In this paper, we describe the strain-dependent behavior of an electric-LC ͑ELC͒ resonator unit cell, commonly used in metamaterial designs. We leverage analytic expression to understand the way strain manifests itself in a change in electromagnetic ͑EM͒ response. We verify the simplified physical models using full-wave simulations and generalize the trends to accommodate the strain profile for any arbitrary plane-stress loading scenario. © 2010 American Institute of Physics. ͓doi:10.1063/1.3507892͔ Metamaterials can greatly expand man's ability to control interactions with electromagnetic radiation and enable such phenomena as cloaking, 1,2 beyond diffraction-limited imaging, 3 gradient negative-index lenses, 4 and perfect absorbers. 5 They are a powerful concept by allowing designers to utilize geometry, and not just material properties, to engineer a structure's electromagnetic response; often providing properties not found in nature.However, transitioning metamaterials into real, operational systems requires knowledge of their behavior in relevant environments. Of significance is the role mechanical loading/strain plays in the electromagnetic response of a metamaterial. Mechanical strain is by definition, a deformation of the geometry of a structure. Since metamaterials rely so heavily on geometry for the desired response, it implies a direct causal relationship between applied strain and electromagnetic performance.Previous efforts investigated the strain 6 and temperature 7 dependent response of magnetic resonant elements; Melik et al. 6 even proposes using metamaterials as wireless strain gauges. Our efforts focused on a critical missing piece, the electric-LC resonator, depicted in Fig. 1. This structure operates at x-band, utilizing two parallel capacitors for enhanced resonant response. Figure 1 depicts the S-parameter curves for the cell.The mechanical model assumes the metamaterial unit cell is part of a large ͑Ͼ10 ͒, load-bearing structure. Mechanical loading on the cell is homogeneous, and the copper contributes insignificantly to the overall stiffness of the composite; therefore, the in-plane strain profile is approximately uniform across the unit cell ͑no local stiffening effects from the adhered copper͒. Due to the uniformity of the strain profile and the resultant absence of higher order differential terms, the linear system of Eq. ͑1͒ can be utilized to describe the deformed geometry of the unit cell as follows: 8The superscript 0 and 1 refer to the undeformed and deformed geometries, respectively, and the 3 ϫ 3 matrix is the mechanical strain tensor. The model accommodates different values of E ZZ in the substrate and copper, due to the differing mechanical properties in the materials. Additionally, the analysis was restricted to plane stress because 1,2 demonstrated that changes in EM performance due to curvature in the unit cell can be neglected. Therefore, terms E XZ and E YZ are equal to zero.The unit cell was modeled in ANSYS-HFSS, 9 utilizing equation surfaces that integrate the strain ...