The Qualitative Analysis of Theoretic Curves Generated by Linear Viscoelasticity Constitutive Equation
<p>The article analyses a one-dimensional linear integral constitutive equation of viscoelasticity with an arbitrary creep compliance function in order to reveal its abilities to describe the set of basic rheological phenomena pertaining to viscoelastoplastic materials at a constant temperatur...
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| Format: | Article |
| Language: | Russian |
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MGTU im. N.È. Baumana
2016-01-01
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| Series: | Nauka i Obrazovanie |
| Subjects: | |
| Online Access: | http://technomag.edu.ru/jour/article/view/869 |
| _version_ | 1811242492059713536 |
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| author | A. V. Khohlov |
| author_facet | A. V. Khohlov |
| author_sort | A. V. Khohlov |
| collection | DOAJ |
| description | <p>The article analyses a one-dimensional linear integral constitutive equation of viscoelasticity with an arbitrary creep compliance function in order to reveal its abilities to describe the set of basic rheological phenomena pertaining to viscoelastoplastic materials at a constant temperature. General equations and basic properties of its quasi-static theoretic curves (i.e. stress-strain curves at constant strain or stress rates, creep, creep recovery, creep curves at piecewise-constant stress and ramp relaxation curves) generated by the linear constitutive equation are derived and studied analytically. Their dependences on a creep function and relaxation modulus and on the loading program parameters are examined.</p><p>The qualitative properties of the theoretic curves are compared to the typical properties of viscoelastoplastic materials test curves to reveal the mechanical effects, which the linear viscoelasticity theory cannot simulate and to find out convenient experimental indicators marking the field of its applicability or non-applicability. The minimal set of general restrictions that should be imposed on a creep and relaxation functions to provide an adequate description of typical test curves of viscoelastoplastic materials is formulated. It is proved, in particular, that an adequate simulation of typical experimental creep recovery curves requires that the derivative of a creep function should not increase at any point. This restriction implies that the linear viscoelasticity theory yields theoretical creep curves with non-increasing creep rate only and it cannot simulate materials demonstrating an accelerated creep stage. It is also proved that the linear viscoelasticity cannot simulate materials with experimental stress-strain curves possessing a maximum point or concave-up segment and materials exhibiting equilibrium modulus dependence on the strain rate or negative rate sensitivity.</p><p>Similar qualitative analysis seems to be an important stage of identification, validation, tuning and application of any constitutive equation for rheonomous materials. It is useful for rational fitting a model and development of its “manual”.</p> |
| first_indexed | 2024-04-12T13:51:57Z |
| format | Article |
| id | doaj.art-3807237ddc6144088d6f559ba3ea3614 |
| institution | Directory Open Access Journal |
| issn | 1994-0408 |
| language | Russian |
| last_indexed | 2024-04-12T13:51:57Z |
| publishDate | 2016-01-01 |
| publisher | MGTU im. N.È. Baumana |
| record_format | Article |
| series | Nauka i Obrazovanie |
| spelling | doaj.art-3807237ddc6144088d6f559ba3ea36142022-12-22T03:30:30ZrusMGTU im. N.È. BaumanaNauka i Obrazovanie1994-04082016-01-0105187245869The Qualitative Analysis of Theoretic Curves Generated by Linear Viscoelasticity Constitutive EquationA. V. Khohlov0Lomonosov Moscow State University, Institute of Mechanics<p>The article analyses a one-dimensional linear integral constitutive equation of viscoelasticity with an arbitrary creep compliance function in order to reveal its abilities to describe the set of basic rheological phenomena pertaining to viscoelastoplastic materials at a constant temperature. General equations and basic properties of its quasi-static theoretic curves (i.e. stress-strain curves at constant strain or stress rates, creep, creep recovery, creep curves at piecewise-constant stress and ramp relaxation curves) generated by the linear constitutive equation are derived and studied analytically. Their dependences on a creep function and relaxation modulus and on the loading program parameters are examined.</p><p>The qualitative properties of the theoretic curves are compared to the typical properties of viscoelastoplastic materials test curves to reveal the mechanical effects, which the linear viscoelasticity theory cannot simulate and to find out convenient experimental indicators marking the field of its applicability or non-applicability. The minimal set of general restrictions that should be imposed on a creep and relaxation functions to provide an adequate description of typical test curves of viscoelastoplastic materials is formulated. It is proved, in particular, that an adequate simulation of typical experimental creep recovery curves requires that the derivative of a creep function should not increase at any point. This restriction implies that the linear viscoelasticity theory yields theoretical creep curves with non-increasing creep rate only and it cannot simulate materials demonstrating an accelerated creep stage. It is also proved that the linear viscoelasticity cannot simulate materials with experimental stress-strain curves possessing a maximum point or concave-up segment and materials exhibiting equilibrium modulus dependence on the strain rate or negative rate sensitivity.</p><p>Similar qualitative analysis seems to be an important stage of identification, validation, tuning and application of any constitutive equation for rheonomous materials. It is useful for rational fitting a model and development of its “manual”.</p>http://technomag.edu.ru/jour/article/view/869linear viscoelasticityintegral constitutive equationcreep compliancerelaxation modulustheoretic stress-strain curvescreep curvescreep recovery curvesrelaxation curvesfading memoryadequacy indicators for linear viscoelasticity |
| spellingShingle | A. V. Khohlov The Qualitative Analysis of Theoretic Curves Generated by Linear Viscoelasticity Constitutive Equation Nauka i Obrazovanie linear viscoelasticity integral constitutive equation creep compliance relaxation modulus theoretic stress-strain curves creep curves creep recovery curves relaxation curves fading memory adequacy indicators for linear viscoelasticity |
| title | The Qualitative Analysis of Theoretic Curves Generated by Linear Viscoelasticity Constitutive Equation |
| title_full | The Qualitative Analysis of Theoretic Curves Generated by Linear Viscoelasticity Constitutive Equation |
| title_fullStr | The Qualitative Analysis of Theoretic Curves Generated by Linear Viscoelasticity Constitutive Equation |
| title_full_unstemmed | The Qualitative Analysis of Theoretic Curves Generated by Linear Viscoelasticity Constitutive Equation |
| title_short | The Qualitative Analysis of Theoretic Curves Generated by Linear Viscoelasticity Constitutive Equation |
| title_sort | qualitative analysis of theoretic curves generated by linear viscoelasticity constitutive equation |
| topic | linear viscoelasticity integral constitutive equation creep compliance relaxation modulus theoretic stress-strain curves creep curves creep recovery curves relaxation curves fading memory adequacy indicators for linear viscoelasticity |
| url | http://technomag.edu.ru/jour/article/view/869 |
| work_keys_str_mv | AT avkhohlov thequalitativeanalysisoftheoreticcurvesgeneratedbylinearviscoelasticityconstitutiveequation AT avkhohlov qualitativeanalysisoftheoreticcurvesgeneratedbylinearviscoelasticityconstitutiveequation |