scholarly journals Refined dimensional reduction for isotropic elastic Cosserat shells with initial curvature

2019 ◽  
Vol 24 (12) ◽  
pp. 4000-4019 ◽  
Author(s):  
Mircea Bîrsan ◽  
Ionel-Dumitrel Ghiba ◽  
Robert J Martin ◽  
Patrizio Neff
Keyword(s):  
Energy Density ◽  
Elastic Shell ◽  
Strain Tensor ◽  
Three Dimensional ◽  
Elastic Strain Energy ◽  
Quadratic Function ◽  
Closed Form Expression ◽  
Plane Stress Condition ◽  
Initial Curvature ◽  
Curvature Effects

Using a geometrically motivated 8-parameter ansatz through the thickness, we reduce a three-dimensional shell-like geometrically nonlinear Cosserat material to a fully two-dimensional shell model. Curvature effects are fully taken into account. For elastic isotropic Cosserat materials, the integration through the thickness can be performed analytically and a generalized plane stress condition allows for a closed-form expression of the thickness stretch and the nonsymmetric shift of the midsurface in bending. We obtain an explicit form of the elastic strain energy density for Cosserat shells, including terms up to order [Formula: see text] in the shell thickness h. This energy density is expressed as a quadratic function of the nonlinear elastic shell strain tensor and the bending–curvature tensor, with coefficients depending on the initial curvature of the shell.

An isotropic elasto-damage-plastic micromechanical framework of innovative pothole patching materials featuring high-toughness, low-viscosity nanomolecular resin

2021 ◽  
pp. 105678952110286
Author(s):  
H Zhang ◽  
J Woody Ju ◽  
WL Zhu ◽  
KY Yuan
Keyword(s):  
Strain Energy ◽  
Three Dimensional ◽  
Elastic Strain Energy ◽  
Companion Paper ◽  
Computational Algorithms ◽  
Mechanical Behaviors ◽  
High Toughness ◽  
Low Viscosity ◽  
Innovative Materials ◽  
Continuum Thermodynamic

In a recent companion paper, a three-dimensional isotropic elastic micromechanical framework was developed to predict the mechanical behaviors of the innovative asphalt patching materials reinforced with a high-toughness, low-viscosity nanomolecular resin, dicyclopentadiene (DCPD), under the splitting tension test (ASTM D6931). By taking advantage of the previously proposed isotropic elastic-damage framework and considering the plastic behaviors of asphalt mastic, a class of elasto-damage-plastic model, based on a continuum thermodynamic framework, is proposed within an initial elastic strain energy-based formulation to predict the behaviors of the innovative materials more accurately. Specifically, the governing damage evolution is characterized through the effective stress concept in conjunction with the hypothesis of strain equivalence; the plastic flow is introduced by means of an additive split of the stress tensor. Corresponding computational algorithms are implemented into three-dimensional finite elements numerical simulations, and the outcomes are systemically compared with suitably designed experimental results.

scholarly journals Alternative derivation of the higher-order constitutive model for six-parameter elastic shells

2021 ◽  
Vol 72 (2) ◽  
Author(s):  
Mircea Bîrsan
Keyword(s):  
Energy Density ◽  
Constitutive Model ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Shell Theory ◽  
Constitutive Relations ◽  
Three Dimensional ◽  
Classical Shell Theory ◽  
Three Dimensional Elasticity ◽  
General Method

AbstractIn this paper, we present a general method to derive the explicit constitutive relations for isotropic elastic 6-parameter shells made from a Cosserat material. The dimensional reduction procedure extends the methods of the classical shell theory to the case of Cosserat shells. Starting from the three-dimensional Cosserat parent model, we perform the integration over the thickness and obtain a consistent shell model of order $$ O(h^5) $$ O ( h 5 ) with respect to the shell thickness h. We derive the explicit form of the strain energy density for 6-parameter (Cosserat) shells, in which the constitutive coefficients are expressed in terms of the three-dimensional elasticity constants and depend on the initial curvature of the shell. The obtained form of the shell strain energy density is compared with other previous variants from the literature, and the advantages of our constitutive model are discussed.

scholarly journals Origin and Application of the Twinned Calcite Strain Gauge

Geosciences ◽  
2021 ◽  
Vol 11 (7) ◽  
pp. 296
Author(s):  
Richard H. Groshong
Keyword(s):  
Stress Analysis ◽  
Strain Gauge ◽  
Strain Tensor ◽  
Three Dimensional ◽  
Constant Strain Rate ◽  
Axis Orientation ◽  
Order Of Magnitude ◽  
Rate Experiment ◽  
Strain Axis ◽  
Expected Values

This paper is a personal account of the origin and development of the twinned-calcite strain gauge, its experimental verification, and its relationship to stress analysis. The method allows the calculation of the three-dimensional deviatoric strain tensor based on five or more twin sets. A minimum of about 25 twin sets should provide a reasonably accurate result for the magnitude and orientation of the strain tensor. The opposite-signed strain axis orientation is the most accurately located. Where one strain axis is appreciably different from the other two, that axis is generally within about 10° of the correct value. Experiments confirm a magnitude accuracy of 1% strain over the range of 1–12% axial shortening and that samples with more than 40% negative expected values imply multiple or rotational deformations. If two deformations are at a high angle to one another, the strain calculated from the positive and negative expected values separately provides a good estimate of both deformations. Most stress analysis techniques do not provide useful magnitudes, although most provide a good estimate of the principal strain axis directions. Stress analysis based on the number of twin sets per grain provides a better than order-of-magnitude approximation to the differential stress magnitude in a constant strain rate experiment.

Stiffness Constants for Composite Beams Including Large Initial Twist and Curvature Effects

1995 ◽  
Vol 48 (11S) ◽  
pp. S61-S67 ◽  
Author(s):  
Carlos E. S. Cesnik ◽  
Dewey H. Hodges
Keyword(s):  
Wave Length ◽  
Three Dimensional ◽  
Radius Of Curvature ◽  
Cross Sectional ◽  
Curvature Effects ◽  
Three Dimensional Representation ◽  
Stiffness Model ◽  
Sectional Analysis ◽  
Three Dimensional Elasticity ◽  
Coupling Phenomena

An asymptotically exact methodology, based on geometrically nonlinear, three-dimensional elasticity, is presented for cross-sectional analysis of initially curved and twisted, nonhomogeneous, anisotropic beams. Through accounting for all possible deformation in the three-dimensional representation, the analysis correctly accounts for the complex elastic coupling phenomena in anisotropic beams associated with shear deformation. The analysis is subject only to the restrictions that the strain is small relative to unity and that the maximum dimension of the cross section is small relative to the wave length of the deformation and to the minimum radius of curvature and/or twist. The resulting cross-sectional elastic constants exhibit second-order dependence on the initial curvature and twist. As is well known, the associated geometrically-exact, one-dimensional equilibrium and kinematical equations also depend on initial twist and curvature. The corrections to the stiffness model derived herein are also necessary in general for proper representation of initially curved and twisted beams.

scholarly journals Thermalization of synchrotron radiation from field-aligned currents

1988 ◽  
Vol 6 (3) ◽  
pp. 493-501 ◽  
Author(s):  
William Peter ◽  
Anthony L. Peratt
Keyword(s):  
Magnetic Field ◽  
Synchrotron Radiation ◽  
Energy Density ◽  
Radiation Spectrum ◽  
Axial Magnetic Field ◽  
Three Dimensional ◽  
Synchrotron Emission ◽  
Microwave Background ◽  
Strong Function ◽  
Current Filaments

Three-dimensional plasma simulations of interacting galactic-dimensioned current filaments show bursts of synchroton radiation of energy density 1·2 ×10−13 erg/cm3 which can be compared with the measured cosmic microwave background energy density of 1·5 × 10−13 erg/cm3. However, the synchrotron emission observed in the simulations is not blackbody. In this paper, we analyze the absorption of the synchrotron emission by the current filaments themselves (i.e., self-absorption) in order to investigate the thermalization of the emitted radiation. It is found that a large number of current filaments (>1031) are needed to make the radiation spectrum blackbody up to the observed measured frequency of 100 GHz. The radiation spectrum and the required number of current filaments is a strong function of the axial magnetic field in the filaments.

Boundary-layer equations in the linear theory of thin elastic shells

1962 ◽  
Vol 269 (1339) ◽  
pp. 481-491 ◽  
Keyword(s):  
Boundary Layer ◽  
Elastic Shell ◽  
Three Dimensional ◽  
Boundary Layer Equations ◽  
Smooth Edge ◽  
Elasticity Equations ◽  
Edge Conditions ◽  
Isotropic Elasticity ◽  
Stress Boundary Conditions ◽  
Stress Boundary

Starting with the three-dimensional equations of classical isotropic elasticity, equations are obtained for boundary-layer effects near any smooth edge of an elastic shell. Solutions of these equations are combined with solutions of the equations of the 'interior’ problem so that any specified edge conditions in terms of stresses can be satisfied. The usual Kirchhoff stress boundary conditions for the major terms of the interior stresses are deduced from the analysis.

Qualitative Analysis of Three-Dimensional Single Food-Chain Model with Variable Consumption Rate in Chemostat

2014 ◽  
Vol 955-959 ◽  
pp. 463-470
Author(s):  
Jing Liu ◽  
Hong Wei Jiang ◽  
Chao Liu
Keyword(s):  
Food Chain ◽  
Consumption Rate ◽  
Three Dimensional ◽  
Quadratic Function ◽  
Positive Equilibrium ◽  
Chain Model ◽  
Equilibrium Solutions ◽  
Existence And Stability ◽  
Variable Consumption ◽  
Food Chain Model

The paper studies three-dimensional food-chain model with variable consumption rate in Chemostat. Assume the prey population's consumption rate of the nutrients is quadratic function, and the predator's consumption rate of the prey population is linear function. Use qualitative theory of ordinary differential equation to analyze the equilibrium solution of the model, especially the existence and stability of positive equilibrium solutions and Hopf bifurcation solutions. Finally,several numerical simulations illustrating the theoretical analysis are also given.

scholarly journals Worldline numerics applied to custom Casimir geometry generates unanticipated intersection with Alcubierre warp metric

2021 ◽  
Vol 81 (7) ◽  
Author(s):  
Harold White ◽  
Jerry Vera ◽  
Arum Han ◽  
Alexander R. Bruccoleri ◽  
Jonathan MacArthur
Keyword(s):  
Energy Density ◽  
Three Dimensional ◽  
Casimir Energy ◽  
Negative Energy ◽  
Vacuum Model ◽  
Energy Density Distribution ◽  
Dynamic Vacuum ◽  
Negative Energy Density ◽  
Funded Project ◽  
Transient Electric Field

AbstractWhile conducting analysis related to a DARPA-funded project to evaluate possible structure of the energy density present in a Casimir cavity as predicted by the dynamic vacuum model, a micro/nano-scale structure has been discovered that predicts negative energy density distribution that closely matches requirements for the Alcubierre metric. The simplest notional geometry being analyzed as part of the DARPA-funded work consists of a standard parallel plate Casimir cavity equipped with pillars arrayed along the cavity mid-plane with the purpose of detecting a transient electric field arising from vacuum polarization conjectured to occur along the midplane of the cavity. An analytic technique called worldline numerics was adapted to numerically assess vacuum response to the custom Casimir cavity, and these numerical analysis results were observed to be qualitatively quite similar to a two-dimensional representation of energy density requirements for the Alcubierre warp metric. Subsequently, a toy model consisting of a 1 $$\upmu $$ μ m diameter sphere centrally located in a 4 $$\upmu $$ μ m diameter cylinder was analyzed to show a three-dimensional Casimir energy density that correlates well with the Alcubierre warp metric requirements. This qualitative correlation would suggest that chip-scale experiments might be explored to attempt to measure tiny signatures illustrative of the presence of the conjectured phenomenon: a real, albeit humble, warp bubble.

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