This communication addresses a computation strategy, based on the adjoint variable approach and BIE/BEM formulations of the direct problem, for evaluating crack or void shape sensitivities of objective functionals. Boundary-only expressions for such sensitivities are sought, in the context of linear elastodynamics. In the case of a void, boundary-only expressions for sensitivities of integral f...

This paper, deals with detecting and identifying unknown scatters (e.g., obstacles) in an elastic background solid through the use of elastic illuminating waves. In this regards, the Linear Sampling Method (LSM) for the reconstruction of the underground obstacles from near-field surface seismic measurements in the time domain is explained. The LSM is an effective approach to image the geometric...

We construct strong solutions for a nonlinear wave equation for a thin vibrating plate described by nonlinear elastodynamics. For sufficiently small thickness we obtain existence of strong solutions for large times under appropriate scaling of the initial values such that the limit system as h → 0 is either the nonlinear von Kármán plate equation or the linear fourth order Germain-Lagrange equa...

A one-dimensional pure stress initial boundary value problem of linear elastodynamics for amicroperiodic layered semi-space in which amicrostructural length is taken into account is revisited. Also, the plane stress harmonic waves propagating in a microperiodic layered infinite elastic space are discussed. It is shown that (i) for a particular system of the length and time units the transient s...

We model the dynamics of shape evolution of liquid crystal elastomers (LCE) in three dimensions using finite element elastodynamics. The model predicts the macroscopic mechanical response induced by changes in nematic order, e.g. by heating or cooling through the isotropic/nematic transition or, in azo-doped materials, by exposure to light. We model the performance of LCE actuator devices inclu...

A phase transition is a jump discontinuity in a solution u to (1.1) between states u(t, x−) and u(t, x+) belonging to different phases. Physical models leading to this setting are provided by liquid vapor phase transitions, elastodynamics or combustion models, see [2, 7, 8, 9, 19, 20] and the references therein. Typically, in the case (1.2) the Riemann problem for (1.1) turns out to be underdet...

Implicit time integration schemes that inherit the conservation laws of total energy, linear and angular momentum are considered for initial boundary-value problems in ®nite-deformation elastodynamics. Conserving schemes are constructed for general hyperelastic material models, both compressible and incompressible, and are formulated in a way that is independent of spatial discretization. Three...

We propose the use of algebras of generalized functions for the analysis of certain highly singular problems in the calculus of variations. After a general study of extremal problems on open subsets of Euclidean space in this setting we introduce the first and second variation of a variational problem. We then derive necessary (Euler-Lagrange equations) and sufficient conditions for extremals. ...