Journal:

Article Title: Encapsulation of Capacitive Micromachined Ultrasonic Transducers Using Viscoelastic Polymer

doi: 10.1109/JMEMS.2010.2076786

Figure Lengend Snippet: Schematic of (a) the nonviscoelastic and (b) the viscoelastic FEM. FLUID 29, PLANE 42, PLANE 182, and TRANS 126 represent the element types used in the ANSYS model. The plots also show the roller boundary conditions (constrained to x-direction) and the anchor boundary conditions (constrained to both x-and y-directions). (c) The Prony series expansion used for PLANE 182 element in the viscoelastic FEM can be represented by a spring in parallel with a series set of a spring and a dashpot.

Article Snippet: The series constants were implemented in ANSYS code by using the “TB, PRONY” command to determine the viscoelastic moduli as functions of time, E ( t ) and ν( t ) [ 29 ], [ 31 ], as follows: E ( t ) = E s + ( E f − E s ) ⋅ exp ( − t T 0 ) ; (2a) υ ( t ) = υ s + ( υ f − υ s ) ⋅ exp ( − t T 0 ) ; (2b) and E f = ( 1 + υ f ) ( 1 − 2 υ f ) ( 1 − υ f ) ⋅ C 11 (2c) where E s = 6.4 MPa [ 32 ]; ν s = 0.48; ν f = 0.40 [ 10 ]; C 11 = ρ ⋅ V l 2 ; V l is the longitudinal wave velocity; and T 0 = 1 e–4 s, the relaxation time constant selected based on the glass-transition loading frequency at room temperature [ 8 ].

Techniques:

Journal: International Journal of Biomedical Imaging

Article Title: Tissue Modeling and Analyzing with Finite Element Method: A Review for Cranium Brain Imaging

doi: 10.1155/2013/781603

Figure Lengend Snippet: Analysis of cranial cavity with Prony model.

Article Snippet: The analysis results of cranial cavity with material properties of Prony model in the Mimics and Ansys software are shown in .

Techniques:

Journal: Frontiers in Cell and Developmental Biology

Article Title: Viscoelasticity Acts as a Marker for Tumor Extracellular Matrix Characteristics

doi: 10.3389/fcell.2021.785138

Figure Lengend Snippet: Four models for viscoelasticity. (A) Classical arm-retraction model, (B) Classical Prony series model, (C) New model and (D) Nonlinear spring-dashpot model.

Article Snippet: The Prony series is mathematically elegant with its exponential time-integration equation , and has therefore been adopted as the standard material model in mainstream numerical programs, such as ANSYS and ABAQUS, for the purpose of modeling material and structural behaviors.

Techniques: