Microscopic Strain Research Articles

G030151 損傷力学に基づくねずみ鋳鉄の材料モデリング([G03015]材料力学部門一般セッション(15):損傷と変形)

The constitutive equation based on the concept of continuum damage mechanics is formulated for the gray cast iron, assuming it as an elastic damage viscoplastic solid. The microscopic stress and strain evaluation is simplified in the two-scale model for the damage evolution. Lots of material parameters in the constitutive equation are determined by using the uniaxial tensile/compressive and the fatigue test results. The local approach to fracture analysis (the uncoupled analysis) for the fatigue tests of notched circular bars is conducted by using the identified constitutive equation model and the commercial three-dimensional finite element program. The validity of the proposed model is illustrated by comparing the calculated results with the experimental results.

Mechanical Forces Regulate Elastase Activity and Binding Site Availability in Lung Elastin

Many fundamental cellular and extracellular processes in the body are mediated by enzymes. At the single molecule level, enzyme activity is influenced by mechanical forces. However, the effects of mechanical forces on the kinetics of enzymatic reactions in complex tissues with intact extracellular matrix (ECM) have not been identified. Here we report that physiologically relevant macroscopic mechanical forces modify enzyme activity at the molecular level in the ECM of the lung parenchyma. Porcine pancreatic elastase (PPE), which binds to and digests elastin, was fluorescently conjugated ( f-PPE) and fluorescent recovery after photobleach was used to evaluate the binding kinetics of f-PPE in the alveolar walls of normal mouse lungs. Fluorescent recovery after photobleach indicated that the dissociation rate constant ( k off) for f-PPE was significantly larger in stretched than in relaxed alveolar walls with a linear relation between k off and macroscopic strain. Using a network model of the parenchyma, a linear relation was also found between k off and microscopic strain on elastin fibers. Further, the binding pattern of f-PPE suggested that binding sites on elastin unfold with strain. The increased overall reaction rate also resulted in stronger structural breakdown at the level of alveolar walls, as well as accelerated decay of stiffness and decreased failure stress of the ECM at the macroscopic scale. These results suggest an important role for the coupling between mechanical forces and enzyme activity in ECM breakdown and remodeling in development, and during diseases such as pulmonary emphysema or vascular aneurysm. Our findings may also have broader implications because in vivo, enzyme activity in nearly all cellular and extracellular processes takes place in the presence of mechanical forces.

Connecting the macro- and microstrain responses in technical porous ceramics: modeling and experimental validations

The relation between the macroscopic and the microscopic (lattice) strain response to external uniaxial stress has been investigated for porous ceramics. Analytical and finite element modeling (FEM) have been performed and neutron diffraction data on porous sintered alumina and extruded honeycomb SiC have been used to validate the theoretical approach. By FEM simulations, it is shown that in spite of the complex pore microstructure, shear stresses are small during uniaxial compression. Analytical modeling shows that while the average microscopic stress depends on the applied macroscopic stress only through the porosity p, the average microscopic strain depends on the macroscopic stress through the pore morphology factor m, as well. Novel relationships are proposed to describe this dependence. Analytical calculations and numerical modeling perfectly agree with each other, and both show good consistency with experiments. As predicted, it has been observed that the microscopic (diffraction) Young’s modulus does not depend on the pore morphology factor, and follows the rule-of-mixtures, while the microscopic Poisson’s ratio does not even depend on porosity, but is equal to the value for the dense material property. A practical implication of these findings is that it is not possible to attach a pore morphology factor to a material, unless the processing conditions are tailored to vary p without varying m. In fact, the different values of m found for the different porosities explain why many models can be used to rationalize the experimental data. With the proposed method, the factor m can be independently evaluated by the use of macro- and micro-elastic properties of the porous body. Analogously, the macroscopic elastic properties of the dense material can be obtained by macroscopic and microscopic values measured on the correspondent porous material.

Time-resolved x-ray diffraction study of the piezoelectric crystal response to a fast change of an applied electric field

Time-resolved measurements of the macroscopic and microscopic strains in piezoelectric crystals were performed with a novel data acquisition technique implemented on the basis of a field programmed gate array system. Both types of strains were induced in a crystal by an applied periodic high voltage with fast (within 100 ns) switches between opposite polarities and measured simultaneously by respective angular shifts and integrated intensities of synchrotron x-ray diffraction rocking curves. The time resolution achieved with the developed data acquisition system was 100 ns. The paper demonstrates the particular application of this technique for the investigations of time dynamics of lattice constants and atomic positions in a unit cell for piezoelectric BiB3O6 and Li2SO4⋅H2O crystals. It has been found that 100 ns fast rising time of an applied external electric field induces oscillations of the crystal lattice constants, visible as oscillations of Bragg peak angular positions. At the same time, these oscillations are not observed for the Bragg intensities, i.e., for fractional positions of atoms in the unit cell and correspondingly for bond lengths. The results allow suggesting a model for the mutual interconnection between the deformation of bond lengths and lattice constants in piezoelectric crystals.

Simulation of deformation and fracture of graphene: effect of size, defects and surface modification

The deformation and fracture of graphene under uniaxial tension is simulated in the framework of quantum mechanics. The deformation forces are calculated as energy gradients from a microscopic strain coordinate in the quantum mechanics approximation. The strain and fracture characteristics (Young's moduli, stiffness coefficients, critical forces and fracture stress) are calculated using macroscopic relations of the linear theory of elasticity. The emphasis in the work is on the analysis of the effect of model sizes, defects and surface modification on the strain characteristics of graphene. The simulation results are compared with available experimental data.

Coarse-graining microscopic strains in a harmonic, two-dimensional solid: Elasticity, nonlocal susceptibilities, and nonaffine noise

In soft matter systems the local displacement field can be accessed directly by video microscopy enabling one to compute local strain fields and hence the elastic moduli in these systems using a coarse-graining procedure. We study this process in detail for a simple triangular, harmonic lattice in two dimensions. Coarse-graining local strains obtained from particle configurations in a Monte Carlo simulation generates nontrivial, nonlocal strain correlations (susceptibilities). These may be understood within a generalized, Landau-type elastic Hamiltonian containing up to quartic terms in strain gradients [K. Franzrahe, Phys. Rev. E 78, 026106 (2008)10.1103/PhysRevE.78.026106]. In order to demonstrate the versatility of the analysis of these correlations and to make our calculations directly relevant for experiments on colloidal solids, we systematically study various parameters such as the choice of statistical ensemble, presence of external pressure and boundary conditions. Crucially, we show that special care needs to be taken for an accurate application of our results to actual experiments, where the analyzed area is embedded within a larger system, to which it is mechanically coupled. Apart from the smooth, affine strain fields, the coarse-graining procedure also gives rise to a noise field (χ) made up of nonaffine displacements. Several properties of χ may be rationalized for the harmonic solid using a simple "cell model" calculation. Furthermore the scaling behavior of the probability distribution of the noise field (χ) is studied. We find that for any inverse temperature β, spring constant f, density ρ and coarse-graining length Λ the probability distribution can be obtained from a master curve of the scaling variable X=χβf/ρΛ(2).

Linear elastic constitutive relation for multiphase porous media using microstructure superposition: Dry media

A constitutive relation for multiphase porous media containing a phase-change constituent is developed based on a periodic representative unit cell, microstructure superposition technique, and homogenization scheme. Multiphase porous mediae, consisting of different solid phases, fluid phases, and phase-change constituents, play an important role in variety engineering applications. A microstructure superposition method, stemmed from linear superposition theory, is devised such that the constitutive relation of the media can be obtained in an analytical form and the derivation is straightforward and tractable. The original microstructure of the media is firstly divided into several simple microstructure configurations. The microscopic stresses and strains are obtained for each individual microstructure configuration based on its own equilibrium and equivalent equations, and complex Fourier series expansion of strains. The microscopic strains are then superposed together to obtain the constitutive relation of the multiphase porous media using homogenization scheme. The derived constitutive relation can be applied to study the mechanical behavior of porous media consisting of two solid phases with one being able to change phase between solid and liquid and one liquid phase. As a particular application of the derived constitutive relation, the mechanical behavior of porous media with a single solid phase under dry condition was studied and the results were consistent with other models and agreed well with available experimental data.

Extended multiscale finite element method for elasto-plastic analysis of 2D periodic lattice truss materials

An extended multiscale finite element method is developed for small-deformation elasto-plastic analysis of periodic truss materials. The base functions constructed numerically are employed to establish the relationship between the macroscopic displacement and the microscopic stress and strain. The unbalanced nodal forces in the micro-scale of unit cells are treated as the combined effects of macroscopic equivalent forces and microscopic perturbed forces, in which macroscopic equivalent forces are used to solve the macroscopic displacement field and microscopic perturbed forces are used to obtain the stress and strain in the micro-scale to make sure the correctness of the results obtained by the downscale computation in the elastic-plastic problems. Numerical examples are carried out and the results verify the validity and efficiency of the developed method by comparing it with the conventional finite element method.

Reply to “Comment on ‘Elastic constants from microscopic strain fluctuations’ ”

We agree with Coupier et al. [Phys. Rev. E 81, 013101 (2010)] that their technique for extracting elastic constants from microscopic strain fluctuations improves upon ours because of a more accurate computation of the integral of the elastic correlation function over sub-blocks. However, we believe that their interpretation of the physical relevance of the elastic correlation length extracted from the fits is misleading.

Comment on “Elastic constants from microscopic strain fluctuations”

Sengupta [Phys. Rev. E 61, 1072 (2000)] presented an elegant and simple finite-size scaling method for the calculation of elastic constants and their corresponding correlation lengths, which is suitable for many finite discrete systems considered through simulations or experiments. We take into account a mathematical finite-size effect that was neglected by the authors in order to propose a more accurate method. Consequences on the authors' results are also discussed.

Low Cycle Fatigue and Cyclic Deformation of TiAl Alloys

The relation between microstructural parameters, microscopic cyclic deformation mechanisms and macroscopic cyclic strain hardening is investigated in the case of a heat treated PM Ti-48Al-2Cr-2Nb alloy at 20°C and at 500°C. In particular it is shown that, for the different microstructures considered, a moderate hardening is related to the formation of highly tangled dislocation structures which is in turn controlled by the dislocation glide mean free path. At 500°C this structures evolves towards a braid like structure for the fine fully lamellar microstructure.

Local and regional mechanical characterisation of a collagen-glycosaminoglycan scaffold using high-resolution finite element analysis

Artificial tissue growth requires cells to proliferate and differentiate within the host scaffold. As cell function is governed by mechano-sensitive selection, tissue type is influenced by the microscopic forces exposed to the cells, which is a product of macroscopically straining the scaffold. Accordingly, the microscopic strain environment within a CG scaffold is offered here. Using μ CT to characterise CG scaffold architecture, two high-resolution 3D FE models were used to predict the deformation mechanics. While also providing an analysis of region-specific features, such as relative density, pore diameters and microstructural elastic stability, the deformation patterns afforded strains to be inferred for seeded cells. The results indicate a regional dependence, in terms of architectural and mechanical properties. Specifically, the peripheral regions demonstrated the lowest volume fraction, the highest stress concentrations and the greatest potential for elastic instability. Conversely, the mid-region exhibited the most homogeneous environment. Based on the proviso of mechano-sensitive proliferation and differentiation, the findings suggest cell function will vary between CG scaffold regions. Further work should investigate the possibility of improving the fabrication process in order to deliver a construct in line with the mid-region, or alternatively, isolation of the mid-region may prove beneficial for cell culturing.

T0201-3-6 円周方向引張負荷に伴うブタ胸大動脈壁内微視的変形挙動の観察([T0201-3]細胞の構造と流れにおけるマイクロ・ナノスケール解析(3))

The artery walls consist of structural components that have various mechanical properties: elastin, collagen and smooth muscle cells. Such variety may cause heterogeneous deformation of the components at a microscopic level when arterial tissue is subjected to macroscopic uniform stretch. To examine this hypothesis, we sliced 15-μm-thick specimens from porcine thoracic aorta with cryotome, and stretched them under a transmitted light microscope to observe their microscopic deformation caused by macroscopic stretch. Microscopic strain was found to be highly heterogeneous: stretch ratio in the elastic lamina (EL) and smooth muscle layer (SML) was 1.1-2.3 and 1.1-2.1, respectively, at circumferential stretch ratio of 1.5. Strain difference between an EL and a SML adjacent to each other could be as high as 6 times. These results suggest that the microscopic deformation in the artery wall is highly heterogeneous. Mechanical environment of the artery wall might not be so homogeneous at a cellular level.

The Emerging Role of Admixture in the Pharmacogenetics of Puerto Rican Hispanics

The Protoplast was prepared from the Penicillium chrysogenum and confirmed by microscopic observation and strains from the Penicillium chrysogenum were intrafused and protoplast was regenerated. The Penicillin was produced by fermentation method. The DNA was isolated from the Sclerotium rolfsii and it was characterized by electrophoresis and Protoplast of Penicillium chrysogenum was transformed with DNA of Sclerotium rolfsii. Penicillin was produced from transformed protoplast of Penicillium chrysogenum and at last HPLC was used to quantify the penicillin. Penicil - lin was isolated and purified and injected into experimental animals, where it was found not only to cure infections but also to possess incredibly low toxicity for the animals. This fact ushered into being the age of antibiotic chemotherapy, and an intense search for similar antimicrobial agents of low toxicity to animals that might prove useful in the treatment of infectious disease. Penicillium and Cephalosporium molds produce beta-lactam antibiotics such as penicillin and cephalosporin and their relatives. They also produce the base molecule for development of semisynthetic beta-lactam antibiotics, such as amoxacillin and ampicillin. Beta-lactams are used to treat about one-third of outpatients with bacte - rial infections.

画像相関法を用いた皮質骨のひずみ分布測定と破壊じん性

Bone fracture toughness has been well studied, however, it is also important to investigate the effect of preservative treatment on the mechanical properties of bones. It is necessary to evaluate crack initiation and propagation after fracture because this process may be different in the case of injured bone tissues. In this study, we attempted to analyze the strain distribution on bone tissue surface by using image correlation techniques in order to elucidate the relationship between microscopic bone damage and strain distribution. Bovine femoral cortical bone was employed as the bone specimen and the three-point bend test method was used to determine the fracture toughness, in accordance with the ASTM E399 guidelines. An Instron type machine was used in the fracture toughness test and the loading rate was set to 1 mm/min. Black and white spray paint was applied in a random pattern to the surface of the specimens, and the specimens were loaded until they were ruptured. Bone surface strain analysis was performed using image correlation techniques and the changes were recorded in a digital image. In order to evaluate the effects of preservative treatment on the mechanical properties of bone, we categorized the specimens into 4 groups: the control group included the specimens that were submitted for testing immediately after machining and the preservation group comprised specimens that were analyzed after preservative treatment with different method (formalin, ethanol and physiological saline solution). A strain analysis performed using image correlation techniques allowed the visualization of the increased strain at the forward end of the slit of the specimens. The strain value at the forward end of the slit (the longitudinal direction of specimens) measured at the time of rupture in the control group was approximately 4 times larger than that in the formalin preservation group, thereby suggesting the embrittlement of bone organic constituents due to preservative treatment.

Formulation of a Homogenization Theory for Discrete Dislocation Dynamics Analysis

In this study, we develop an extended version of homogenization theories for composite materials consisting of inclusions and a matrix. The extension allows discrete dislocations to move in a matrix based on dislocation dynamics. Macroscopic stress-strain response and microscopic stress distribution in representative volume elements (RVEs) are analyzed on the assumption that the periodic arrangement of RVEs is subjected to macroscopic uniform deformation. The periodicity, which enforces the periodic distributions of microscopic stress and strain as well as dislocations, is used as boundary conditions on the surface of RVEs. It is shown that elastic fields of periodically arranged dislocations in an infinite medium have no contribution to macroscopic relations, and that discontinuous displacements resulting from dislocation motions in each RVE are introduced as a macroscopic plastic strain. From these relations, a set of homogenization equations is derived, in which two boundary value problems in integral form are solved for analyzing perturbed displacements due to the presence of inclusions and due to the interaction of inclusions with dislocations, respectively. Finally, the influence of periodic boundary conditions on macroscopic and microscopic responses is investigated by performing the RVE analysis of a model composite.

Spatially resolved x-ray diffraction study of GaSb layers grown laterally on SiO2-masked GaAs substrates

In this work spatially resolved x-ray diffraction (SRXRD) is used to analyze strain in GaSb layers grown by epitaxial lateral overgrowth (ELO) on SiO2-masked (001) GaAs substrates. We show that this heteroepitaxial structure contains local mosaicity in the wing area that cannot be detected by selective etching. While the standard x-ray diffraction measurements only suggest the presence of grain structure of the ELO layer, SRXRD allows examining the microscopic strain distribution in the sample. In particular, size of microblocks and their relative misorientation are determined.

Influence of boundary conditions on strain field analysis for polycrystalline finite element simulations

This paper presents a first validation of a novel methodology for identifying the parameters of a crystallographic elastoplastic constitutive law. This is accomplished by comparing simulation and experimental results at different length scales: the microstructure scale and the representative volume element scale. Experimentally, the microscopic strain fields and the microstrucural characteristics can be obtained only at the surface of the specimen. As a consequence, in finite element simulations only at the surface there is a oneto- one correspondence between the mesh and the experimental observed grain morphology. In this paper, the morphology of the subsurface grains is obtained by a simple extension in the thickness direction of the surface morphology. The aim of this study is then to verify whether the surface data contain sufficient information for the identification of the parameters of the constitutive law.

Micromechanical enhancement of the macroscopic strain state for advanced composite materials

A computationally efficient method for determining the microscopic strain field within the separate phases of heterogeneous medium consisting of collimated, continuous fibers within an isotropic matrix is presented with the goal of providing one of the essential links in a multi-scale analysis of a composite structure which relates structural loading and deformations at the macro-scale to the state of strain within the fiber and matrix phases at the micro scale. The model utilizes a conventional influence function formulation and considers thermo-mechanical deformations.

Controlled chemical phase separation in binary and ternary composites: A pathway to isotropic optical and electrical behavior for device applications

AbstractThere are many applications for nanocrystalline thin films in optical devices that require isotropic optical properties. A novel way to obtain these isotropic properties for the index of refraction and/or optical absorption constant, etc., and at the same time to minimize microscopic strain is presented in this article. This approach is based on strain reduction mechanisms that occur in the intermediate phases, IPs, of non‐crystalline glasses and thin films. In these compositional regimes, either site percolation, or volume percolation, each above an applicable critical value, provides a quantitative understanding of the microscopic bonding arrangements associated with strain‐reducing chemical bonding self‐organizations. A similar framework, presented for the first time in this article, develops a microscopic understanding of macroscopic strain reduction in several different phase‐separated composites. This understanding has emerged from focussed research on qualitatively different hetero‐structure device structure constituents, e.g.; (i) high‐k replacement dielectrics for SiO2 in field effect transistors gate stacks for advanced semiconductor devices, and (ii) active and passive thin films for optically switched memory cells. In each instance strain reduction and its intrinsic relationship to low densities of defects and defect precursors has provided a driving force in the identification of a narrow range of compositions that satisfy technological needs. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)