A class of initially isotropic elastic materials

1988 ◽  
Vol 417 (1852) ◽  
pp. 133-154
Keyword(s):  
Differential Equations ◽  
Large Deformation ◽  
Elastic Moduli ◽  
Elastic Potential ◽  
Experimental Results ◽  
Elastic Materials ◽  
Foam Rubber ◽  
Isotropic Materials ◽  
Principal Stretches ◽  
Hyperbolic Differential Equations

Basic results of Biot and Hill concerning (i) the elastic moduli of initially isotropic materials and (ii) Cauchy symmetry for large deformation are combined. The result is a system of hyperbolic differential equations to be satisfied by the elastic potential as a function of the principal stretches. Imposing these restrictions, the elastic potential for any strain is shown to be a functional of the elastic potential for pure dilatation. The theory is to some extent corroborated by experimental results on foam rubber by Blatz & Ko ( Trans. Soc. Rheol . 6, 223 (1962)).

Mechanical Characterization of Apricena Marble by Ultrasonic Immersion Tests

2014 ◽  
Vol 628 ◽  
pp. 109-116 ◽  
Author(s):  
Anna Castellano ◽  
Pilade Foti ◽  
Aguinaldo Fraddosio ◽  
Salvatore Marzano ◽  
Mario Daniele Piccioni
Keyword(s):  
Wave Propagation ◽  
Elastic Moduli ◽  
Mechanical Characterization ◽  
Experimental Results ◽  
Elastic Response ◽  
Ultrasonic Velocities ◽  
Elastic Materials

We characterize the elastic response of Apricena marble by using advanced ultrasonic nondestructive techniques. An innovative experimental device for ultrasonic immersion tests is employed for the determination of ultrasonic velocities of waves travelling into the sample for any angle of propagation. The interpretation of the experimental results within the theoretical framework of wave propagation in elastic materials allows for both the classification of the anisotropy and the determination of the elastic moduli.

Buckling Behavior of Tire Breaker Structure

1983 ◽  
Vol 11 (1) ◽  
pp. 3-19
Author(s):  
T. Akasaka ◽  
S. Yamazaki ◽  
K. Asano
Keyword(s):  
Elastic Foundation ◽  
Elastic Moduli ◽  
Wave Length ◽  
Bending Moment ◽  
Experimental Results ◽  
Automobile Tire ◽  
Buckling Behavior ◽  
Post Buckling ◽  
Steel Cord ◽  
Interlaminar Shear

Abstract The buckled wave length and the critical in-plane bending moment of laminated long composite strips of cord-reinforced rubber sheets on an elastic foundation is analyzed by Galerkin's method, with consideration of interlaminar shear deformation. An approximate formula for the wave length is given in terms of cord angle, elastic moduli of the constituent rubber and steel cord, and several structural dimensions. The calculated wave length for a 165SR13 automobile tire with steel breakers (belts) was very close to experimental results. An additional study was then conducted on the post-buckling behavior of a laminated biased composite beam on an elastic foundation. This beam is subjected to axial compression. The calculated relationship between the buckled wave rise and the compressive membrane force also agreed well with experimental results.

PROPOSAL OF HYSTERESIS MODEL USING DIFFERENTIAL EQUATIONS CONSIDERING OF CYCLIC DEGRADATION UNDER LARGE DEFORMATION

2020 ◽  
Vol 85 (773) ◽  
pp. 921-931
Author(s):  
Tsuyoshi FUKASAWA ◽  
Shigeki OKAMURA ◽  
Takahiro SOMAKI ◽  
Takayuki MIYAGAWA ◽  
Tomohiko YAMAMOTO ◽  
...  
Keyword(s):  
Differential Equations ◽  
Large Deformation ◽  
Hysteresis Model ◽  
Cyclic Degradation

Mixed Problems for Linear Systems of first Order Equations

1958 ◽  
Vol 10 ◽  
pp. 127-160 ◽  
Author(s):  
G. F. D. Duff
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Partial Differential ◽  
Auxiliary Data ◽  
First Order ◽  
Independent Variables ◽  
Mixed Problems ◽  
Linear Partial Differential Equations ◽  
Data Problem ◽  
Hyperbolic Differential Equations

A mixed problem in the theory of partial differential equations is an auxiliary data problem wherein conditions are assigned on two distinct surfaces having an intersection of lower dimension. Such problems have usually been formulated in connection with hyperbolic differential equations, with initial and boundary conditions prescribed. In this paper a study is made of the conditions appropriate to a system of R linear partial differential equations of first order, in R dependent and N independent variables.

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