Free energy and states of fractional-order hereditariness

Luca Deseri; Mario Di Paola; Massimiliano Zingales

doi:10.1016/j.ijsolstr.2014.05.008

Free energy and states of fractional-order hereditariness

Luca Deseri, Mario Di Paola, Massimiliano Zingales

Research output: Contribution to journal › Article › peer-review

28 Scopus citations

Abstract

Complex materials, often encountered in recent engineering and material sciences applications, show no complete separations between solid and fluid phases. This aspect is reflected in the continuous relaxation time spectra recorded in cyclic load tests. As a consequence the material free energy cannot be defined in a unique manner yielding a significative lack of knowledge of the maximum recoverable work that can extracted from the material. The non-uniqueness of the free energy function is removed in the paper for power-laws relaxation/creep function by using a recently proposed mechanical analogue to fractional-order hereditariness.

Original language	English (US)
Pages (from-to)	3156-3167
Number of pages	12
Journal	International Journal of Solids and Structures
Volume	51
Issue number	18
DOIs	https://doi.org/10.1016/j.ijsolstr.2014.05.008
State	Published - Sep 2014

Keywords

Dissipation rate
Fractional derivatives
Free energy
Material state
Power-law creep/relaxation

ASJC Scopus subject areas

Mechanical Engineering
Mechanics of Materials
Materials Science(all)
Condensed Matter Physics
Applied Mathematics
Modeling and Simulation

Access to Document

10.1016/j.ijsolstr.2014.05.008

Cite this

@article{30e6f7cccd2d45bdaf42380abf99e54f,

title = "Free energy and states of fractional-order hereditariness",

abstract = "Complex materials, often encountered in recent engineering and material sciences applications, show no complete separations between solid and fluid phases. This aspect is reflected in the continuous relaxation time spectra recorded in cyclic load tests. As a consequence the material free energy cannot be defined in a unique manner yielding a significative lack of knowledge of the maximum recoverable work that can extracted from the material. The non-uniqueness of the free energy function is removed in the paper for power-laws relaxation/creep function by using a recently proposed mechanical analogue to fractional-order hereditariness.",

keywords = "Dissipation rate, Fractional derivatives, Free energy, Material state, Power-law creep/relaxation",

author = "Luca Deseri and {Di Paola}, Mario and Massimiliano Zingales",

note = "Funding Information: Mario Di Paola and Massimiliano Zingales are very grateful to the financial support provided by the PRIN2010-11 “Stability, Control and Reliability of Flexible Structures” with National Coordinator Prof. A. Luongo. Luca Deseri acknowledges the Department of Mathematical Sciences and the Center for Nonlinear Analysis, Carnegie Mellon University through the NSF Grant No. DMS-0635983 and the financial support from Grant PIAP-GA-2011-286110-INTERCER2 “Modelling and optimal design of ceramic structures with defects and imperfect interfaces”. ",

year = "2014",

month = sep,

doi = "10.1016/j.ijsolstr.2014.05.008",

language = "English (US)",

volume = "51",

pages = "3156--3167",

journal = "International Journal of Solids and Structures",

issn = "0020-7683",

publisher = "Elsevier Limited",

number = "18",

}

TY - JOUR

T1 - Free energy and states of fractional-order hereditariness

AU - Deseri, Luca

AU - Di Paola, Mario

AU - Zingales, Massimiliano

N1 - Funding Information: Mario Di Paola and Massimiliano Zingales are very grateful to the financial support provided by the PRIN2010-11 “Stability, Control and Reliability of Flexible Structures” with National Coordinator Prof. A. Luongo. Luca Deseri acknowledges the Department of Mathematical Sciences and the Center for Nonlinear Analysis, Carnegie Mellon University through the NSF Grant No. DMS-0635983 and the financial support from Grant PIAP-GA-2011-286110-INTERCER2 “Modelling and optimal design of ceramic structures with defects and imperfect interfaces”.

PY - 2014/9

Y1 - 2014/9

N2 - Complex materials, often encountered in recent engineering and material sciences applications, show no complete separations between solid and fluid phases. This aspect is reflected in the continuous relaxation time spectra recorded in cyclic load tests. As a consequence the material free energy cannot be defined in a unique manner yielding a significative lack of knowledge of the maximum recoverable work that can extracted from the material. The non-uniqueness of the free energy function is removed in the paper for power-laws relaxation/creep function by using a recently proposed mechanical analogue to fractional-order hereditariness.

AB - Complex materials, often encountered in recent engineering and material sciences applications, show no complete separations between solid and fluid phases. This aspect is reflected in the continuous relaxation time spectra recorded in cyclic load tests. As a consequence the material free energy cannot be defined in a unique manner yielding a significative lack of knowledge of the maximum recoverable work that can extracted from the material. The non-uniqueness of the free energy function is removed in the paper for power-laws relaxation/creep function by using a recently proposed mechanical analogue to fractional-order hereditariness.

KW - Dissipation rate

KW - Fractional derivatives

KW - Free energy

KW - Material state

KW - Power-law creep/relaxation

UR - http://www.scopus.com/inward/record.url?scp=84904255954&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84904255954&partnerID=8YFLogxK

U2 - 10.1016/j.ijsolstr.2014.05.008

DO - 10.1016/j.ijsolstr.2014.05.008

M3 - Article

AN - SCOPUS:84904255954

VL - 51

SP - 3156

EP - 3167

JO - International Journal of Solids and Structures

JF - International Journal of Solids and Structures

SN - 0020-7683

IS - 18

ER -

Free energy and states of fractional-order hereditariness

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this