Merge pull request pybamm-team#3576 from abillscmu/omega-stoich-2

Make mechanical properties a function of stoichiometry and sometimes temperature

CHANGELOG.md

@@ -3,6 +3,7 @@
 ## Features
 
 - Serialisation added so models can be written to/read from JSON ([#3397](https://github.com/pybamm-team/PyBaMM/pull/3397))
+- Mechanical parameters are now a function of stoichiometry and temperature ([#3576](https://github.com/pybamm-team/PyBaMM/pull/3576))
 
 ## Bug fixes
 

pybamm/models/submodels/particle/base_particle.py

@@ -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, T))
+            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)

pybamm/models/submodels/particle_mechanics/base_mechanics.py

@@ -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, T))
         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)

pybamm/parameters/lithium_ion_parameters.py

@@ -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(
@@ -349,6 +346,22 @@ def C_dl(self, T):
             f"{Domain} electrode double-layer capacity [F.m-2]", inputs
         )
 
+    def Omega(self, sto, T):
+        """Dimensional partial molar volume of Li in solid solution [m3.mol-1]"""
+        Domain = self.domain.capitalize()
+        inputs = {f"{Domain} particle stoichiometry": sto, "Temperature [K]": T}
+        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}