Implicit constitutive relations are proposed for electro-elastic and thermo-electro-elastic solids, which cannot be classified as Cauchy or Green elastic bodies, i.e., where in general it is not assumed that the stresses and one of the electric variables are given as functions (or the derivative of an energy function) in terms of the strains, and the independent electric variable. Some subclasses of the above implicit relations are studied in detail, in particular some constitutive equations that appear in the case the mechanical and electrical behaviour of the body is in general nonlinear, but the strains are assumed to be small (small gradient of the displacement field). The first and second laws of thermodynamics are used to impose restrictions on the above implicit constitutive relations and equations.

提出了对于电弹性和热电弹性固体的隐式本构关系，它们不能归类为柯西或绿色弹性体，即，通常不假定应力和电变量之一作为函数给出（或能量函数的导数）的应变和独立的电变量。详细研究了上述隐式关系的一些子类，特别是一些在主体的机械和电气行为总体上是非线性的情况下出现的本构方程，但是假定应变很小（位移场的梯度很小） ）。热力学的第一定律和第二定律用于对上述隐式本构关系和方程式施加限制。