We theoretically study the indentation response of a compressible soft electroactive material by a rigid punch. The half-space material is assumed to be initially subjected to a finite deformation and an electric bias...We theoretically study the indentation response of a compressible soft electroactive material by a rigid punch. The half-space material is assumed to be initially subjected to a finite deformation and an electric biasing field. By adopting the linearized theory for incremental fields, which is established on the basis of a general nonlinear theory for electroelasticity, the appropriate equations governing the perturbed infinitesimal elastic and electric fields are derived particularly when the material is subjected to a uniform equibiaxial stretch and a uniform electric displacement. A general solution to the governing equations is presented, which is concisely expressed in terms of four quasi-harmonic functions. By adopting the potential theory method, exact contact solutions for three common perfectly conducting rigid indenters of fiat-ended circular, conical and spherical geometries can be derived, and some explicit relations that are of practical importance are outlined.展开更多
Soft electroactive materials(SEAMs)with large elastic deformation capacity as well as excellent electromechanical coupling characteristic have attracted increasing attention in the fields of mechanics and related engi...Soft electroactive materials(SEAMs)with large elastic deformation capacity as well as excellent electromechanical coupling characteristic have attracted increasing attention in the fields of mechanics and related engineering disciplines.Based on the nonlinear theory of electroelasticity and its linearized version for incremental fields,we derive the state-space formulations for small-amplitude free vibrations of an SEAM circular plate under large predeformation due to static biasing fields.An exact three-dimensional solution is then obtained by adopting the finite Hankel transform for the plate with an elastic simple support at the circular boundary.The exact solution for an isotropic linear elastic circular plate can be obtained as a particular and degenerated case.The model of generalized neo-Hookean compressible material is considered in numerical simulations.It is found that the natural frequency,while depending on the intrinsic parameters of the plate(e.g.,initial thickness and electromechanical coupling coefficients),can be controlled effectively by the extrinsic factors(e.g.,pre-stretch and biasing electric displacement).Results further indicate that Euler’s instability will occur under a certain combination of the biasing electric displacement and pre-stretch,which should be of practical importance when one intends to tune the dynamic characteristics of a plate by means of external loading.展开更多
基金supported by the National Natural Science Foundation of China(10832009 and 11090333)the Fundamental Research Funds for Central Universities(2011XZZX002)
文摘We theoretically study the indentation response of a compressible soft electroactive material by a rigid punch. The half-space material is assumed to be initially subjected to a finite deformation and an electric biasing field. By adopting the linearized theory for incremental fields, which is established on the basis of a general nonlinear theory for electroelasticity, the appropriate equations governing the perturbed infinitesimal elastic and electric fields are derived particularly when the material is subjected to a uniform equibiaxial stretch and a uniform electric displacement. A general solution to the governing equations is presented, which is concisely expressed in terms of four quasi-harmonic functions. By adopting the potential theory method, exact contact solutions for three common perfectly conducting rigid indenters of fiat-ended circular, conical and spherical geometries can be derived, and some explicit relations that are of practical importance are outlined.
基金This work was supported by the National Natural Science Foundation of China(Nos.11872329 and 11621062).
文摘Soft electroactive materials(SEAMs)with large elastic deformation capacity as well as excellent electromechanical coupling characteristic have attracted increasing attention in the fields of mechanics and related engineering disciplines.Based on the nonlinear theory of electroelasticity and its linearized version for incremental fields,we derive the state-space formulations for small-amplitude free vibrations of an SEAM circular plate under large predeformation due to static biasing fields.An exact three-dimensional solution is then obtained by adopting the finite Hankel transform for the plate with an elastic simple support at the circular boundary.The exact solution for an isotropic linear elastic circular plate can be obtained as a particular and degenerated case.The model of generalized neo-Hookean compressible material is considered in numerical simulations.It is found that the natural frequency,while depending on the intrinsic parameters of the plate(e.g.,initial thickness and electromechanical coupling coefficients),can be controlled effectively by the extrinsic factors(e.g.,pre-stretch and biasing electric displacement).Results further indicate that Euler’s instability will occur under a certain combination of the biasing electric displacement and pre-stretch,which should be of practical importance when one intends to tune the dynamic characteristics of a plate by means of external loading.
