We extend the study on the homogenization problem for an elastic material containing a distributed array of gas bubbles to the case when the body force depends on time. By technically constructing an approximating sequence, we are able to show the convergence of semigroups and therefore prove the main result that such spongy material can be approximated by an elastic material without holes in t...

We present expressions for the Green's tensors in terms of lattice sums for general two-dimensional arrays in both elastostatics and elastodynamics. We represent the lattice sums in rapidly{convergent forms by Fourier transform methods. We compare the static lattice sums with recently published, highly accurate values for square arrays. We also establish Rayleigh identities for elastostatic and...

The rapid development of different areas of engineering, creation of new structures make the computational fracture mechanics a topic area. Among the most important applied problems there are structural strength problems, complicated by various flaws (cracks, delaminations, etc). The presence of cracks and delaminations considerably decreases the strength and the lifetime of the composite struc...

We analyze the application to elastodynamic problems of mixed finite element methods for elasticity with weakly imposed symmetry of stress. Our approach leads to a semidiscrete method which consists of a system of ordinary differential equations without algebraic constraints. Our error analysis, which is based on a new elliptic projection operator, applies to several mixed finite element spaces...

The behavior of elastic waves in a three-dimensional isotropic incompressible material is studied. Unlike compressible elastodynamics, where there are nonlinear interactions of shear and pressure waves, with incompressible elastodynamics the only waves present are shear waves. In an isotropic system, shear waves are linearly degenerate, and therefore global solutions to the perturbative incompr...

A high-order Absorbing Boundary Condition (ABC) is devised on an artificial boundary for time-dependent elastic waves in unbounded domains. The configuration considered is that of a two-dimensional elastic waveguide. The proposed ABC is an extension of the Hagstrom-Warburton ABC which was originally designed for acoustic waves, and is applied directly to the displacement field. The order of the...