scholarly journals An unified formulation of strong non-local elasticity with fractional order calculus

Meccanica ◽  
2021 ◽  
Author(s):  
Gioacchino Alotta ◽  
Mario Di Paola ◽  
Francesco Paolo Pinnola
Keyword(s):  
Fractional Order ◽  
Long Memory ◽  
Stress Strain ◽  
Viscoelastic Models ◽  
Strain Relation ◽  
Stress Strain Relation ◽  
Proposed Model ◽  
Riesz Operators ◽  
Local Relation ◽  
Non Local

AbstractThe research of a formulation to model non-local interactions in the mechanical behavior of matter is currently an open problem. In this context, a strong non-local formulation based on fractional calculus is provided in this paper. This formulation is derived from an analogy with long-memory viscoelastic models. Specifically, the same kind of power-law time-dependent kernel used in Boltzmann integral of viscoelastic stress-strain relation is used as kernel in the Fredholm non-local relation. This non-local formulation leads to stress-strain relation based on the space Riesz integral and derivative of fractional order. For unbounded domain, proposed model can be defined in stress- and in strain-driven formulation and in both cases the stress–strain relation represent a strong non-local model. Also, the proposed strain driven and stress driven formulations defined in terms of Riesz operators are proved to be fully consistent each another. Moreover, the proposed model posses a mechanical meaning and for unbounded non-local rod is described and discussed in detail.

Fractional Order Constitutive Model of Geomaterials Under the Condition of Triaxial Test

2011 ◽  
Author(s):  
Deshun Yin ◽  
Hao Wu ◽  
Chen Cheng ◽  
YangQuan Chen
Keyword(s):  
Fractional Calculus ◽  
Constitutive Model ◽  
Fractional Order ◽  
Triaxial Test ◽  
Constitutive Models ◽  
Constant Strain Rate ◽  
Stress Strain ◽  
Good Tool ◽  
Strain Relation ◽  
Stress Strain Relation

Fractional calculus has been successfully applied to characterize the rheological property of viscoelastic materials, however, geomaterials were seldom involved in fractional order constitutive models (FOCM), and the issue of first loading and then unloading is rarely discussed through fractional calculus. It is considered that all materials are arranged in a queue and ideal solid and Newtonian fluid are located at both ends of the queue in FOCM. On the basis of FOCM, stress-strain relation under the condition of first loading and then unloading, besides creep, stress-relaxation and loading of constant strain rate are obtained. The stress-strain relation is utilized to fit triaxial test results of geomaterials under the corresponding conditions. The comparison between the test and fitting results reveals that FOCM can reasonably describe the stress-strain, stress-time or strain-time characteristics of geomaterials, which shows that fractional calculus is a good tool to constitutive model research of geomaterials.

scholarly journals Limit analysis of narrow support elements in W7-X considering the serration effect of the stress–strain relation at 4K

2011 ◽  
Vol 86 (6-8) ◽  
pp. 1462-1465 ◽  
Author(s):  
E. Briani ◽  
C. Gianini ◽  
F. Lucca ◽  
A. Marin ◽  
J. Fellinger ◽  
...  
Keyword(s):  
Limit Analysis ◽  
Stress Strain ◽  
Strain Relation ◽  
Stress Strain Relation

Analytical stress-strain relation for soils

2021 ◽  
Author(s):  
Kristian Krabbenhoft ◽  
J. Wang
Keyword(s):  
Test Data ◽  
Narrow Range ◽  
Strain Range ◽  
Data Sets ◽  
Soil Tests ◽  
Stress Strain ◽  
Strain Relation ◽  
Stress Strain Relation ◽  
Typical Test ◽  
Typical Soil

A new stress-strain relation capable of reproducing the entire stress-strain range of typical soil tests is presented. The new relation involves a total of five parameters, four of which can be inferred directly from typical test data. The fifth parameter is a fitting parameter with a relatively narrow range. The capabilities of the new relation is demonstrated by the application to various clay and sand data sets.

Stress-Strain Relations and Vibrations of a Granular Medium

1957 ◽  
Vol 24 (4) ◽  
pp. 585-593
Author(s):  
J. Duffy ◽  
R. D. Mindlin
Keyword(s):  
Energy Dissipation ◽  
Contact Forces ◽  
Face Centered Cubic ◽  
Stress Strain ◽  
Differential Stress ◽  
Elastic Bodies ◽  
Strain Relation ◽  
Stress Strain Relation ◽  
Face Centered ◽  
Experimental Values

Abstract A differential stress-strain relation is derived for a medium composed of a face-centered cubic array of elastic spheres in contact. The stress-strain relation is based on the theory of elastic bodies in contact, and includes the effects of both normal and tangential components of contact forces. A description is given of an experiment performed as a test of the contact theories and the differential stress-strain relation derived from them. The experiment consists of a determination of wave velocities and the accompanying rates of energy dissipation in granular bars composed of face-centered cubic arrays of spheres. Experimental results indicate a close agreement between the theoretical and experimental values of wave velocity. However, as in previous experiments with single contacts, the rate of energy dissipation is found to be proportional to the square of the maximum tangential contact force rather than to the cube, as predicted by the theory for small amplitudes.

scholarly journals CONCENTRIC LOADING TESTS OF CONCRETE FILLED SPIRAL STEEL TUBES AND STRESS-STRAIN RELATION OF CONCRETE CONFINED BY STEEL TUBES

2009 ◽  
Vol 65 (4) ◽  
pp. 548-563 ◽  
Author(s):  
Mitsuyoshi AKIYAMA ◽  
Hideki NAITO ◽  
Kiyoshi ONO ◽  
Nobutaka SHIRAHAMA ◽  
Daisuke MATSUMOTO ◽  
...  
Keyword(s):  
Stress Strain ◽  
Steel Tubes ◽  
Strain Relation ◽  
Stress Strain Relation ◽  
Loading Tests ◽  
Concentric Loading
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