Summary
The paper explores the theory of reactive porous media for the modelling of creep and plasticity due to chemo-mechanical couplings at the macro-level of material description. The formulation is based upon thermodynamics of open porous media composed of a skeleton and several fluid phases saturating the porous space. This theoretical framework allows to introduce the kinetics of a chemical reaction directly at the macro-level of material description. In turn, it is used to model creep due to chemo-mechanical couplings within a closed reactive porous continuum, as well as ageing creep due to two chemical reactions, one associated with the apparent creep phenomenon, the other with the apparent ageing phenomenon. Furthermore, it is shown how the modelling can be extended to account for plastic (i.e. permanent) phenomena, including hardening/softening and damage phenomena, coupled with a chemical reaction (chemical hardening).
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Abbreviations
- A :
-
reactant phase
- A m,A x :
-
chemical affinities of reactions of extent ζ andx
- Axo :
-
initial affinity
- Ax :
-
plastic affinity
- B :
-
product phase
- B:
-
tensor of chemical dilatation coefficients
- E a ,E x :
-
activation energies relative to reactions of extent andx
- f :
-
loading function
- g :
-
plastic potential
- g m j :
-
free mass enthalpy of fluid phasej
- H :
-
hardening modulus
- h :
-
hardening potential
- l:
-
2nd-order unit tensor
- K :
-
bulk modulus
- k d :
-
viscous coefficient associated to a micro-diffusion process
- k :
-
coefficient
- M Oi :
-
external mass supply rate of fluidi
- m j O :
-
increase in fluid mass of phasej
- m i→j :
-
rate of mass change from phasei to phasej
- R :
-
universal constant for ideal gas
- S :
-
entropy
- T :
-
temperature
- t :
-
time
- Uχ:
-
frozen energy due to hardening/softening
- x:
-
extent of the ageing reaction
- β:
-
isotropic chemical dilatation coefficient
- χ, χ:
-
hardening/softening/damage variable (scalar, tensor)
- ε:
-
strain tensor
- ε:
-
volume strain (trε)
- εv, εv :
-
viscous strain tensor; viscous volume strain (trεv)
- εp, εp :
-
plastic strain tensor; plastic volume strain (trεp)
- Φ1 :
-
intrinsic dissipation of the open elementary system
- ΦA→B :
-
chemical dissipation of the open elementary system
- ϕ1 :
-
intrinsic dissipation of the closed porous medium
- ηi :
-
viscosity relative to physico-chemical phenomenoni
- K :
-
material parameter
- dλ:
-
plastic multiplier
- μ(t):
-
maturity function or equivalent age
- σ:
-
stress tensor; initial stress tensor
- σ, σ0 :
-
mean stress, initial mean stress
- ξ, ξo :
-
extent of the creep reaction, creep reaction rate
- ψ:
-
free energy of the open elementary system
- ψ:
-
free energy of the closed elementary system
- ξ, ξ:
-
hardening force
- \(\dot x\)=dx/dt :
-
time derivative of functionx
- x o :
-
rate of quantityx
- () ∶ ():
-
double tensor contraction
- () · ():
-
scalar product
- tr():
-
first invariant of tensor ()
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Coussy, O., Ulm, F.J. Creep and plasticity due to chemo-mechanical couplings. Arch. Appl. Mech. 66, 523–535 (1996). https://doi.org/10.1007/BF00808142
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DOI: https://doi.org/10.1007/BF00808142