Method for Upscaling from Microstructure to Continuum using a Mesoscale, Heterogeneous Homogenization

1 . A method for upscaling from a microstructure to generate a coarsened heterogeneous spatial distribution of porosity and a set of porosity dependent constitutive relationships, comprising the steps of:

receiving a three dimensional (3D) microstructure model for each of a plurality of battery components, wherein the battery components comprise an anode, a cathode, and a separator;

receiving bulk material properties and/or porosity for each of the battery components;

calculating a coarsened porosity model with emergent properties from the battery component microstructures as a function of the porosity;

for each battery component sub region, calculating Bruggeman coefficients from the group of effective ionic conductivity, electric and thermal conductivity, and ionic diffusivity; and

creating a heterogeneous mesoscale 3D battery model, further comprising the steps of:

combining the anode, cathode, and separator materials into a single cell structure; and

separately partitioning each of the anode, cathode, and separator into coarse voxels to create a 3D model of porosity.

2 . The method of claim 1 , wherein the porosity of the received bulk material properties comprises a fine resolution model comprising a plurality of elements, wherein each element is characterized as either a solid having a porosity of substantially zero or a pore having porosity of 100%.

3 . The method of claim 2 , wherein calculating emergent properties from the battery component microstructures as a function of the porosity further comprises the steps of:

computing an average porosity in sub regions of each material;

assigning each element of the coarsened porosity model the average porosity for all elements within a region; and

assigning the average porosities to individual elements of a finite element mesh.

4 . The method of claim 1 , wherein the voxels are uniquely defined with a uniform voxel size throughout for each of the anode, cathode, and separator.

5 . The method of claim 1 , further comprising the step of creating an Abaqus input file using the coarsened image and constitutive relationships.

6 . The method of claim 1 , further comprising the step of receiving the coarsened porosity model and associated constitutive relationships are received as input into a continuum electrochemical solver.

7 . The method of claim 1 , further comprising the step of:

determining effective properties as a function of saturation.

8 . The method of claim 1 , further comprising the steps of:

computing a capillary pressure vs saturation curve; and

calculating a change in pore pressure with saturation changes.

9 . The method of claim 6 , further comprising the step of simulating a 3D Newman model ( 165 ), wherein the continuum electrochemical solver comprises a 3D Newman model simulator.

10 . The method of claim 9 , further comprising the step of computing performance and aging metrics ( 170 ) from degrees of freedom of the 3D Newman model ( 165 ).

11 . The method of claim 10 , further comprising the step of determining a point where lithium plating on a surface of the 3D Newman model ( 165 ) becomes thermodynamically favorable.

12 . The method of claim 11 , further comprising the step of optimizing microstructure of the anode and cathode materials of the 3D Newman model.

13 . The method of claim 12 , further comprising the step of introducing a plurality of high porosity channels into anode and cathode materials of the 3D Newman model.

14 . The method of claim 1 , further comprising the step of printing the heterogeneous mesoscale 3D battery model to a file.

15 . The method of claim 14 , further comprising the step of providing the heterogeneous mesoscale 3D battery model file to a continuum modeler.