Electro-mechanical coupling

Electro-mechanical model of IPMC can be represented by a transformer circuit [Newbury and Leo (2003a)] as shown in Fig. 9.6. It is assumed that the electrical and the mechanical component of the systems are coupled 

The constitutive equation of IPMC based upon small deflections may be derived based on the constitutive equation of piezoelectricity  

Both sides of Eq. (9.14) are integrated over the IPMC sample with width w, and length Lt to get the total charge  

Input-output relations can be obtained from the transformer circuit in Fig. 9.6. Mesh equations are calculated for analyzing the relationship between voltage and current for ideal transformer  

Tests were conducted to capture IPMC voltage produced under various deformation conditions bending, extension, and shear, as shown in Fig. 9.7. In case of the bending and extension modes, one end of the IPMC was 

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Even for poly(y-methyl L-glutamate) with a high piezoelectric constant (d= 10 7 cgsesu), the electro-mechanical coupling constant k defined by... 

This scattering mode occurs only in piezoelectric materials, i.e., in crystals without inversion symmetry, and is caused by the electric field associated with acoustical phonons. Zinc oxide exhibits very high electro-mechanical coupling coefficients P (see later), exceeding that of quartz [42,59], which is one of the mostly used piezoelectric materials. Zook [60] has calculated the piezoelectrically limited mobility on the basis of the elastic and piezoelectric constants as (see also Rode [54]) ... 

Fig. 7 Unidirectional chemo-electro-mechanical coupling scheme (chemical field, (19) electrical field, (20) mechanical field, (22))...

In Fig. 8, the chemo-electro-mechanical coupling scheme is shown. For one time step, all the involved fields are used in iteration loops until a converged solution is obtained. Then, the same procedure for the next time step will be applied. 

Summarizing, a change of the concentration in the solution by a chemical stimulation provokes a change of the concentration, of the electric potential, and of the gel domain. This fully chemo-electro-mechanical coupling is quite robust and works as a kind of limiter for the change of the chemical, electrical and mechanical unknowns compared to the unidirectional chemo-electrical to mechanical coupling. 

Electrospinning technique has been used not only for the deposition of polymeric nanofibres but also for the production of ceramic nanofibres of PZT. PZT is commonly used in micro- and macro-scale piezoelectric energy harvesting devices due to its high electro-mechanical coupling coefficient of -500-600pC ) as compared... 

This provides us the electro-mechanical coupling coefficient d for the measured tip displacement (F = 0 in Fig. 2.36) ... 

Soh, A.K., Song, Y.C., and Ni, Y. 2006. Phase field simulations of hysteresis and butterfly loops in ferroelectrics subjected to electro-mechanical coupled loading. Journal of the American Ceramic Society 89[2] 652-661. 

To determine the current, a measuring instrument with low inherent resistance is used such that the caused voltage drop is low. In the ideal case, this corresponds to connected electrodes. Then the difference of electric potential ip at the opposing electrodes levels out, and thus the electric field strength E is cancelled. This permits us to draw the conclusions as of Eq. (4.37). Consequently, the mechanical state of the system can be determined with the aid of the principle of virtual work formulation of Eq. (4.38). Via the electro-mechanically coupled constitutive relation, the outcome may then be utilized to deduce the electric flux density, charge, and finally the current being proportional to the strain rate. 

Extension of Dirichlet s principle of minimum potential energy to electro-mechanically coupled problems. 

K. Ghandi, N.W. Hagood, Nonlinear modeling and characterisation techniques for phase transition in electro-mechanically coupled devices. Ph.D. Thesis, Massachusetts Inst, of Tech. (1998)... 

Electromechanical Controls. Electro-mechanical control devices are typically used for load control (lighting, ventilation, and heating) in buildings with no feedback signal. The most common device is the electromechanical timer, in which a small motor coupled to a gearbox is able to switch electrical contacts according to a predefined time schedule. They are still in use today, applied to loads with simple scheduling requirements. 

Moyne, C. and Murad, M. (2002) Electro-chemo-mechanical couplings in swelling clays derived from a micro/macro homogenization procedure, International J. Solids and Structures 25(1), 11-112... 

In the last couple of decades, both Micro-electro-mechanical systems (MEMS) and microbiology achieved remarkable progress. MEMS provide very small systems, made of very small electrical and mechanical components. These systems range in size from sub micrometer level to millimeter level, and can include any component number, from a few to millions, in a particular system. MEMS extend the fabrication... 

To gain a more precise insight into the phenomena occurring in gels, the Theory of Porous Media (TPM), or the coupled chemo-electro-mechanical formulation is a good choice. Normally, the TPM is applied for the gel only, while the coupled multi-field formulation incorporates the gel and the surrounding solution. 

The coupled chemo-electro-mechanical multi-field formulation is a model on the micro-mesoscopic scale. It has been developed to gain a more precise insight into... 

In this test case, the chemical stimulation of the gel film placed in the solution bath is investigated by the fuUy coupled chemo-electro-mechanical formulation. That is additionally, the mechanical deformation of the gel domain is considered and the chemo-electro-mechanical field is directly solved on the deformed domain. 

Fig. 16 Coupled chemo-electro-mechanical simulation Steady-state results (a) of the mobile concentrations and c and (b) of the electric potential after chemical stimulation...

The coupled chemo-electro-mechanical formulation is a quite powerful tool for capturing the behaviour of the chemical, electrical and mechanical unknowns. In order to compare numerical results with experimental results, the numerically obtained relative swelling ratio q versus the prescribed concentration in the solution is depicted in Fig. 17. The initial state of the test cases discussed in Sect 2 has been taken as reference value. 

In this chapter numerical simulations by applying the coupled chemo-electro-mechanical multi-field formulation on a deforming mesh have been performed. It has been shown that this formulation is an excellent method for describing the coupled behaviour of polymer gels in a solution. This method is capable to explain the mechanisms of the behaviour of polyelectrolyte gels under chemical and electrical stimulation, the ion distributions as well as the swelling and bending behaviour. 

Wallmersperger T, Ballhause D (2008) Coupled chemo-electro-mechanical FE-simulation of hydrogels-part II electrical stimulation. Smart Mater Struct 17 045012... 

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