## 2 Model of the Chevron Type Microactuator  
### Governing Equations  
As mentioned in the previous paragraph actuation of the thermal microactuator is caused due to the electrical current \(I\), which is converted to the heat according to the [PERSON] law [34]:  
\[Q=RI^{2}t, \tag{1}\]  
where \(Q\) is internal heat generated, \(R\) is electrical resistivity and \(t\) is the time. The thermal strain occurring in the longitudinal arms causes structural deflection. Usually such an actuator is affected by the voltage of the magnitude of a few volts, which causes an increase of temperature, even above 1200 K. Nevertheless, the linear behavior of the microactuator with respect to electric, thermal and mechanical effects is preserved. Such a phenomenon is described by the partial differential equation of electrostatics, Equation (2); heat conduction, Equation (3); and thermoelasticity, Equation (4) [35]. \[\phi_{,ii}-\frac{\rho}{\varepsilon_{0}}=0, \tag{2}\] \[kT_{,ii}+Q=0,\] (3) \[\mu\,u_{i,jj}+(\mu+\lambda)u_{j,ji}-(3\lambda+2\mu)\alpha_{t}T_{,j }=0, \tag{4}\]  
where \(\phi\) is electric potential, \(T\) is the temperature, \(u\) represents the displacement values, \(\rho\) is charge flux density, \(\varepsilon_{0}\) is electric constant, \(k\) is thermal conductivity, \(Q\) is internal heat source, \(\alpha_{t}\) is the linear expansion coefficient, and \(\mu\) and \(\lambda\) are the Lame constants, which can be expressed as follows:  
\[\mu=G=\frac{E}{2(1+\
u)}\lambda=\frac{Ev}{(1-2\
u)(1+\
u)}, \tag{5}\]  
where \(\
u\), \(E\) and \(G\) are [PERSON]'s ratio, [PERSON]'s modulus and the shear modulus, respectively. Figure 2: Map of equivalent von Mises stress: (**a**) sharp corner; (**b**) rounded corner. The structure considered here is an electro-thermo-elastic body of the domain \(\Omega\), with the boundary area \(\Gamma\) (Figure 3). Partial differential Equations (2)-(4) have to be supplemented by boundary conditions. * For electrostatics: \[ \begin{array}{ll}x\in\Gamma_{\phi}:&\phi(x)=\phi^{0}(x)\\ x\in\Gamma_{\rho}:&\rho(x)=\rho^{0}(x)\end{array} ,\] (6) where \(\phi^{0}(x)\) and \(\rho^{0}(x)\) denote known electric potential and electric charge flux density on the appropriate parts of the boundary \(\Gamma_{\phi}\) and \(\Gamma_{\rho}\);  
* For the heat conduction problem, boundary conditions are as follows: \[ \begin{array}{ll}x\in\Gamma_{\Gamma}:&T(x)=T^{0}(x)\\ x\in\Gamma_{q}:&q(x)=q^{0}(x)\\ x\in\Gamma_{c}:&q(x)=\alpha(T(x)-T^{\infty}(x))\end{array} ,\] (7) where \(T^{0}(x)\) and \(q^{0}(x)\) are known temperature and heat flux on the parts \(\Gamma_{T}\) and \(\Gamma_{q}\) of the boundary. The third type of thermal boundary condition (Robin condition) is convection condition, for which \(T^{\infty}(x)\) is an ambient temperature, whereas \(\alpha\) is a heat convection coefficient. * For the elasticity problem boundary condition can be defined as: \[ \begin{array}{ll}x\in\Gamma_{u}:&u(x)=u^{0}(x)\\ x\in\Gamma_{p}:&p(x)=p^{0}(x)\end{array} ,\] (8) where \(u^{0}(x)\) and \(p^{0}(x)\) are known displacement and mechanical loads on the parts \(\Gamma_{u}\) and \(\Gamma_{p}\). Separate parts of the boundaries where electrical, thermal and mechanical boundary conditions are specified define the boundary of the body. When no electrical, thermal or mechanical boundary conditions are specified on the particular parts of the boundary, it corresponds to the charge flux density free, heat flux free or traction-free conditions respectively. The relationships between separate parts of the boundary \(\Gamma\) can be written as:  
\[\Gamma=\Gamma_{\phi}+\Gamma_{\rho}=\Gamma_{T}+\Gamma_{q}+\Gamma_{c}=\Gamma_{u} +\Gamma_{p}. \tag{9}\]  
The finite element method (FEM) has been used for solving the electro-thermo-mechanical problem [36; 37].