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1 /10 M.Chrzanowski: Strength of Materials SM2-13: Rheology RHEOLOGY (time-dependent behaviour of materials)

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2 /10 M.Chrzanowski: Strength of Materials SM2-13: Rheology Πάντα ῥ ε ῖ κα ὶ ο ὐ δ ὲ ν μένει panta rhei kai ouden menei everything flows and nothing remains still Heraclitus of Ephesus (540-480 BC) Ἡ ράκλειτος ὁ Ἐ φέσιος (Herakleitos ho Ephesios)

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3 /10 M.Chrzanowski: Strength of Materials SM2-13: Rheology Tempus fugit, aeternitas manet t - time Hourglass is the trademark of Rheological Society

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4 /10 M.Chrzanowski: Strength of Materials SM2-13: Rheology Euclid, ~ 300 BC R.Hooke, 1635-1703 B.Pascal, 1629-1662 I.Newton, 1643-1727 SolidsFluids p0p0 p0p0 e=0 e0e0 e Elastic body Stiff body Viscous fluid Perfect fluid p –loadinge – deformation e=0 e0e0 e0e0p0p0 p0p0 Elastic bodyViscous fluid

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5 /10 M.Chrzanowski: Strength of Materials SM2-13: Rheology Dots indicate time derivatives T – temperature

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6 /10 M.Chrzanowski: Strength of Materials SM2-13: Rheology Elementary rheological models NEWTONHOOKE NEWTON HOOKE MAXWELL MODEL KELVIN MODEL SERIES coupling PARALELL coupling

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7 /10 M.Chrzanowski: Strength of Materials SM2-13: Rheology NEWTONHOOKE NEWTON HOOKE MAXWELL MODEL KELVIN MODEL SERIES coupling PARALELL coupling Time derivative notation

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8 /10 M.Chrzanowski: Strength of Materials SM2-13: Rheology MAXWELL M. Loading Steady creep, unbounded (linear) Loading „CREEP (of deformation) programme” „RELAXATION (of stress) programme” Complete relaxation (nonlinear)

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9 /10 M.Chrzanowski: Strength of Materials SM2-13: Rheology KELVIN M. Loading Nonsteady creep, bounded (nonlinear) Loading „CREEP (of deformation) programme” „RELAXATION (of stress) programme” No relaxation response!

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10 /10 M.Chrzanowski: Strength of Materials SM2-13: Rheology There are two fundamental characteristics of rheological processes: Its dependence on the history of loading Energy dissipation - causing irreversibility Macroscopically observable effects are due to material microstructure changes (see material science and Ashby maps). These changes can lead not only to irreversible deformation and stress relaxation but to the formation and growth of microstructural defects. Following this deterioration process a structure can be fatally damaged at arbitrary level of loading or deformation – after a sufficiently long period of loading time. This is, however, a subject of another important branch of solid mechanics – mechanics of damage and failure.

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11 /10 M.Chrzanowski: Strength of Materials SM2-13: Rheology stop

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