scholarly journals A Cosserat Model of Elastic Solids Reinforced by a Family of Curved and Twisted Fibers

Symmetry ◽  
2020 ◽  
Vol 12 (7) ◽  
pp. 1133 ◽  
Author(s):  
Milad Shirani ◽  
David J. Steigmann
Keyword(s):  
Cross Sections ◽  
Fiber Orientation ◽  
Material Symmetry ◽  
Equilibrium Equations ◽  
Elastic Solids ◽  
Cosserat Theory ◽  
Matrix Deformation ◽  
Cosserat Model ◽  
Local Fiber

A Cosserat theory for fiber-reinforced elastic solids developed in Steigmann (2012) is generalized to accommodate initial curvature and twist of the fibers. The basic variables of the theory are a conventional deformation field and a rotation field that describes the local fiber orientation. Constraints on these fields are introduced to model the materiality of the fibers with respect to the underlying matrix deformation. A variational argument delivers the relevant equilibrium equations and boundary conditions and furnishes the interpretation of the Lagrange multipliers associated with the constraints as shear tractions acting on the fiber cross sections. Finally, the theory of material symmetry for such solids is developed and applied to the classification of some explicit constitutive functions.

scholarly journals Mechanics-based analysis of selected features of the exoskeletal microstructure of Popillia japonica

2009 ◽  
Vol 24 (11) ◽  
pp. 3253-3267 ◽  
Author(s):  
Liang Cheng ◽  
Liyun Wang ◽  
Anette M. Karlsson
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Fiber Orientation ◽  
Fracture Resistance ◽  
Interfacial Strength ◽  
Maximum Tensile Stress ◽  
Popillia Japonica ◽  
Japanese Beetle ◽  
Mechanical Responses ◽  
Helicoidal Structure

We explore key mechanical responses of the layered microstructure found in selected parts of the exoskeletons (pronotum, leg and elytron) of Popillia japonica (Japanese beetle). Image analyses of exoskeleton cross-sections reveal four distinct layered regions. The load-bearing inner three regions (exocuticle, mesocuticle, and endocuticle) consist of multiple chitin-protein layers, in which chitin fibers align in parallel. The exocuticle and mesocuticle have a helicoidal structure, where the stacking sequence is characterized by a gradual rotation of the fiber orientation. The endocuticle has a pseudo-orthogonal structure, where two orthogonal layers are joined by a thin helicoidal region. The mechanics-based analyses suggest that, compared with the conventional cross-ply structure, the pseudo-orthogonal configuration reduces the maximum tensile stress over the exoskeleton cross-section and increases the interfacial fracture resistance. The coexistence of the pseudo-orthogonal and helicoidal structures reveals a competition between the in-plane isotropy and the interfacial strength in nature’s design of the biocomposite.

scholarly journals INFLUENCE OF PERIODIC SHADING ON THE LENGTH AND SOLIDNESS OF THE INTERNODES OF RESCUE WHEAT

1960 ◽  
Vol 40 (1) ◽  
pp. 183-187 ◽  
Author(s):  
N. D. Holmes ◽  
R. I. Larson ◽  
L. K. Peterson ◽  
M. D. MacDonald
Keyword(s):  
Light Intensity ◽  
Cross Sections ◽  
Strongly Correlated ◽  
Boot Stage ◽  
Stem Solidness ◽  
Heading Stage

Shading at the initiation of elongation shortened the internodes of Rescue wheat whereas shading later in the elongation period caused the internodes to elongate as much as or more than if they had not been shaded.The solidness of the bottom Internode, 1, was reduced mainly by shading from the 2-leaf to the boot stage, while that of Internodes 2 and 3 was reduced mainly by shading from the 4-leaf to the boot stage. The solidness of Internode 4 was reduced mainly by shading from the boot to the heading stage. The solidness in the lower 3 internodes was affected by reduction in light intensity even after the boot stage. Severe lodging occurred only in stems shaded from the boot to the heading stage.Two methods were used for rating stem solidness, namely, measurement in the split stem of proportion of the internode filled with pith, and classification of solidness of cross-sections at designated points in each internode. They were strongly correlated and appeared to give equally accurate estimates of solidness, although their degrees of sensitivity varied with the amount of stem solidness present.

scholarly journals PECULIARITIES OF MODELING OF STRESS-STRAIN STATE OF PIPELINES THROUGH WHICH GAS-LIQUID MIXTURES WITH AGGRESSIVE COMPONENTS ARE TRANSPORTED

2019 ◽  
pp. 128-135
Author(s):  
A. P. Oliinyk ◽  
B. S. Nezamay ◽  
L. I. Feshanych
Keyword(s):  
Internal Pressure ◽  
Cross Sections ◽  
Strain State ◽  
Smoothing Splines ◽  
Liquid Mixtures ◽  
Equilibrium Equations ◽  
Stress Strain ◽  
Stress Strain State ◽  
Current State ◽  
The Given

The task of estimating the stress-strain state of pipelines through which gas-liquid mixtures with aggressive components are transported is considered, the purpose, object and object of research are established. The analysis of the current state of scientific and technical researches on the given subject is carried out, the circle of unresolved problems is revealed. The combined effect on the pipelines through which gas-liquid mixtures with aggressive components are transported stress – strained state change  is estimated by two models - the model for determining the change of the stress-strain state of the pipeline by data on the surface points certain set displacement   taking into account the quasi-stationarity of the process. The device uses interpolation smoothing splines and methods of differential geometry, 6 components of strain and stress tensors are determined. In order to substantiate the method of estimation of annular stresses at the wear of the pipeline walls due to the action of the aggressive components of the transported mixtures, systems of equilibrium equations for pipeline sections and for quasi-rectilinear sections with altered cross-section configuration have been derived. Boundaryt conditions for equilibrium equations are established. Calculation formulas for estimation of annular stresses arising under the action of internal pressure for sections with shape defects caused by the action of aggressive components are established. The results of calculations that allow to quantify the change of the most significant ring stresses arising in the pipeline material under the action of internal pressure in the pipeline cross sections, which were exposed to the aggressive components, are presented. It is assumed that the deformed sections are little different from the shape of the circle.

scholarly journals Oriented collagen fibers direct tumor cell intravasation

2016 ◽  
Vol 113 (40) ◽  
pp. 11208-11213 ◽  
Author(s):  
Weijing Han ◽  
Shaohua Chen ◽  
Wei Yuan ◽  
Qihui Fan ◽  
Jianxiang Tian ◽  
...  
Keyword(s):  
Breast Cancer ◽  
Extracellular Matrix ◽  
Tumor Cell ◽  
Tumor Cells ◽  
Fiber Orientation ◽  
Breast Cancer Cells ◽  
Protein Concentration ◽  
Collagen Fiber ◽  
Fiber Alignment ◽  
Local Fiber

In this work, we constructed a Collagen I–Matrigel composite extracellular matrix (ECM). The composite ECM was used to determine the influence of the local collagen fiber orientation on the collective intravasation ability of tumor cells. We found that the local fiber alignment enhanced cell–ECM interactions. Specifically, metastatic MDA-MB-231 breast cancer cells followed the local fiber alignment direction during the intravasation into rigid Matrigel (∼10 mg/mL protein concentration).

scholarly journals Alterations in Microstructure and Local Fiber Orientation of White Matter Are Associated with Outcome after Mild Traumatic Brain Injury

2020 ◽  
Vol 37 (24) ◽  
pp. 2616-2623
Author(s):  
Mehrbod Mohammadian ◽  
Timo Roine ◽  
Jussi Hirvonen ◽  
Timo Kurki ◽  
Jussi P. Posti ◽  
...  
Keyword(s):  
Traumatic Brain Injury ◽  
Brain Injury ◽  
White Matter ◽  
Mild Traumatic Brain Injury ◽  
Fiber Orientation ◽  
Local Fiber

Region-of-Interest X-Ray Tomography for the Non-Destructive Characterization of Local Fiber Orientation in Large Fiber Composite Parts

2019 ◽  
Vol 809 ◽  
pp. 587-593
Author(s):  
Simon Zabler ◽  
Katja Schladitz ◽  
Kilian Dremel ◽  
Jonas Graetz ◽  
Dascha Dobrovolskij
Keyword(s):  
Computed Tomography ◽  
Spatial Resolution ◽  
Fiber Orientation ◽  
Fiber Composite ◽  
Three Dimensional ◽  
Region Of Interest ◽  
Micro Computed Tomography ◽  
X Ray ◽  
Anisotropic Thermal Conductivity ◽  
Local Fiber

To detect and characterize materials defects in fiber composites as well as for evaluatingthe three-dimensional local fiber orientation in the latter, X-ray micro-CT is the preferred methodof choice. When micro computed tomography is applied to inspect large components, the method isreferred to as region-of-interest computed tomography. Parts can be as large as 10 cm wide and 1 mlong, while the measurement volume of micro computed tomography is a cylinder of only 4 − 5 mmdiameter (typical wall thickness of fiber composite parts). In this report, the potentials and limits ofregion-of-interest computed tomography are discussed with regard to spatial resolution and precisionwhen evaluating defects and local fiber orientation in squeeze cast components. The micro computedtomography scanner metRIC at Fraunhofer‘s Development Center X-ray Technology EZRT deliversregion-of-interest computed tomography up to a spatial resolution of 2 μm/voxel, which is sufficientfor determining the orientation of natural or synthetic fibers, wood, carbon and glass. The mean localfiber orientation is estimated on an isotropic structuring element of approximately 0.1 mm length bymeans of volume image analysis (MAVI software package by Fraunhofer ITWM). Knowing the exactlocal fiber orientation is critical for estimating anisotropic thermal conductivity and materials strength.

scholarly journals Uncertainty quantification of fiber orientation distribution measurements for long-fiber-reinforced thermoplastic composites

2017 ◽  
Vol 52 (13) ◽  
pp. 1781-1797 ◽  
Author(s):  
Bhisham N Sharma ◽  
Diwakar Naragani ◽  
Ba Nghiep Nguyen ◽  
Charles L Tucker ◽  
Michael D Sangid
Keyword(s):  
Cross Sections ◽  
Fiber Orientation ◽  
Surface Preparation ◽  
Orientation Distribution ◽  
Elastic Stiffness ◽  
Thermoplastic Composites ◽  
Fiber Reinforced ◽  
Fiber Orientation Distribution ◽  
Discontinuous Fiber ◽  
Reinforced Thermoplastics

We present a detailed methodology for experimental measurement of fiber orientation distribution in injection-molded discontinuous fiber composites using the method of ellipses on two-dimensional cross sections. Best practices to avoid biases occurring during surface preparation and optical imaging of carbon-fiber-reinforced thermoplastics are discussed. A marker-based watershed transform routine for efficient image segmentation and the separation of touching fiber ellipses is developed. The sensitivity of the averaged orientation tensor to the image sample size is studied for the case of long-fiber thermoplastics. A Mori–Tanaka implementation of the Eshelby model is then employed to quantify the sensitivity of elastic stiffness predictions to biases in the fiber orientation distribution measurements.

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