Tangent Second-Order Estimates for the Large-Strain, Macroscopic Response of Particle-Reinforced Elastomers

2012 ◽  
Vol 112 (2) ◽  
pp. 139-183 ◽  
Author(s):  
Reza Avazmohammadi ◽  
Pedro Ponte Castañeda
Keyword(s):  
Large Strain ◽  
Second Order ◽  
Macroscopic Response

scholarly journals Fully optimized second-order variational estimates for the macroscopic response and field statistics in viscoplastic crystalline composites

2015 ◽  
Vol 471 (2184) ◽  
pp. 20150665 ◽  
Author(s):  
P. Ponte Castañeda
Keyword(s):  
Composite Materials ◽  
Variational Principle ◽  
Variational Method ◽  
Single Crystal ◽  
Second Order ◽  
Duality Gaps ◽  
Nonlinear Composite ◽  
Constitutive Response ◽  
Correction Terms ◽  
Macroscopic Response

A variational method is developed to estimate the macroscopic constitutive response of composite materials consisting of aggregates of viscoplastic single-crystal grains and other inhomogeneities. The method derives from a stationary variational principle for the macroscopic stress potential of the viscoplastic composite in terms of the corresponding potential of a linear comparison composite (LCC), whose viscosities and eigenstrain rates are the trial fields in the variational principle. The resulting estimates for the macroscopic response are guaranteed to be exact to second order in the heterogeneity contrast, and to satisfy known bounds. In addition, unlike earlier ‘second-order’ methods, the new method allows optimization with respect to both the viscosities and eigenstrain rates, leading to estimates that are fully stationary and exhibit no duality gaps. Consequently, the macroscopic response and field statistics of the nonlinear composite can be estimated directly from the suitably optimized LCC, without the need for difficult-to-compute correction terms. The method is applied to a simple example of a porous single crystal, and the results are found to be more accurate than earlier estimates.

Single-Mode Polymer Optical Fiber Sensors for Large Strain Applications

2006 ◽  
Vol 969 ◽  
Author(s):  
Sharon M. Kiesel ◽  
Kara Peters ◽  
Tasnim Hassan ◽  
Mervyn Kowalsky
Keyword(s):  
Optical Fiber ◽  
Mechanical Response ◽  
Large Strain ◽  
Small Deformation ◽  
Single Mode ◽  
Second Order ◽  
Secant Modulus ◽  
Polymer Optical Fiber ◽  
Yield Strain ◽  
Deformation Regime

AbstractThis paper characterizes an intrinsic, single-mode, polymer optical fiber (POF) sensor for use in large-strain applications such as civil infrastructures subjected to earthquake loading or systems with large shape changes such as morphing aircraft. The opto-mechanical response was formulated for the POF including a second-order (in strain) photoelastic effect as well as a second-order (in strain) solution for the deformation of the POF during loading. It is shown that four independent mechanical and opto-mechanical constants are required for the small deformation regime and six additional independent mechanical and opto-mechanical constants are required for the large deformation regime. The mechanical nonlinearity of a typical polymer optical fiber was experimentally measured in tension at various loading rates. The secant modulus of elasticity measured at small strains, roughly up to 2% strain, was measured to be ∼4GPa whereas at larger strains, roughly up to 4.5% strain, the secant modulus was measured to be ∼4.8GPa. As the loading rate was increased the yield strain increased, ranging from ∼3.2% at 1mm/min to ∼5% at 305 mm/min.

Disappearance Voltage Determinations Using a Convergent Beam

1971 ◽  
Vol 29 ◽  
pp. 184-185
Author(s):  
W. L. Bell
Keyword(s):  
Second Order ◽  
Objective Method ◽  
Uniform Thickness ◽  
Rocking Curve ◽  
Crystal Perfection ◽  
Kikuchi Line ◽  
Central Maximum ◽  
Diffraction Patterns ◽  
Convergent Beam ◽  
Beam Technique

Disappearance voltages for second order reflections can be determined experimentally in a variety of ways. The more subjective methods, such as Kikuchi line disappearance and bend contour imaging, involve comparing a series of diffraction patterns or micrographs taken at intervals throughout the disappearance range and selecting that voltage which gives the strongest disappearance effect. The estimated accuracies of these methods are both to within 10 kV, or about 2-4%, of the true disappearance voltage, which is quite sufficient for using these voltages in further calculations. However, it is the necessity of determining this information by comparisons of exposed plates rather than while operating the microscope that detracts from the immediate usefulness of these methods if there is reason to perform experiments at an unknown disappearance voltage.The convergent beam technique for determining the disappearance voltage has been found to be a highly objective method when it is applicable, i.e. when reasonable crystal perfection exists and an area of uniform thickness can be found. The criterion for determining this voltage is that the central maximum disappear from the rocking curve for the second order spot.

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