Summary: Implicit constitutive relations are proposed for large deformations of electroelastic bodies, and approximations to these are developed within the context of small displacement gradients. The resultant theories lead to the interesting situation wherein the constitutive relationships are nonlinear though the strain is ‘linearized’. In the absence of the effects due to the electrical field, the models reduce to a class of constitutive relations that have been studied recently, which have applications in the fracture of, and propagation of cracks in, brittle elastic bodies. The current class of electroelastic bodies have applications in a variety of important areas such as the response of piezoelectric bodies, electro-sensitive elastomers and biological matter.
For Part II, see [the authors, ibid. 469, No. 2155, Article ID 20130106, 20. p (2013; Zbl 1371.74096)].