Time-harmonic Dynamic Fundamental Solutions for Transversely Isotropie Magnetoelectroelastic Media under Anti-plane Deformation

Author(s):  
De-Liang Ren ◽  
Jin-Xi Liu
Author(s):  
Habib Ammari ◽  
Elie Bretin ◽  
Josselin Garnier ◽  
Hyeonbae Kang ◽  
Hyundae Lee ◽  
...  

This chapter considers the perturbations of the displacement (or traction) vector that are due to the presence of a small crack with homogeneous Neumann boundary conditions in an elastic medium. It derives an asymptotic formula for the boundary perturbations of the displacement as the length of the crack tends to zero. Using analytical results for the finite Hilbert transform, the chapter derives an asymptotic expansion of the effect of a small Neumann crack on the boundary values of the solution. It also derives the topological derivative of the elastic potential energy functional and proves a useful representation formula for the Kelvin matrix of the fundamental solutions of Lamé system. Finally, it gives an asymptotic formula for the effect of a small linear crack in the time-harmonic regime.


A procedure is described to generate fundamental solutions or Green’s functions for time harmonic point forces and sources. The linearity of the field equations permits the Green’s function to be represented as an integral over the surface of a unit sphere, where the integrand is the solution of a one-dimensional impulse response problem. The method is demonstrated for the theories of piezoelectricity, thermoelasticity, and poroelasticity. Time domain analogues are discussed and compared with known expressions for anisotropic elasticity.


Author(s):  
H. Huang ◽  
T. Pamphile

Lamb wave is a special type of elastic wave that is widely employed in structural health monitoring systems for damage detection. Recently, piezoelectric (piezo) patches are becoming popular for Lamb wave excitation and sensing because it can be utilized as an actuator and a sensor. All published work assumed that the Lamb wave displacement field generated by a piezo patch actuator is axi-symmetric. However, we experimentally observed that the displacement fields excited by the piezo patch actuator are directional and this directionality is frequency dependent. In this paper, we present a simulation model that explains this phenomenon by incorporating the bending deformation of the piezo actuator into the calculations of the Lamb wave generation. The driving forces acting on the host plate are calculated from the out-of-plane deformation of the piezo patch through the deformation of the bonding layer. Treating these forces as tone-burst point loads, the displacement field excited by the piezo patch is constructed from the displacement solutions of time-harmonic point loads. Simulation results confirmed that a piezo patch vibrating at certain vibration mode can result in the directional and frequency dependant displacement fields observed by the experiment.


TAPPI Journal ◽  
2012 ◽  
Vol 11 (1) ◽  
pp. 61-66 ◽  
Author(s):  
DOEUNG D. CHOI ◽  
SERGIY A. LAVRYKOV ◽  
BANDARU V. RAMARAO

Delamination between layers occurs during the creasing and subsequent folding of paperboard. Delamination is necessary to provide some stiffness properties, but excessive or uncontrolled delamination can weaken the fold, and therefore needs to be controlled. An understanding of the mechanics of delamination is predicated upon the availability of reliable and properly calibrated simulation tools to predict experimental observations. This paper describes a finite element simulation of paper mechanics applied to the scoring and folding of multi-ply carton board. Our goal was to provide an understanding of the mechanics of these operations and the proper models of elastic and plastic behavior of the material that enable us to simulate the deformation and delamination behavior. Our material model accounted for plasticity and sheet anisotropy in the in-plane and z-direction (ZD) dimensions. We used different ZD stress-strain curves during loading and unloading. Material parameters for in-plane deformation were obtained by fitting uniaxial stress-strain data to Ramberg-Osgood plasticity models and the ZD deformation was modeled using a modified power law. Two-dimensional strain fields resulting from loading board typical of a scoring operation were calculated. The strain field was symmetric in the initial stages, but increasing deformation led to asymmetry and heterogeneity. These regions were precursors to delamination and failure. Delamination of the layers occurred in regions of significant shear strain and resulted primarily from the development of large plastic strains. The model predictions were confirmed by experimental observation of the local strain fields using visual microscopy and linear image strain analysis. The finite element model predicted sheet delamination matching the patterns and effects that were observed in experiments.


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