uniaxial tension test of two phase and three-phase materials was simulated and compared with FE based simulations. The predictions using multiscale PIC method showed that accuracy of field variables could be improved by up to 7%. This can lead to more accurate forming and springback predictions for materials with important multiphase microstructural effects.

Multiscale analysis of protein functions and stochastic modelling of gene transcriptional regulatory networks

Genomic and proteomic analyses have attracted a great deal of interests in biological research in recent years. Many methods have been applied to discover useful information contained in the enormous databases of genomic sequences and amino acid sequences. The results of these investigations inspire further research in biological fields in return. These biological sequences, which may be considered as multiscale sequences, have some specific features which need further efforts to characterise using more refined methods. This project aims to study some of these biological challenges with multiscale analysis methods and stochastic modelling approach. The first part of the thesis aims to cluster some unknown proteins, and classify their families as well as their structural classes. A development in proteomic analysis is concerned with the determination of protein functions. The first step in this development is to classify proteins and predict their families. This motives us to study some unknown proteins from specific families, and to cluster them into families and structural classes. We select a large number of proteins from the same families or superfamilies, and link them to simulate some unknown large proteins from these families. We use multifractal analysis and the wavelet method to capture the characteristics of these linked proteins. The simulation results show that the method is valid for the classification of large proteins. The second part of the thesis aims to explore the relationship of proteins based on a layered comparison with their components. Many methods are based on homology of proteins because the resemblance at the protein sequence level normally indicates the similarity of functions and structures. However, some proteins may have similar functions with low sequential identity. We consider protein sequences at detail level to investigate the problem of comparison of proteins. The comparison is based on the empirical mode decomposition (EMD), and protein sequences are detected with the intrinsic mode functions. A measure of similarity is introduced with a new cross-correlation formula. The similarity results show that the EMD is useful for detection of functional relationships of proteins. The third part of the thesis aims to investigate the transcriptional regulatory network of yeast cell cycle via stochastic differential equations. As the investigation of genome-wide gene expressions has become a focus in genomic analysis, researchers have tried to understand the mechanisms of the yeast genome for many years. How cells control gene expressions still needs further investigation. We use a stochastic differential equation to model the expression profile of a target gene. We modify the model with a Gaussian membership function. For each target gene, a transcriptional rate is obtained, and the estimated transcriptional rate is also calculated with the information from five possible transcriptional regulators. Some regulators of these target genes are verified with the related references. With these results, we construct a transcriptional regulatory network for the genes from the yeast Saccharomyces cerevisiae. The construction of transcriptional regulatory network is useful for detecting more mechanisms of the yeast cell cycle.

A dual-scale modelling approach for drying hygroscopic porous media

A new dualscale modelling approach is presented for simulating the drying of a wet hygroscopic porous material that couples the porous medium (macroscale) with the underlying pore structure (microscale). The proposed model is applied to the convective drying of wood at low temperatures and is valid in the so-called hygroscopic range, where hygroscopically held liquid water is present in the solid phase and water exits only as vapour in the pores. Coupling between scales is achieved by imposing the macroscopic gradients of moisture content and temperature on the microscopic field using suitably-defined periodic boundary conditions, which allows the macroscopic mass and thermal fluxes to be defined as averages of the microscopic fluxes over the unit cell. This novel formulation accounts for the intricate coupling of heat and mass transfer at the microscopic scale but reduces to a classical homogenisation approach if a linear relationship is assumed between the microscopic gradient and flux. Simulation results for a sample of spruce wood highlight the potential and flexibility of the new dual-scale approach. In particular, for a given unit cell configuration it is not necessary to propose the form of the macroscopic fluxes prior to the simulations because these are determined as a direct result of the dual-scale formulation.

Hierarchical multiscale model for biomechanics analysis of microfilament networks

The mechanisms of force generation and transference via microfilament networks are crucial to the understandings of mechanobiology of cellular processes in living cells. However, there exists an enormous challenge for all-atom physics simulation of real size microfilament networks due to scale limitation of molecular simulation techniques. Following biophysical investigations of constitutive relations between adjacent globular actin monomers on filamentous actin, a hierarchical multiscale model was developed to investigate the biomechanical properties of microfilament networks. This model was validated by previous experimental studies of axial tension and transverse vibration of single F-actin. The biomechanics of microfilament networks can be investigated at the scale of real eukaryotic cell size (10 μm). This multiscale approach provides a powerful modeling tool which can contribute to the understandings of actin-related cellular processes in living cells.

Multiscale investigation of microfilament networks disruption in living cells

Actin is the most abundantly distributed protein in living cells which plays critical roles in the cell interior force generation and transmission. The fracture mechanism of microfilament networks, whose principle component is actin, would provide insights which can contribute to the understandings of self-protective characters of cytoskeleton. In this study, molecular simulations are conducted to investigate the molecular mechanisms of disruption of microfilament networks from the viewpoint of biophysics. By employing a coarse-grained (CG) model of actin filament networks, we focused on the ultimate strength and crack growth mode of microfilament networks that have dependency on the crack length. It can be found that, the fracture mechanism of microfilament network has dependency on the structural properties of microfilament networks. The structure flaws marginally change the strength of microfilament networks which would explain the self-protective characters of cytoskeleton.

A multiscale road map of cancer spheroids : incorporating experimental and mathematical modelling to understand cancer progression

Computational models represent a highly suitable framework, not only for testing biological hypotheses and generating new ones but also for optimising experimental strategies. As one surveys the literature devoted to cancer modelling, it is obvious that immense progress has been made in applying simulation techniques to the study of cancer biology, although the full impact has yet to be realised. For example, there are excellent models to describe cancer incidence rates or factors for early disease detection, but these predictions are unable to explain the functional and molecular changes that are associated with tumour progression. In addition, it is crucial that interactions between mechanical effects, and intracellular and intercellular signalling are incorporated in order to understand cancer growth, its interaction with the extracellular microenvironment and invasion of secondary sites. There is a compelling need to tailor new, physiologically relevant in silico models that are specialised for particular types of cancer, such as ovarian cancer owing to its unique route of metastasis, which are capable of investigating anti-cancer therapies, and generating both qualitative and quantitative predictions. This Commentary will focus on how computational simulation approaches can advance our understanding of ovarian cancer progression and treatment, in particular, with the help of multicellular cancer spheroids, and thus, can inform biological hypothesis and experimental design.

Multiscale coupling and multiphysics approaches in earth sciences : theory

Measuring Earth material behaviour on time scales of millions of years transcends our current capability in the laboratory. We review an alternative path considering multiscale and multiphysics approaches with quantitative structure-property relationships. This approach allows a sound basis to incorporate physical principles such as chemistry, thermodynamics, diffusion and geometry-energy relations into simulations and data assimilation on the vast range of length and time scales encountered in the Earth. We identify key length scales for Earth systems processes and find a substantial scale separation between chemical, hydrous and thermal diffusion. We propose that this allows a simplified two-scale analysis where the outputs from the micro-scale model can be used as inputs for meso-scale simulations, which then in turn becomes the micro-model for the next scale up. We present two fundamental theoretical approaches to link the scales through asymptotic homogenisation from a macroscopic thermodynamic view and percolation renormalisation from a microscopic, statistical mechanics view.