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Advances in Minimal Viscoelastoplasticity: Unifying Plasticity, Rheology, and Thermodynamics

This work explores the synergistic relationship between minimal viscoelastoplasticity, plasticity, and rheology, focusing on reduced empirical freedoms and the establishment of constitutive relations through differential equations. It addresses classical and thermodynamic plasticity, emphasizing the evolution of plastic strain, dissipation potentials, and isothermal entropy balance in small strain scenarios. The paper discusses non-associative flow behavior in soils and presents generalizations related to finite strain and numerical stability. Ultimately, it seeks to unify dissipative processes under a coherent thermodynamic framework.

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Advances in Minimal Viscoelastoplasticity: Unifying Plasticity, Rheology, and Thermodynamics

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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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