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We examine the specific role of the interplay between hardening and disorder characteristics of a representative quasi-brittle material on its failure mechanisms using a random spring network model. The model incorporates quasi-brittleness in its spring constants and disorder in the failure strain threshold and is shown to be effective in simulating the experimentally observed tensile and fracture behaviour of a quasi-brittle epoxy resin-based polymer. It is shown that rapid localization of deformation and associated damage growth occurs for a weakly hardening solid while for a linear elastic material, damage nucleates at multiple independent sites, and there is significant growth of damage, independent of other nucleating sites, prior to maximum load. The failure mechanism is shown to crossover from an avalanche-dominated fracture for a linear elastic material to nucleation-dominated fracture for a weakly hardening material. [ABSTRACT FROM AUTHOR]

Haversian remodeling is known to result in improved resistance to compressive fracture in healthy cortical bone. Here, we examine the individual roles of the mean porosity, structure of the network of pores and remodeled bone matrix properties in the fracture behavior of Haversian bone. The detailed structure of porosity network is obtained both pre- and post-testing of dry cubical bone samples using micro-Computed Tomography. Based on the periodicity in the features of porosity along tangential direction, we develop a two dimensional porosity-based random spring network model for Haversian bone. The model is shown to capture well the macroscopic response and reproduce the avalanche statistics similar to recently reported experiments on porcine bone. The predictions suggest that at the millimeter scale, the remodeled bone matrix of Haversian bone is less stiff but tougher than that of plexiform/primary bone. [ABSTRACT FROM AUTHOR]

Tensile tests of a single cell were simulated in order to understand the effects of the initial orientation of actin fibers (AFs) on global tensile properties. The properties examined included cell deformation, stiffness, and AF behavior. In the model used, the mechanical properties of cellular components, including the cell membrane with an associated actin network, nuclear envelope, and AFs, are expressed as a result of springs that generate force as a function of their extension. Cell shape during the tensile test was determined by a quasi-static approach couched in the framework of the minimum energy concept. Cells with various initial AF orientations were prepared; in particular, AFs in four different initial orientations, namely random (mean ± SD of the initial orientation angle, 46.4 ± 26.9°), parallel to the stretched direction (3.8 ± 3.5°), perpendicular (85.9 ± 2.6°), and diagonally oriented (44.5 ± 3.6°) were examined. The results show a significant drop in initial stiffness with an increase in mean initial AF orientation angles of 0 to 45°. The initial stiffness of the cell with parallel-oriented AFs was much larger than that with perpendicularly oriented AFs. The results also demonstrate that cell elongation induces a passive reorientation of AFs in a stretched direction, thereby causing an increase in cell stiffness. When comparing the rate of change for cell stiffness of the diagonally oriented model with that of the randomly oriented model, our data reveal that the rate of change of cell stiffness is characterized not only by the mean of the initial AF orientation angle, but also by the variation of their distribution.

In the present article, a version of the lattice or spring network method is proposed to model the mechanical response of elastic particulate composites with a high volume fraction of spherical particles and with a much weaker matrix compared to the stiffness of the particles. The main subject of the article is the determination of the axial stiffnesses of the springs of the cell. A comparison of the mechanical response of a three-dimensional particulate composite cube obtained using the finite element method and the proposed methodology showed that the efficiency of the proposed methodology increases with an increasing volume fraction of the particles.

In modeling of elastic objects in a flow such as red blood cells, white blood cells, or tumor cells, several elastic moduli are involved. One of them is the area conservation modulus. In this paper, we focus on spring network models, and we introduce a new way of modeling the area preservation modulus. We take into account the current shape of the individual triangles and find the proportional allocation of area conservation forces, which would for individual triangles preserve their shapes. The analysis shows that this approach tends to regularize the triangulation. We demonstrate this effect on individual triangles as well as on the complete triangulations. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Mechanical ventilation is necessary for treatment of the acute respiratory distress syndrome but leads to overdistension of the open regions of the lung and produces further damage. Although we know that the excessive stresses and strains disrupt the alveolar epithelium, we know little about the relationship between epithelial strain and epithelial leak. We have developed a computational model of an epithelial monolayer to simulate leak progression due to overdistension and to explain previous experimental findings in mice with ventilator-induced lung injury. We found a nonlinear threshold-type relationship between leak area and increasing stretch force. After the force required to initiate the leak was reached, the leak area increased at a constant rate with further increases in force. Furthermore, this rate was slower than the rate of increase in force, especially at end-expiration. Parameter manipulation changed only the leak-initiating force; leak area growth followed the same trend once this force was surpassed. These results suggest that there is a particular force (analogous to ventilation tidal volume) that must not be exceeded to avoid damage and that changing cell physical properties adjusts this threshold. This is relevant for the development of new ventilator strategies that avoid inducing further injury to the lung. [ABSTRACT FROM AUTHOR]

A statistical approach is taken to model the complex fracture process involved in the mode-I and mixed-mode translaminar growth of a macroscopic crack in a representative woven composite material. A two dimensional rectangular elastic spring network with nearest and next-nearest neighbour interactions was used to discretise a typical fracture specimen. An arrangement of rigid truss elements was introduced at the top and bottom edges of the network to model the displacement boundary conditions realistically. Heterogeneous properties of the woven composites were incorporated in the model by defining four types of regions composed of different combinations of hard and soft bonds. Among the model parameters, the ratio between the modulus of hard and soft bonds was found to have minimal effect on the fracture process as well as the macroscopic response. However, the ratio between the mean failure threshold strains is shown to be critical in simulating nucleation of damage at multiple sites around the initial crack plane resulting in large process zones and higher dissipation of energy during crack growth that is typical of composite materials as reported in existing literature. [ABSTRACT FROM AUTHOR]

In the present paper, a possibility of an approximation of elastic particulate composite with a network of elastic springs that undertake only axial forces is considered. It is assumed that the springs are equivalent to two hemispheres interacting through a weaker interface member. In a frame of the suggested approach, the description of the composite is limited to translational degrees of freedom, therefore, only a normal interaction between the spheres was considered. The methodology for calculation of the axial stiffness of the elastic springs and obtained solutions of the stiffness in explicit form are the main novelty of the article. A comparison of the stiffnesses of the springs obtained by the proposed methodology and by the three dimensional Finite Element Method (FEM) has shown a good agreement between them in a wide range of the ratio of the modulus of elasticity of the particles and matrix at four different distances between surfaces of the particles. A possibility of the approximation of particulate composite by springs was tested and discussed in details by comparing results of a mechanical response of a sample (under three different loading cases) modelled as a three dimensional solid and as a system comprised of the springs. The solutions were obtained by the FEM. [ABSTRACT FROM AUTHOR]

The forces of mechanical interdependence between the airways and the parenchyma in the lung are powerful modulators of airways responsiveness. Little is known, however, about the extent to which adjacent airways affect each other's ability to narrow due to distortional forces generated within the intervening parenchyma. We developed a two-dimensional computational model of two airways embedded in parenchyma. The parenchyma itself was modeled in three ways: 1) as a network of hexagonally arranged springs, 2) as a network of triangularly arranged springs, and 3) as an elastic continuum. In all cases, we determined how the narrowing of one airway was affected when the other airway was relaxed vs. when it narrowed to the same extent as the first airway. For the continuum and triangular network models, interactions between airways were negligible unless the airways lay within about two relaxed diameters of each other, but even at this distance the interactions were small. By contrast, the hexagonal spring network model predicted that airway-airway interactions mediated by the parenchyma can be substantial for any degree of airway separation at intermediate values of airway contraction forces. Evidence to date suggests that the parenchyma may be better represented by the continuum model, which suggests that the parenchyma does not mediate significant interactions between narrowing airways. [ABSTRACT FROM AUTHOR]

Microscopic flow-fiber interaction is frequently encountered in biofluid systems. In this paper, we propose a three-dimensional numerical model for such systems, including a spring network model for the elastic fiber, the lattice Boltzmann method for the fluid flow, and the immersed boundary method for the flow-structure interaction. Simulations are also conducted to examine the fiber deformation under constant and sinusoidal shear conditions. While an equilibrium state can be reached under a constant shear, periodic oscillation in fiber shape is observed in a sinusoidal shear flow, at a frequency identical to that of the imposed shear flow. A continuous phase shift of the fiber oscillation is also noticed along the fiber. These simulations demonstrate the potential usefulness of this model in microscopic biofluid and other systems, and further studies are necessary to investigate the dynamic flow-fiber interaction in various flow situations. [ABSTRACT FROM AUTHOR]

Abstract: The explanted lung slice has become a popular in vitro system for studying how airways contract. Because the forces of airway-parenchymal interdependence are such important modulators of airway narrowing, it is of significant interest to understand how the parenchyma around a constricting airway in a lung slice behaves. We have previously shown that the predictions of the 2-dimensional distortion field around a constricting airway are substantially different depending on whether the parenchyma is modeled as an elastic continuum versus a network of hexagonally arranged springs, which raises the question as to which model best explains the lung slice. We treated lung slices with methacholine and then followed the movement of a set of parenchymal landmarks around the airway as it narrowed. The resulting parenchymal displacement field was compared to the displacement fields predicted by the continuum and hexagonal spring network models. The predictions of the continuum model were much closer to the measured data than were those of the hexagonal spring network model, suggesting that the parenchyma in the lung slice behaves like an elastic continuum rather than a network of discrete springs. This may be because the alveoli of the lung slice are filled with agarose in order to provide structural stability, causing the parenchyma in the slice to act like a true mechanical continuum. How the air-filled parenchyma in the intact lung behave in vivo remains an open question. [Copyright &y& Elsevier]

Non-uniform distribution of moisture contents inside of the porous materials during drying results in compressional stresses inside of the material and tensional ones close to the surface. The tensional stresses together with brittleness of dry material are the reasons of fracturing of the material. The proposed model consists of two parts. The mass transfer is described by simple diffusion equation. The mechanical behaviour of the material is modelled with the network model in which the material is modelled as the set of small particles interconnected elastically via springs. The spring constants and strengths depend on Young modulus and the material tensional strength. The dependences of these material parameters on the moisture content are determined. Then two 2D initial-boundary problems are solved. The results show possible way of cracks initiation and generation by drying. [ABSTRACT FROM AUTHOR]

Abstract: The physical behaviour of materials and complicated components is nowadays numerically predicted by using the Finite Element Method (FEM). Another method, older than the finite element idea, is the Discrete Element Method (DEM), with which it is possible to make continuum-based calculations not only in the mechanical field but also in the thermal field, as will be shown in this paper. One major drawback of the FEM is that continuum-based methods are unable to include the stochastically distributed microscopic effects in the macroscopically oriented calculations. The Discrete Element Method is one method with which these effects can be considered. For making realistic fracture and life time predictions for components at high temperatures, it is important to adapt the DEM for the thermal field. This paper describes the mathematical proof of the 2D Discrete Element Method (or Lattice Model) for the thermal field. It will specifically be shown that the heat flux inside the framework can be transferred to the heat conduction equation. Furthermore, some examples demonstrate how the heat flux can be calculated with this method and how the corresponding material parameters are found and implemented. Also, as will be shown in this paper, anisotropic or orthotropic heat flux effects can be integrated in the DEM model. [Copyright &y& Elsevier]

We developed a mechano-cell model incorporating a cell membrane, a nuclear envelope, and actin filaments to simulate the mechanical behavior of a cell during tensile tests. The computational model depicts a cell as a combination of various spring elements in the framework of the minimum energy concept. A cell membrane and a nuclear envelope are both modeled as shells of a spring network that express elastic resistance to changes in bending, stretching, and surface area. A bundle of actin filaments is represented by a mechanical spring that generates a force as a function of its extension. The interaction between the nuclear envelope and the cell membrane is expressed by a potential energy function with respect to the distance between them. Incompressibility of a cell is assured by a volume elastic energy function. The cell shape during a tensile test is determined by a quasi-static approach, such that the total elastic energy converges to the minimum. The load–deformation curve obtained from the simulation shows a significant increase in stretching load with deformation of the cell and lies within a range of experimentally obtained load–deformation curves. The total elastic energy is dominated by the energy stored in the actin fibers. Actin fibers that are randomly oriented before loading tend to become aligned, passively, in the stretched direction. These results attribute the non-linearity in the load–deformation curve to passive reorientation of actin fibers in the stretched direction. [ABSTRACT FROM AUTHOR]

Stylolites are localized dissolution surfaces commonly found in sedimentary rocks. Stylolites have been extensively studied due to their important role in controlling dissolution, precipitation, defonnation, and fluid transport in rocks. Field observations indicate that stylolite formation and morphology are strongly correlated both with the surrounding stress and with the distribution of clays within the host rock, yet the mechanism by which they form remains enigmatic. We present results from a newly developed two-dimensional Spring-Network Model that studies stylolite formation by pressure-solution with and without the presence of clays, where clays play a role of enhancing pressure solution. We use our model to test the relative role of stress and clays in controlling the localization of dissolution into stylolites. In contrast to the common paradigm, our results suggest that pressure solution alone, in the absence of catalyzing clays, does not lead to spontaneous localization of dissolution into stylolites. Instead, we propose a new coupled clay-pressure-solution feedback to localize stylolites, a coupling that we observe in our model: a region with a slightly larger clay fraction will experience enhanced dissolution, and will thus accumulate more residual clays, which will act to further enhance pressure solution in that region, and accumulate even more clays. Stress is a necessary component in this feedback as it controls the direction of stylolite propagation, and facilitates lateral propagation. [ABSTRACT FROM AUTHOR]

Constructing a method for representing natural objects and natural phenomena is one of the important topics of research in the field of computer graphics. In the current research, the authors propose a method of realistically representing cracks that occur in 3D objects in computer graphics. Cracking is a familiar natural phenomenon that is seen on mud walls, the surface of rice fields, ceramics, and the bark of trees. The objective of the current research is to reproduce the cracking that occurs when an object that consists of mud or clay shrinks when it dries out. To represent cracking in computer graphics, rules based on observation or approaches based on simple physical models have been considered. However, the current research uses a method based on a physical model since changes in the material properties, environment, or external forces can easily be represented. Specifically, by introducing a spring network model to represent the shrinking, elasticity, and pliability of the clay and a moisture content model to represent the moisture movement within the object due to drying and integrating these two models, the authors simulate a mechanism for generating cracks due to drying. They also investigate a method of measuring the physical parameters that are used based on the moisture content. Finally, they performed experiments for 3D objects having various shapes to verify the effectiveness of the proposed method. © 2007 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 90(5): 50– 59, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.20317 [ABSTRACT FROM AUTHOR]

Abstract: Compaction bands are zones of localized grain crushing and porosity reduction, which form spontaneously in high porosity rock under certain compressive stress conditions. Recent experiments show that compaction bands may nucleate at the edges of notches, holes and cracks subjected to compressive stress. We present an elasto-plastic model, used to investigate compaction band formation under a variety of boundary conditions. When simulating a notched specimen and a specimen with a central hole, compaction initiated at the macroscopic void''s tips, and propagated in a step-wise manner, in agreement with experimental results. This step-wise manner of propagation is different from the compaction band run-away observed when compaction bands nucleate from pre-existing compaction bands. In addition, heterogeneity in rock properties, such as heterogeneity in local compressive strength, was found to control the morphology of compaction features initiating from voids. [Copyright &y& Elsevier]

This paper sets forth a method for creating models of soft 3-dimensional objects that are capable of describing the deformations that are easily produced in these objects by various external forces. In addition to virtual objects such as spheres and cubes, the authors have attempted to model the facial region of the human head. Their technique for modeling soft objects is to represent them by networks of springs and masses (i.e., by a spring network model). Using CT images to guide them, the authors construct a spring network model by first partitioning the head region with a tetrahedral mesh, and then using the bubble-mesh method to generate a close-packed structure that specifies the initial positions of the nodes. This procedure ensures that the springs all have almost the same length. In simulating the deformation, the response of the soft object is modeled by incorporating both a spring force and a volume-conserving force. Physical phenomena such as reaction forces arising from mutual contact between the surfaces of soft objects, such as hands with faces, and normal counterforces, are well described in the calculations. After verifying that deformations owing to contact between a sphere and a cube are well described, they developed their model of the human head and used it to simulate the effects of external forces exerted by a model hand. It was confirmed that the simulated deformations of the virtual head and hand that accompanied contact between them conserved volumes well. In addition, by introducing frictional forces, it was possible to simulate the deformations that accompany physical actions such as pushing up and tugging at lips, thereby confirming the effectiveness of the simulation method. © 2005 Wiley Periodicals, Inc. Syst Comp Jpn, 36(13): 23–34, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/scj.20325 [ABSTRACT FROM AUTHOR]

A discrete Lagrangian approach is the basis for modelling the macroscale elastic response of a solid material, which can be homogeneous as well as a periodic composite. The basic topology is a square "heuristic molecule" that is an assemblage of four rigid bodies with a definite shape bonded by elastic springs. This is the minimum unit cell, UC, that contains all the macroscopic mechanical properties of the solid material, object of study. The paper presents 4 unit cells, in progression from a basic molecule bonded by 2 types of central forces, to a refined "Cosserat-auxetic" molecule that is connected by 4 types of shear and central bond-springs. The emphasis is given to the isotropic response in relation to the value of the macroscopic Poisson ratio, and the four examples of UC topologies are presented showing their relationship to different materials at the macro-scale: from a "rari-constant" continuum, through a standard isotropic Cauchy continuum, up to an isotropic centre-symmetric auxetic Cosserat solid. [ABSTRACT FROM AUTHOR]

In the present article, a version of the lattice or spring network method is proposed to model the mechanical response of elastic particulate composites with a high volume fraction of spherical particles and with a much weaker matrix compared to the stiffness of the particles. The main subject of the article is the determination of the axial stiffnesses of the springs of the cell. A comparison of the mechanical response of a three-dimensional particulate composite cube obtained using the finite element method and the proposed methodology showed that the efficiency of the proposed methodology increases with an increasing volume fraction of the particles. [ABSTRACT FROM AUTHOR]

The forces of mechanical interdependence between the airways and the parenchyma in the lung are powerful modulators of airways responsiveness. Little is known, however, about the extent to which adjacent airways affect each other's ability to narrow due to distortional forces generated within the intervening parenchyma. We developed a two-dimensional computational model of two airways embedded in parenchyma. The parenchyma itself was modeled in three ways: 1) as a network of hexagonally arranged springs, 2) as a network of triangularly arranged springs, and 3) as an elastic continuum. In all cases, we determined how the narrowing of one airway was affected when the other airway was relaxed vs. when it narrowed to the same extent as the first airway. For the continuum and triangular network models, interactions between airways were negligible unless the airways lay within about two relaxed diameters of each other, but even at this distance the interactions were small. By contrast, the hexagonal spring network model predicted that airway-airway interactions mediated by the parenchyma can be substantial for any degree of airway separation at intermediate values of airway contraction forces. Evidence to date suggests that the parenchyma may be better represented by the continuum model, which suggests that the parenchyma does not mediate significant interactions between narrowing airways.