The effective equilibrium law for a highly heterogeneous elastic periodic medium

2013 ◽  
Vol 143 (3) ◽  
pp. 507-561 ◽  
Author(s):  
Hamid Charef ◽  
Ali Sili
Keyword(s):  
Elastic Medium ◽  
Elastic Material ◽  
Equilibrium Equation ◽  
Elasticity Tensor ◽  
Periodic Medium ◽  
Special Assumption ◽  
Linearized System ◽  
Rigid Material ◽  
Small Deformations

We study the homogenization of the linearized system of elasticity standing for the equilibrium equation of a highly periodic heterogeneous elastic medium submitted to small deformations and made of two different materials: a very rigid material located in a set Fε (ε being the size of the period of the medium) of vertical fibres surrounded by a soft elastic material localized in the set Mε. The ratio between the coefficients of the elasticity tensor of the two materials is assumed to be 1/ε4. We deal with the general case without any special assumption, such as isotropy, on the material.

Deformations and Stress Intensities Due to a Craze in an Extended Elastic Material

1984 ◽  
Vol 51 (1) ◽  
pp. 84-92 ◽  
Author(s):  
J. R. Walton ◽  
Y. Weitsman
Keyword(s):  
Analytical Solution ◽  
Elastic Medium ◽  
Finite Length ◽  
Elastic Material ◽  
Integrodifferential Equation ◽  
Numerical Scheme ◽  
Time Dependent ◽  
Stress Fields ◽  
Singular Integrodifferential Equation

This paper presents an analytical solution, accompanied by a numerical scheme, to determine the displacement and stress fields in an extended elastic medium due to a thin craze of finite length directed transversely to the load at infinity. Crazes are thin elongated defects containing fine fibrils that connect their opposite interfaces. These fibrils are modeled as a distributed spring, leading to a formulation in terms of a singular integrodifferential equation. The paper also contains a treatment of central cracks within the craze and time-dependent craze response, and includes a discussion of “tip zone” correction.

Extensive Theory of Force-Approach Relations of Elastic Spheres in Compression and in Impact

1989 ◽  
Vol 111 (2) ◽  
pp. 163-168 ◽  
Author(s):  
Yoichi Tatara
Keyword(s):  
Elastic Medium ◽  
Relative Position ◽  
Large Deformations ◽  
Hard Spheres ◽  
Center Of Mass ◽  
Initial Position ◽  
Experimental Result ◽  
Hertz Theory ◽  
Wide Range ◽  
Small Deformations

The prevailing Hertz theory in contact and in impact is based on the total compressive displacement of a semi-infinite elastic body. This paper considers displacements of finite elastic medium in each of elastic spheres and presents analytically extensive force-approach relations of the Hertz theory for two elastic spheres in statical compression and in impact. In the statical conditions, expansive displacements of the mutual surf ace of contact due to compressive displacements by the reactions, which act on the opposite surfaces in a distance equal to each diameter, are considered analytically in two approximate cases. The force-approach relations obtained here are much closer than the Hertz’s one in a wide range of deformations to one experimental result carried out for one rubber sphere. In impact, it is considered that relative position of each center of mass of the impacting spheres accompanying asymmetrical deformations is shifted from the initial position. The force-approach relation has another extensive term different from the Hertz’s relation and from the above relations in the statical conditions. In the case of very small deformations for hard spheres, the extensive terms can be neglected and the Hertz theory is valid in compression and in impact. The present force-approach relations can be applicable to the cases of large deformations in compression and in impact.

Material symmetry: a key to specification of interatomic potentials

2013 ◽  
Vol 61 (2) ◽  
pp. 441-450 ◽  
Author(s):  
K. Nalepka
Keyword(s):  
Large Deformations ◽  
Defect Formation ◽  
Elasticity Tensor ◽  
Interatomic Potentials ◽  
Material Symmetry ◽  
Atomistic Model ◽  
Elementary Processes ◽  
Cubic Crystals ◽  
Small Strains ◽  
Small Deformations

Abstract The paper shows that symmetry forms a basis for relations between different properties of material. In this way, the key quantities for specification of an atomistic model are identified. Material symmetry distinguishes representative processes of small strains. It is proved that the errors in the densities of the energies stored in these processes determine the range of inaccuracies with which an atomistic model recreates processes of small deformations. The errors are equal to the inaccuracies in the eigenvalues of the elasticity tensor, that is in the Kelvin moduli. For cubic crystals, the elementary processes indicated by the symmetry initiate the key paths of large deformations: Bain and trigonal ones. Therefore, the substantial errors in the Kelvin moduli lead to incorrect reconstructing the metastable phases: bcc, sc and bct. The elastic constants commonly used in the literature do not provide such information as the Kelvin moduli. Using the eigenvalues of the elasticity tensor as well as other key properties indicated by the symmetry, the EAM model proposed by A.F. Voter for copper is specified. The obtained potential more accurately reproduces small and large deformations and additionally, correctly describes defect formation as well as Cu dimer properties

In-plane hygro-viscoelasticity of paper at small deformations

2005 ◽  
Vol 20 (2) ◽  
pp. 139-149 ◽  
Author(s):  
Jan Lif ◽  
Sören Östlund ◽  
Christer Fellers
Keyword(s):  
Small Deformations

Contribution to the determination of relative increment of internal energy at low deformation of cross-linked rubber

1980 ◽  
Vol 45 (8) ◽  
pp. 2315-2318 ◽  
Author(s):  
Vladimír Pollák ◽  
Andrej Romanov
Keyword(s):  
Internal Energy ◽  
Vinyl Acetate ◽  
Temperature Changes ◽  
Relative Increment ◽  
Poly Ethylene ◽  
Small Deformations

The relative charge of the internal energy, fU/f, during deformation of cross-linked elastomers, poly(ethylene-co-propylene) and poly(ethylene-co-vinyl acetate), was determined at various temperatures. Anomalies in the dependence of fU/f on relative dilatation in the region of small deformations ( 35%) are to a large extent besides other factors due to the sensibility of the formula used to calculate fU/f to temperature changes.

Elastoplasticity beyond small deformations

2006 ◽  
Vol 182 (1-2) ◽  
pp. 31-111 ◽  
Author(s):  
H. Xiao ◽  
O. T. Bruhns ◽  
A. Meyers
Keyword(s):  
Small Deformations

Comparison between elastic and porous elastic material models for sediment acoustical behavior in an aluminum-sediment double layer

2021 ◽  
Vol 43 (5) ◽  
Author(s):  
Omid Bahrami Khameslouie ◽  
Mohammad Hossein Soorgee ◽  
Ehsan Ghafarallahi ◽  
Seyed Ebrahim Moussavi Torshizi
Keyword(s):  
Double Layer ◽  
Elastic Material ◽  
Material Models

scholarly journals Superconducting Order Parameter Nucleation and Critical Currents in the Presence of Weak Stray Fields in Superconductor/Insulator/Ferromagnet Hybrids

Coatings ◽  
2021 ◽  
Vol 11 (5) ◽  
pp. 507
Author(s):  
Vasiliy N. Kushnir ◽  
Serghej L. Prischepa ◽  
Michela Trezza ◽  
Carla Cirillo ◽  
Carmine Attanasio
Keyword(s):  
Phenomenological Theory ◽  
Critical Currents ◽  
Superconducting Phase ◽  
Stray Field ◽  
Superconducting Properties ◽  
Ginzburg Landau ◽  
Ferromagnetic Layers ◽  
Linearized System ◽  
Critical Current Density Jc ◽  
Usadel Equations

The stray fields produced by ferromagnetic layers in Superconductor/Insulator/Ferromagnet (S/I/F) heterostructures may strongly influence their superconducting properties. Suitable magnetic configurations can be exploited to manipulate the main parameters of the hybrids. Here, the nucleation of the superconducting phase in an external magnetic field that periodically oscillates along the film width is studied on the base of the numerical solution of the linearized system of Usadel equations. In addition, the effect of the magnetic configuration of the F-layer on the temperature dependence of the critical current density, Jc(T), is investigated in the framework of the Ginzburg–Landau phenomenological theory on the base of the oscillating model of a stray field. By following this approach, the Jc(T) dependence of a Nb/SiO2/PdNi trilayer is reproduced for different magnetic configurations of the PdNi layer.

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