Advanced Search

Query:

Fill in the form and click »Search«...

Format:

Display: entries per page entries

Zbl 0943.74008
Enelund, Mikael; Lesieutre, George A.
Time-domain modeling of damping using anelastic displacement fields and fractional calculus. (English)
[J] Int. J. Solids Struct. 36, No.29, 4447-4472 (1999). ISSN 0020-7683

Summary: We develop a fractional derivative model of linear viscoelasticity based on the decomposition of the displacement field into an anelastic part and an elastic part. The evolution equation for the anelastic part is a differential equation of fractional order in time. By using a fractional-order evolution equation for the anelastic strain, the present model becomes very flexible for describing the weak frequency dependence of damping characteristics. To illustrate the modeling capability, we fit the model parameters to available frequency domain data for a high-damping polymer. By studying the relaxation modulus and the relaxation spectrum, we examine the physical meaning of material parameters of the present viscoelastic model. The use of this viscoelastic model in structural modeling is discussed, and the corresponding finite element equations are outlined, including the treatment of boundary conditions. The anelastic displacement field is mathematically coupled to the total displacement field through a convolution integral with a kernel of Mittag-Leffler function type. Finally, we give a time-step algorithm for solving the finite element equations, and discuss some numerical examples.

MSC 2000:: *74D05 Linear constitutive equations
74S05 Finite element methods

Keywords: decomposition of displacement field; fractional derivative model; linear viscoelasticity; anelastic part; elastic part; fractional-order evolution equation; frequency domain data; high-damping polymer; relaxation modulus; relaxation spectrum; finite element equations; convolution integral; time-step algorithm

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Advanced Search

Zentralblatt MATH Berlin [Germany]