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Make mechanical properties a function of stoichiometry and sometimes temperature #3576

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merged 5 commits into from
Dec 5, 2023
Merged

Make mechanical properties a function of stoichiometry and sometimes temperature #3576

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09f6bc8
add omega
aabills Nov 29, 2023
242c1c1
fix test failure
aabills Nov 29, 2023
65c6dcb
add youngs modulus
aabills Nov 29, 2023
31e08c7
update changelog
aabills Dec 5, 2023
0fd0385
make partial molar volume also a function of temperature
aabills Dec 5, 2023
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5 changes: 3 additions & 2 deletions pybamm/models/submodels/particle/base_particle.py
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Original file line number Diff line number Diff line change
Expand Up @@ -56,8 +56,9 @@ def _get_effective_diffusivity(self, c, T, current):

if stress_option == "true":
# Ai2019 eq [12]
Omega = domain_param.Omega
E = domain_param.E
sto = c / phase_param.c_max
Omega = pybamm.r_average(domain_param.Omega(sto))
E = pybamm.r_average(domain_param.E(sto, T))
nu = domain_param.nu
theta_M = Omega / (param.R * T) * (2 * Omega * E) / (9 * (1 - nu))
stress_factor = 1 + theta_M * (c - domain_param.c_0)
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11 changes: 9 additions & 2 deletions pybamm/models/submodels/particle_mechanics/base_mechanics.py
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Expand Up @@ -43,12 +43,19 @@ def _get_mechanical_results(self, variables):
sto_rav = variables[f"R-averaged {domain} particle concentration"]
c_s_surf = variables[f"{Domain} particle surface concentration [mol.m-3]"]
T_xav = variables["X-averaged cell temperature [K]"]
phase_name = self.phase_name
T = pybamm.PrimaryBroadcast(
variables[f"{Domain} electrode temperature [K]"],
[f"{domain} {phase_name}particle"],
)
eps_s = variables[f"{Domain} electrode active material volume fraction"]

Omega = domain_param.Omega
#use a tangential approximation for omega
sto = variables[f"{Domain} particle concentration"]
Omega = pybamm.r_average(domain_param.Omega(sto))
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while we're here, could Omega also depend on T?

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No, that would be a thermal expansion coefficient, generally called α

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I mean I guess they're the same thing really, but in some ways that's an entirely different model.

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I'll do it anyway

R0 = domain_param.prim.R
c_0 = domain_param.c_0
E0 = domain_param.E
E0 = pybamm.r_average(domain_param.E(sto, T))
nu = domain_param.nu
L0 = domain_param.L
sto_init = pybamm.r_average(domain_param.prim.c_init / domain_param.prim.c_max)
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21 changes: 17 additions & 4 deletions pybamm/parameters/lithium_ion_parameters.py
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Expand Up @@ -303,14 +303,11 @@ def _set_parameters(self):

# Mechanical parameters
self.nu = pybamm.Parameter(f"{Domain} electrode Poisson's ratio")
self.E = pybamm.Parameter(f"{Domain} electrode Young's modulus [Pa]")
self.c_0 = pybamm.Parameter(
f"{Domain} electrode reference concentration for free of deformation "
"[mol.m-3]"
)
self.Omega = pybamm.Parameter(
f"{Domain} electrode partial molar volume [m3.mol-1]"
)

self.l_cr_0 = pybamm.Parameter(f"{Domain} electrode initial crack length [m]")
self.w_cr = pybamm.Parameter(f"{Domain} electrode initial crack width [m]")
self.rho_cr = pybamm.Parameter(
Expand Down Expand Up @@ -349,6 +346,22 @@ def C_dl(self, T):
f"{Domain} electrode double-layer capacity [F.m-2]", inputs
)

def Omega(self, sto):
"""Dimensional partial molar volume of Li in solid solution [m3.mol-1]"""
Domain = self.domain.capitalize()
inputs = {f"{Domain} particle stoichiometry": sto}
return pybamm.FunctionParameter(
f"{Domain} electrode partial molar volume [m3.mol-1]", inputs
)

def E(self, sto, T):
"""Dimensional Young's modulus"""
Domain = self.domain.capitalize()
inputs = {f"{Domain} particle stoichiometry": sto, "Temperature [K]": T}
return pybamm.FunctionParameter(
f"{Domain} electrode Young's modulus [Pa]", inputs
)

def sigma(self, T):
"""Dimensional electrical conductivity in electrode"""
inputs = {"Temperature [K]": T}
Expand Down
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