Structures made of transforming materials exhibit a striking capacity to hysteretically recover significant deformation with a controllable amount of energy absorbed in the process. The unusual properties of these materials are due to the fact that large deformations and inelastic behavior are accomplished by coordinated migration of mobile phase or domain boundaries. Intensive research in rece...

In this work, we present a numerical method for solving the diffraction of transient elastic waves by cracks of arbitrary shapes in complex media, with Signorini’s boundary conditions on the crack. We use a fictitious domain method based on a mixed displacement–stress formulation for elastodynamics. We propose an off-centered time discretisation scheme for enforcing the stability.

Time-harmonic waves are scattered by obstacles, through which waves can also travel. Various examples from acoustics, elastodynamics and electromagnetics are discussed, including imperfect interfaces, chiral materials and wood. The paper gives a very subjective overview but with emphasis on the contributions and influence of Ralph Kleinman.

We give an overview on existence results in nonlinear peridynamics, a nonlocal elasticity theory, and compare these results with those known for classical nonlinear elastodynamics. In peridynamics, it is possible to obtain stronger results under equal or even less restrictive assumptions on the stress.

The boundary initial value problems of elastodynamics are formulated as boundary integral equations. It is shown that these integral equations may be solved by time-stepping numerical methods for the unknown boundary values, A specific numerical scheme is presented for antiplane strain problems and a numerical example is given,

The paper concerns the validation of a method for solving elastodynamics problems for cracked solids. The proposed method is based on the application of boundary integral equations. The problem of an interface penny-shaped crack between two dissimilar elastic half-spaces under harmonic loading is considered as an example.

• Mixed methods for elastodynamics with weak symmetry. • Mixed finite elements for elasticity on quadrilateral meshes. • Finite element differential forms on curvilinear cubic meshes and their approximation properties. Numer. • Nonconforming tetrahedral mixed finite elements for elasticity. • Mixed finite element approximation of the vector Laplacian with Dirichlet boundary conditions. Math. • ...