A Note on the Pure Bending of Nonhomogeneous Prismatic Bars

2009 ◽  
Vol 37 (2) ◽  
pp. 118-129 ◽  
Author(s):  
Attila Baksa ◽  
István Ecsedi
Keyword(s):  
Composite Beam ◽  
Strain Energy ◽  
Elastic Strain Energy ◽  
Functionally Graded ◽  
Bending Stress ◽  
Pure Bending ◽  
Small Strains ◽  
Compressive Stresses ◽  
Elastic Bar

The paper examines the pure bending of a linearly elastic, isotropic, nonhomogeneous bar. The bending stress, elastic strain energy and the end cross-section rotations are determined for in-plane variation of the Young's modulus with small strains and displacements. It is shown that the governing formulae for elastic pure bending of nonhomogeneous bars have same forms as formulae for symmetrical bending (bending in the principal planes) of homogeneous bars. Two examples illustrate the application of the developed formulae. In the first, a composite beam is considered; the second deals with the determination of the maximum tensile and compressive stresses in a bent functionally graded elastic bar.

Translation Order Domains of Coherent Particles in Ni Alloys During Coarsening.

2000 ◽  
Vol 6 (S2) ◽  
pp. 346-347
Author(s):  
H. A. Calderon ◽  
L. Calzado ◽  
T. Mori
Keyword(s):  
Strain Energy ◽  
Critical Size ◽  
Elastic Strain Energy ◽  
Elastic Interaction ◽  
Total Surface Energy ◽  
Particle Volume ◽  
Ni Alloys ◽  
Particle Alignment ◽  
Regular Arrays

Coarsening of particles involves a reduction of the total energy of the system. In fluids, the tendency for larger particles to grow at the expense of smaller ones is driven by the reduction of the total surface energy. In solids, the elastic strain energy Eel also needs to be considered. Reduction of Eel gives rise to particle alignment along elastically soft directions and changes of morphology as the particle volume increases. In addition according to several authors, reduction of Eel produces the splitting of particles that reach a critical size. Regular arrays of two, four and eight particles have been observed and explained in terms of splitting. However, splitting is unlikely from a micromechanical standpoint or as a consequence of the elastic interaction between particles. This investigation deals with the determination of translation order domains in coherent γ′ particles.

Thermodynamic Assessment and Determination of Spinodal Lines for Al-Zn Binary System

2014 ◽  
Vol 794-796 ◽  
pp. 634-639 ◽  
Author(s):  
Shosuke Kogo ◽  
Shoichi Hirosawa
Keyword(s):  
Free Energy ◽  
Binary System ◽  
Gibbs Free Energy ◽  
Strain Energy ◽  
Thermodynamic Assessment ◽  
Metastable Phase ◽  
Elastic Strain Energy ◽  
Miscibility Gap ◽  
Good Agreement

Calphad type thermodynamic assessment of Al-Zn binary system was performed to calculate the metastable phase diagram including not only miscibility gap but also spinodal lines. The Gibbs free energy for liquid, fcc and hcp phases was evaluated by taking into account available experimental data, and most of them were satisfactorily reproduced by our thermodynamic descriptions. Furthermore, the Gibbs free energy for GP zones was also expressed by combining the chemical energy for solid solution of fcc-Al with appropriate elastic strain energy, in good agreement with experimentally reported solubility limits. Therefore, the spinodal lines derived from the differential of the Gibbs free energy could be also reasonably estimated, although those are quite difficult to be measured experimentally.

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 Determination of time-dependent strengths of salt pillars based on strain energy principle

2019 ◽  
Vol 29 (2) ◽  
pp. 273-279 ◽  
Author(s):  
Prapasiri Junthong ◽  
Supattra Khamrat ◽  
Suratwadee Sartkaew ◽  
Kittitep Fuenkajorn
Keyword(s):  
Strain Energy ◽  
Time Dependent ◽  
Energy Principle

Investigation of Nanometric Thin-Film Bismuth Piezoresistors Deposited on Silicon Substrates

2012 ◽  
Vol 1477 ◽  
Author(s):  
Horacio V. Estrada
Keyword(s):  
Thin Film ◽  
Axial Strain ◽  
High Sensitivity ◽  
Metal Alloys ◽  
Silicon Substrates ◽  
Transverse Strain ◽  
Bending Stress ◽  
Pure Bending ◽  
Strain Fields ◽  
Strain Axis

ABSTRACTThin film bismuth piezoresistors, defined on oxidized silicon wafers, are investigated as a function of their orientation for their eventual integration on micro-electro-mechanical (MEMS) microsensors. Bismuth’s piezoresistance (or elasto-resistance) is experimentally investigated to accurately determine its longitudinal and transverse strain sensitivities. Whisker-shaped resistive elements defined on different orientations (from 0o, the beam’s main strain axis, to 90o, perpendicular to that axis) undergo changes of resistance (ΔR), associated with the induced strains on silicon cantilevers beam’s surface when these are mechanically loaded under pure bending stress conditions. For Bi-resistors, the traditional gage factor concept, (ΔR/Ro)/εl, is found to be equal to +16 and +33, for elements oriented along 0 and 90o, respectively, considerably larger than those for metals or metal alloys. These high sensitivity values and the “unusual” positive, higher value for the 90o (perpendicular) resistors can be of considerable interest for microsensors applications. The results of this study enable us to precisely determine the bismuth’s longitudinal and transverse strain sensitivities that are calculated to be equal to +26 and +40.5 respectively. This experimental study is extended to explore the Bi-films’ response to bi-axial strain fields.

Analysis of Energy Balance When Using Cohesive Zone Models to Simulate Fracture Processes

2002 ◽  
Vol 124 (4) ◽  
pp. 440-450 ◽  
Author(s):  
C. Shet ◽  
N. Chandra
Keyword(s):  
Cohesive Energy ◽  
Cohesive Zone ◽  
Strain Energy ◽  
Fracture Process ◽  
Fracture Process Zone ◽  
Process Zone ◽  
Elastic Strain Energy ◽  
Inelastic Strain ◽  
External Work ◽  
Cohesive Zone Models

Cohesive Zone Models (CZMs) are being increasingly used to simulate fracture and fragmentation processes in metallic, polymeric, and ceramic materials and their composites. Instead of an infinitely sharp crack envisaged in fracture mechanics, CZM presupposes the presence of a fracture process zone where the energy is transferred from external work both in the forward and the wake regions of the propagating crack. In this paper, we examine how the external work flows as recoverable elastic strain energy, inelastic strain energy, and cohesive energy, the latter encompassing the work of fracture and other energy consuming mechanisms within the fracture process zone. It is clearly shown that the plastic energy in the material surrounding the crack is not accounted in the cohesive energy. Thus cohesive zone energy encompasses all the inelastic energy e.g., energy required for grainbridging, cavitation, internal sliding, surface energy but excludes any form of inelastic strain energy in the bounding material.

Bifurcation of rotating circular cylindrical elastic membranes

1980 ◽  
Vol 87 (2) ◽  
pp. 357-376 ◽  
Author(s):  
D. M. Haughton ◽  
R. W. Ogden
Keyword(s):  
Axial Force ◽  
Strain Energy ◽  
Elastic Strain Energy ◽  
Strain Energy Function ◽  
Angular Speed ◽  
Elastic Membrane ◽  
Axial Extension ◽  
End Conditions ◽  
Elastic Membranes ◽  
Realistic Choice

SummaryBifurcation from a finitely deformed circular cylindrical configuration of a rotating circular cylindrical elastic membrane is examined. It is found (for a physically realistic choice of elastic strain-energy function) that the angular speed attains a maximum followed by a minimum relative to the increasing radius of the cylinder for either a fixed axial extension or fixed axial force.At fixed axial extension (a) a prismatic mode of bifurcation (in which the cross-section of the cylinder becomes uniformly non-circular) may occur at a maximum of the angular speed provided the end conditions on the cylinder allow this; (b) axisyim-metric modes may occur before, at or after the angular speed maximum depending on the length of the cylinder and the magnitude of the axial extension; (c) an asymmetric or ‘wobble’ mode is always possible before either (a) or (b) as the angular speed increases from zero for any length of cylinder or axial extension. Moreover, ‘wobble’ occurs at lower angular speeds for longer cylinders.At fixed axial force the results are similar to (a), (b) and (c) except that an axisym-metric mode necessarily occurs between the turning points of the angular speed.

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