Mechanical energy can be converted to electrical energy by using a dielectric elastomer generator. The elastomer is susceptible to various modes of failure, including electrical breakdown, electromechanical instability, loss of tension, and rupture by stretch. The modes of failure define a cycle of maximal energy that can be converted. This cycle is represented on planes of work-conjugate coordinates and may be used to guide the design of practical cycles. Diverse technologies are being

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... d to harvest energy from renewable sources. 1-3 This letter focuses on one particular technology: dielectric elastomer ͑DE͒ generators. 4-8 When a membrane of a DE is prestretched and precharged, a reduction in the tensile force under the opencircuit condition increases the voltage ͑Fig. 1͒. Thus, a cycle can be designed to convert mechanical energy into electrical energy. Experiments have shown that DEs can convert energy up to 0.4 J/g, which is at least an order of magnitude higher than the specific energies of piezoelectric ceramics and electromagnetic generators. 5 DE generators have been designed to harvest energy from walking, 5,6 ocean waves, 7 wind, and combustion. 8 These generators are lightweight, compliant, and rust-free, allowing them to be deployed widely. This letter describes a method to calculate the maximal energy that can be converted by a DE generator. The elastomer is susceptible to various modes of failure. 9,10 We use these modes of failure to define a cycle on the forcedisplacement plane and the voltage-charge plane. The area enclosed by the cycle gives the maximal energy of conversion. Such a diagram may be used to guide the design of practical cycles. Our method is based on a nonlinear theory of elastic dielectrics. 11-18 With reference to Fig. 1 , consider a membrane of a DE, of sides L 1 , L 2 , and L 3 in its undeformed state. The two faces of the membrane are coated with compliant electrodes. When the electrodes are subject to a voltage ⌽ and the membrane is subject to forces P 1 and P 2 , the electrodes gain charges +Q and −Q, and the membrane deforms to a state of sides 1 L 1 , 2 L 2 , and 3 L 3 , where 1 , 2 , and 3 are the stretches of the membrane in the three directions. The membrane is taken to be incompressible, so that 1 2 3 =1. Define the nominal stresses by s 1 = P 1 / L 2 L 3 and s 2 = P 2 / L 1 L 3 , the nominal electric field by Ẽ = ⌽ / L 3 , and the nominal electric displacement by D = Q / L 1 L 2 . By contrast, the true stresses 1 and 2 , the true electric field E, and the true electric displacement D are the same quantities divided by the dimensions of the membrane in the deformed state. The true quantities relate to the nominal ones as 1 =