On inefficiency of the shape memory alloys in dynamically loaded sandwich plates with structural damping: New 3D zigzag-viscoelasticity theory and asymmetric transformations

An accurate hyperelasticity‐based plate theory and nonlinear energy‐based micromechanics for impact and shock analyses of compliant particle‐reinforced FG hyperelastic plates

“…Based on the superiorities explained in Ref. [34], the following description that takes the transverse deformability of the plate into account is used: $$\begin{equation} \def\eqcellsep{&}\begin{array}{@{}*{1}{c}@{}} {u\left( {x,y,z,t} \right) = {u_0}\left( {x,y,t} \right) + {{{\Lambda}}_x}\left( {x,y,t} \right)z + {z^2}\left[ {{\vartheta _x}\left( {x,y,t} \right)\sinh \left( {\dfrac{z}{h}} \right) + {\lambda _x}\left( {x,y,t} \right)\cosh \left( {\dfrac{z}{h}} \right)} \right]}\\[15pt] {v\left( {x,y,z,t} \right) = {v_0}\left( {x,y,t} \right) + {{{\Lambda}}_y}\left( {x,y,t} \right)z + {z^2}\left[ {{\vartheta _y}\left( {x,y,t} \right)\sinh \left( {\dfrac{z}{h}} \right) + {\lambda _y}\left( {x,y,t} \right)\cosh \left( {\dfrac{z}{h}} \ri...$$…”

“…Based on the superiorities explained in Ref. [34], the following description that takes the transverse deformability of the plate into account is used:…”

“…In writing Equation (34), the potential energy due to indentation was not included. If this energy is included as well as the work of the external traction and the work due to the d'Alembert (inertia) forces, one may write…”