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Caltech team uses computational topology optimization to design silicon anode structures for Li-ion batteries

Researchers at Caltech have used computational topology optimization methods to design optimal multifunctional silicon anode structures for lithium-ion batteries. A paper on their work is published in the Journal of Power Sources.

Sarah Mitchell and Michael Ortiz set out to address two problems related to silicon anodes: lithiation-induced mechanical degradation due to volumetric expansion and the low intrinsic electrical conductivity of silicon.

One method to improve the Li-ion battery performance is to replace the traditional graphite anode with silicon. In addition to being an abundant, inexpensive, and sustainable material, silicon has the highest known theoretical specific capacity for Li-ion intercalation of 4200 mA h/g, over ten times greater than that of graphite. Unfortunately, this excellent capacity comes at the expense of a 310% volume expansion and contraction of the silicon anode during lithium insertion and extraction, compared to the 6-10% volume expansion observed for a graphite anode. This large change in volume causes severe detrimental effects that render the battery impractical for commercialization unless significant anode design changes are made.

In terms of adverse effects, the anode experiences extremely high compressive stresses upon lithiation due to the restrained volumetric expansion, resulting in pulverization of the active particles. Furthermore, the volume contraction upon delithiation induces large tensile stresses that cause cracking and fracture of the anode structure, and therefore disconnected charge transport paths. These effects result in incomplete intercalation and a high irreversible capacity loss.

Furthermore, silicon is considered a semiconductor and, as such, has a low intrinsic electric conductivity. … In order to utilize high capacity silicon as a new anode material, several important design requirements must therefore be met. Firstly, the silicon anode structure must adequately accommodate the volume expansion upon lithiation, and reduce the associated induced mechanical stress. The design must also maximize electrical conduction through the structure to compensate for the low conductivity of silicon and ensure good rate capability of the battery.

… silicon anode designs, crafted by experimentalists, are primarily based on design intuition and historical testing results. Despite showing some very promising results, the anode structures are not necessarily optimal from the outset. As such, there exists huge potential to use structural optimization methods to produce high performance silicon anode designs. These optimal designs may verify the experimentalists’ design choices, or may provide new structural designs that could then be manufactured, tested and further refined.

—Mitchell and Ortiz (2016)

Recommended optimal silicon anode structures. Mitchell and Ortiz. Click to enlarge.

Topology optimization is a generalized structural optimization method; it determines the optimal material distribution within a design for a given set of loading and boundary conditions. The optimum topology design is not based on a predefined structural configuration—as are, for example, sizing and shape optimization. Topology optimization provides a true optimum in a design space for a specific problem, the authors noted.

Topology optimization methods have yet to be applied to the silicon anode design problem, and have been underutilized for battery applications in general, they added.

For their study, Mitchell and Ortiz used a density-based multiobjective topology optimization method, using a porous nanoscale structure as the underlying design in order to capitalize on the performance advantages of size-induced ductility, small Li-ion diffusion distances, and the porosity of the structure helping to accommodate the volume change upon lithiation.

They first optimized the requirements individually: a minimum compliance objective subject to design dependent volumetric expansion, and a maximum electrical conduction objective, respectively.

To produce multifunctional designs, they subsequently use a bi-objective formulation for both criteria.

They found that a rigid frame structure provided an “excellent” compromise between the structural and conduction design criteria, providing both the required structural rigidity and direct conduction pathways.

The developments and results presented in this computational study provide a solid foundation for the informed design and development of optimal multifunctional silicon anode structures for use in lithium-ion batteries. The next phase would be for these structures to be manufactured and tested by experimentalists. The recommended optimal silicon anode structures … exhibit features similar to various silicon anode structures that have been manufactured experimentally … It is therefore anticipated that similar methods of manufacture could be used to produce these optimal designs, namely deposition and electrochemical etching techniques.

—Mitchell and Ortiz

The research was supported by the Caltech Innovation Initiative (CI2), by Robert Bosch GmbH through the Bosch Energy Research Network (BERN) Project No.: 07-15-CS13 and by the US National Science Foundation through the Partnership for International Research and Education (PIRE) on Science at the Triple Point Between Mathematics, Mechanics and Materials Science, Award Number 0967140.


  • Sarah L. Mitchell, Michael Ortiz (2016) “Computational multiobjective topology optimization of silicon anode structures for lithium-ion batteries,” Journal of Power Sources, Volume 326, Pages 242-251 doi: 10.1016/j.jpowsour.2016.06.136



Let's go from computerized designs to prototypes soonest and produce an improved battery.

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