Modelling 2D wave motion in microstructured solids

• The Mindlin-type model describes the propagation of 2D deformation waves in solids.
• The number of the equations is reduced due to the small size of the microstructure.
• The KP-type evolution equation is derived by applying the perturbation method.
• The simulations show the essential effects grasped by the evolution equation.

The Mindlin-type model is used for describing the deformation waves in microstructured solids. The 2D evolution equation (one-wave equation) is derived based on hierarchical governing equations by using the perturbation method. This equation is of the Zabolotskaya–Khokhlov-type and is integrated numerically under localized initial conditions (related to appropriate boundary value problems) by the FFT-based pseudospectral method. Analysis of results demonstrates that the derived evolution equation is able to grasp essential nonlinear effects of microinertia and elasticity of microstructure. Such an equation can be used in the NDT of microstructured materials in order to model wave beams generated by ultrasonic transducers.