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Minimal, simple small strain viscoelastoplastic ity Minimal – reduction of empirical freedom

Minimal, simple small strain viscoelastoplastic ity Minimal – reduction of empirical freedom plasticity, rheology Simple – differential equation ( 1D, homogeneous ).

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Minimal, simple small strain viscoelastoplastic ity Minimal – reduction of empirical freedom

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  1. Minimal, simple small strain viscoelastoplasticity Minimal – reduction of empirical freedom plasticity, rheology Simple – differential equation (1D, homogeneous) Thermodynamics, plasticity and rheologyVán P.RMKI, Dep. Theor. Phys., Budapest, Hungary Montavid Research Group, Budapest, Hungary

  2. Min? • Classical plasticity • Elastic stress strain relations • Plastic strain: • Yield condition –f: • Plastic potential – g: • (non-associative) • Evolution of plastic strain • (non-ideal) • → Three empirical functions: • static potential s, yield functionf,plastic potentialg • → Second Law?

  3. Min? • Thermodynamic plasticity (Ziegler, Maugin, …, Bazant, Houlsby,…) • Thermostatics – elastic stress strain relations • Plastic strain is a special internal variable • Dissipation potential = plastic potential • First order homogeneity • → Relation to Second Law is established, evolution of plastic strain is derived. • →Two empirical functions: • static potential s, dissipation potential Φ

  4. Min? Thermodynamic rheology (Verhás, 1997) entropy Entropy balance: isothermal, small strain

  5. Min? Linear relations: isotropy, one dimension, … Ideal elastic: Second Law: The internal variable can (must?) be eliminated: Jeffreys body relaxation material inertia creep

  6. Further motivation: • Rheology (creep and relaxation)+plasticity • Non associated flow – soils • dissipation potentials=normality • = (nonlinear) Onsagerian symmetry • Is the thermodynamic framework too strong?? • → computational and numerical stability ? Truesdell +dual variables (JNET, 2008, 33, 235-254.) rheological thermodynamics (KgKK, 2008, 6, 51-92)

  7. min+min=simple? Unification: dissipation potential – constitutive relations Differential equation

  8. simple Strain hardening:

  9. simple Loading rate dependence:

  10. simple Creep: like Armstrong-Frederic kinematic hardening

  11. simple Hysteresis, Bauschinger effect, ratcheting: overshoot ratcheting

  12. simple? Non-associative, Mohr-Coulomb, dilatancy (according to Houlsby and Puzrin):

  13. Discussion • Minimal viscoelastoplasticity • Possible generalizations • finite strain, • objective derivatives, • gradient effects, • modified Onsagerian coefficients, • yield beyond Tresca, etc... • Non-associative? + thermo • More general constitutive relations (gyroscopic forces?) + thermo • Differential equation (can be incremental) • Numerical stability (thermo)

  14. Thank you for your attention!

  15. P +R+ T Interlude – damping and friction Dissipation in contact mechanics: F S Mechanics – constant force Plasticity: (spec. )

  16. Impossible world – Second Law is violated Real world – Second Law is valid Ideal world – there is no dissipation Thermodinamics - Mechanics

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