Finite element modeling of transient ultrasonic waves in linearviscoelastic media

摘要

Linear viscoelasticity offers a minimal framework within which tonconstruct a causal model for wave propagation in absorptive media.nViscoelastic media are often described as media with `fading memory,'nthat is, the present state of stress is dependent on the present strainnand the complete time history of strain convolved with appropriatentime-dependent shear and bulk stress relaxation moduli. An axisymmetric,ndisplacement-based finite element method for modeling pulsed ultrasonicnwaves in linear, homogeneous, and isotropic (LHI) viscoelastic media isndeveloped that does not require storage of the complete time history ofndisplacement at every node. This is accomplished by modeling stressnrelaxation moduli as discrete or continuous spectra of decayingnexponentials and relaxation times. Details of the construction andncomputation of the time-dependent stiffness matrix are presented. As annapplication of the finite element method, a finite number ofnexponentials (amplitudes and relaxation times) are employed to representna typical model for a continuous relaxation spectrum. It is demonstratednthat a small number of discrete exponentials are required to modelnultrasonic wave propagation of a typical band-limited pulse in a modelnmaterial accurately. Previous work has shown this model to be consistentnwith other analytic models for wave propagation in viscoelastic media