A selective mass scaling method for shear wave propagation analyses in nearly incompressible materials

Abstract

SUMMARYThis paper describes a selective mass scaling method which is designed for the analysis of wave propagation problems in nearly incompressible materials. The incompressibility of materials leads to a high value of the compressional wave speed, which makes the time step extremely small in explicit time integration method. The proposed selective mass scaling method selects the eigenfrequencies related to volumetric deformation modes to decrease them, while it keeps the shear eigenmodes unchanged. This makes the time step no longer limited by the compressional wave speed but by the shear wave speed. A significant reduction of CPU time is obtained with a good accuracy for transient problems in small strains on free or largely prestressed media.

A 2D finite element model for shear wave propagation in biological soft tissues: Application to magnetic resonance elastography

“…It is thus not adapted to the simulation of transient but of harmonic shear waves only, at the opposite of some of the FEM previously proposed for elastography. 33,34 The displacement fields computed from the 2D-FEM are in good agreement with those obtained experimentally in both the background of the phantom and in the soft inclusion ( Figure 6). The agreement is better in wavelength than in amplitude and attenuation.…”

“…The FSDT 2D‐FEM focuses in the investigation of the steady‐state response. It is thus not adapted to the simulation of transient but of harmonic shear waves only, at the opposite of some of the FEM previously proposed for elastography …”

“…FEMs have been used to simulate impulsive excitations and shear wave propagation in transversely isotropic elastic or viscoelastic soft tissues in 2D or 3D models, mostly solved with commercialized software. A mass‐scaling method coupled with a viscohyperelastic Landau's model has been recently proposed to simulate nonlinear transient elastography using plane‐strain hypothesis . 3D‐FEMs are computationally expensive compared to 2D‐FEMs.…”

“…A mass-scaling method coupled with a viscohyperelastic Landau's model has been recently proposed to simulate nonlinear transient elastography using plane-strain hypothesis. 33,34 3D-FEMs are computationally expensive compared to 2D-FEMs. In most cases, MRE data are 2D images and most MRE methods perform identification on 2D, with corresponding available information.…”

A model/solution‐adaptive explicit‐implicit time‐marching technique for wave propagation analysis

“…Many procedures can be employed to improve stability and accuracy of time‐integration algorithms, such as subcycling techniques, mass scaling procedures, high‐order accurate schemes, and automatic time step control. As a matter of fact, a lot of research is continuously devoted to this field and several time‐marching techniques are available nowadays for transient analyses …”