哈佛大学Gordon McKay教授、我校“长江学者”讲座教授锁志刚将为我校师生作报告。
报告时间：2007年 8月17日上午10：00
报告地点：强度与振动教育部重点实验室会议室（教一楼南208）
报告题目：A nonlinear field theory of dielectric elastomers

Our interest in active soft materials has been stimulated by recent development in the fields of dielectric elastomer actuators and stimuli-responsive gels.  In this talk I'll focus on our new formulation of nonlinear field theory of elastic dielectrics, and the use of the theory to analyze an electromechanical instability of dielectric elastomer actuators.

Two difficulties have long troubled the field theory of finite deformation in dielectric solids.  First, when two electric charges are placed inside a dielectric solid, the force between them is not a measurable quantity.  Second, when a dielectric solid deforms, the true electric field and true electric displacement are not work conjugates.  These difficulties are circumvented in our new formulation of the theory. Imagine that each material particle in a dielectric is attached with a weight and a battery, and prescribe a field of virtual displacement and a field of virtual voltage.  Associated with the virtual work done by the weights and inertia, define the nominal stress as the conjugate to the gradient of the virtual displacement.  Associated with the virtual work done by the batteries, define the nominal electric displacement as the conjugate to the gradient of virtual voltage. 

Our approach does not start with Newton’s laws of mechanics and Maxwell-Faraday theory of electrostatics, but produces them as consequences.  We show that the notion of Maxwell stress, which is widely used in the literature, has no general theoretical basis.  However, for a very special class of materials, which we call ideal dielectric elastomers, the theory recovers the Maxwell stress. 

As an illustration of the theory, we analyze the electromechanical instability of dielectric elastomer actuators.  We find that the free energy functions of dielectric elastomers are often non-convex, leading to coexistent states.  Our calculation shows that stability of the actuators is markedly enhanced by pre-stresses, agreeing with existing experimental observations.