Controllability, uniqueness and existence of the incremental response

A mathematical criterion for elastoplastic constitutive laws

Giuseppe Buscarnera*, Giuseppe Dattola, Claudio Di Prisco

*Corresponding author for this work

Research output: Contribution to journalArticle

39 Citations (Scopus)

Abstract

In this paper the onset of instabilities in elastoplastic materials is theoretically studied and a conceptual basis for understanding the physical implications of a loss of uniqueness and/or existence of the incremental response is provided. For this purpose, the concept of test controllability is reinterpreted and mixed stress-strain loading programmes are accounted for. A set of scalar indices, the moduli of instability, related with the inception of an unstable response is introduced and their dependency on the loading programme is explicitly illustrated. The paper shows that the use of these newly defined scalar measures provides support for an alternative definition for mechanical stability, which is closely related with the mathematical notions of existence and uniqueness of the predicted incremental response. In the final section, some mathematical properties of the moduli of instability are discussed, suggesting a novel reinterpretation of other well established theories and providing additional tools for the future application of the proposed framework.

Original languageEnglish (US)
Pages (from-to)1867-1878
Number of pages12
JournalInternational Journal of Solids and Structures
Volume48
Issue number13
DOIs
StatePublished - Jun 15 2011

Fingerprint

Constitutive Law
controllability
uniqueness
Elasto-plastic
Controllability
Existence and Uniqueness
Modulus
Scalar
Mechanical stability
scalars
Uniqueness
Unstable
Alternatives

Keywords

  • Elastoplasticity
  • Mechanical instability
  • Non-associativity
  • Second-order work
  • Test controllability

ASJC Scopus subject areas

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

Cite this

@article{b910f96e916f4c12a732700b8973d63d,
title = "Controllability, uniqueness and existence of the incremental response: A mathematical criterion for elastoplastic constitutive laws",
abstract = "In this paper the onset of instabilities in elastoplastic materials is theoretically studied and a conceptual basis for understanding the physical implications of a loss of uniqueness and/or existence of the incremental response is provided. For this purpose, the concept of test controllability is reinterpreted and mixed stress-strain loading programmes are accounted for. A set of scalar indices, the moduli of instability, related with the inception of an unstable response is introduced and their dependency on the loading programme is explicitly illustrated. The paper shows that the use of these newly defined scalar measures provides support for an alternative definition for mechanical stability, which is closely related with the mathematical notions of existence and uniqueness of the predicted incremental response. In the final section, some mathematical properties of the moduli of instability are discussed, suggesting a novel reinterpretation of other well established theories and providing additional tools for the future application of the proposed framework.",
keywords = "Elastoplasticity, Mechanical instability, Non-associativity, Second-order work, Test controllability",
author = "Giuseppe Buscarnera and Giuseppe Dattola and {Di Prisco}, Claudio",
year = "2011",
month = "6",
day = "15",
doi = "10.1016/j.ijsolstr.2011.02.016",
language = "English (US)",
volume = "48",
pages = "1867--1878",
journal = "International Journal of Solids and Structures",
issn = "0020-7683",
publisher = "Elsevier Limited",
number = "13",

}

Controllability, uniqueness and existence of the incremental response : A mathematical criterion for elastoplastic constitutive laws. / Buscarnera, Giuseppe; Dattola, Giuseppe; Di Prisco, Claudio.

In: International Journal of Solids and Structures, Vol. 48, No. 13, 15.06.2011, p. 1867-1878.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Controllability, uniqueness and existence of the incremental response

T2 - A mathematical criterion for elastoplastic constitutive laws

AU - Buscarnera, Giuseppe

AU - Dattola, Giuseppe

AU - Di Prisco, Claudio

PY - 2011/6/15

Y1 - 2011/6/15

N2 - In this paper the onset of instabilities in elastoplastic materials is theoretically studied and a conceptual basis for understanding the physical implications of a loss of uniqueness and/or existence of the incremental response is provided. For this purpose, the concept of test controllability is reinterpreted and mixed stress-strain loading programmes are accounted for. A set of scalar indices, the moduli of instability, related with the inception of an unstable response is introduced and their dependency on the loading programme is explicitly illustrated. The paper shows that the use of these newly defined scalar measures provides support for an alternative definition for mechanical stability, which is closely related with the mathematical notions of existence and uniqueness of the predicted incremental response. In the final section, some mathematical properties of the moduli of instability are discussed, suggesting a novel reinterpretation of other well established theories and providing additional tools for the future application of the proposed framework.

AB - In this paper the onset of instabilities in elastoplastic materials is theoretically studied and a conceptual basis for understanding the physical implications of a loss of uniqueness and/or existence of the incremental response is provided. For this purpose, the concept of test controllability is reinterpreted and mixed stress-strain loading programmes are accounted for. A set of scalar indices, the moduli of instability, related with the inception of an unstable response is introduced and their dependency on the loading programme is explicitly illustrated. The paper shows that the use of these newly defined scalar measures provides support for an alternative definition for mechanical stability, which is closely related with the mathematical notions of existence and uniqueness of the predicted incremental response. In the final section, some mathematical properties of the moduli of instability are discussed, suggesting a novel reinterpretation of other well established theories and providing additional tools for the future application of the proposed framework.

KW - Elastoplasticity

KW - Mechanical instability

KW - Non-associativity

KW - Second-order work

KW - Test controllability

UR - http://www.scopus.com/inward/record.url?scp=79955550285&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79955550285&partnerID=8YFLogxK

U2 - 10.1016/j.ijsolstr.2011.02.016

DO - 10.1016/j.ijsolstr.2011.02.016

M3 - Article

VL - 48

SP - 1867

EP - 1878

JO - International Journal of Solids and Structures

JF - International Journal of Solids and Structures

SN - 0020-7683

IS - 13

ER -