Phase-field models for crack propagation enable the simulation of complex crack patterns without complex and expensive tracking and remeshing as cracks grow. In the setting without inertia, the crack evolution is obtained from a variational energetic starting point, and leads to an equation for the order parameter coupled to elastostatics. Careful mathematical analysis has shown that this is co...

The three-dimensional linearized theory of elastodynamics mathematical formulation of the forced vibration of a prestretched plate resting on a rigid half-plane is given. The variational formulation of corresponding boundary-value problem is constructed. The first variational of the functional in the variational statement is equated to zero. In the framework of the virtual work principle, it is...

We present a theoretical framework for acoustic wave propagation in metasurface comprising hexagonal lattice of hard spherical inclusions embedded soft elastic medium. Each layer the direction sound is approximated as homogenized with effective geometric and material properties. To account multiple scattering effects resonant inclusions, an analogy between fluid dynamics creeping flows elastody...

A port-Hamiltonian formulation for general linear coupled thermoelasticity and the thermoelastic bending of thin structures is presented. The construction exploits intrinsic modularity systems to obtain a as an interconnection elastodynamics heat equations. derived model can be readily discretized by using mixed finite elements. discretization structure-preserving, since main features system ar...

In this short note, we consider some issues regarding the instability of elastodynamical problems when elasticity tensor is not positive definite. By using so-called logarithmic convexity argument, prove solutions time derivative semi-definite negative or it satisfies another restriction on coefficients. The uniqueness solution also concluded. Finally, a simple one-dimensional example provided ...