Stress grading of Nanodielectrics using Topology optimization with Embedded Breakdown Sensitivity

Dielectric topology optimization (TO) typically maximizes the Schwaiger Factor a.k.a Field Uniformity Factor (FUF) of an electrostatic system by redistributing high-permittivity material toward high-field regions, but this can conflict with electrical reliability when breakdown strength varies non-monotonically with permittivity, for example when high-permittivity phases have lower breakdown strength than low-permittivity phases. This paper proposes a local damage-driven TO framework for functionally graded LDPE–alumina nanocomposites, in which the objective and constraints are posed on minimizing the square of local damage metric: defined as the ratio of local electric field magnitude to breakdown strength in the nanocomposite. The corresponding sensitivities are derived using a continuum formulation compatible with standard electrostatic TO implementations. The breakdown strength and dielectric constant of LDPE–alumina nanocomposites at filler volume fractions of 0% (neat LDPE), 0.5%, 1%, and 2% are taken from literature. This data is embedded into the TO framework to synthesize spatial nanofiller distributions that reduces the local damage in 2D electrostatic configurations. Two numerical case studies are presented: (i) a slab–plane geometry used to validate the proposed local-damage sensitivity, and (ii) an electrode termination in stacked polymer film capacitor treated with a hybrid (energy + damage) sensitivity to illustrate how dielectric geometry and nanofiller distribution inside it modify both energy variation and damage margin. The results show that local-damage-aware TO produces materially different topologies catered for dielectric reliability compared to traditional energy sensitivity based TO.