Partner: Prof. Andrzej Hanyga, PhD, DSc

University of Bergen (NO)

Habilitation thesis
1976Rozwiązania problemu Riemanna dla dowolnych hiperbolicznych układów praw zachowania 
Recent publications
1.Hanyga A., Seredyńska M., Positivity of Green's functions for a class of partial integro-differential equations including viscoelasticity, WAVE MOTION, ISSN: 0165-2125, Vol.47, No.8, pp.648-662, 2010
2.Seredyńska M., Hanyga A., Relaxation, dispersion, attenuation and finite propagation speed in viscoelastic media, JOURNAL OF MATHEMATICAL PHYSICS, ISSN: 0022-2488, Vol.51, No.9, pp.092901-1-16, 2010
3.Seredyńska M., Hanyga A., Cones of material response functions in 1D and anisotropic linear viscoelasticity, PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, ISSN: 1364-503X, DOI: 10.1098/rspa.2009.0305, Vol.465, pp.3751-3770, 2009
Abstract:

Viscoelastic materials have non-negative relaxation spectra. This property implies that viscoelastic response functions satisfy certain necessary and sufficient conditions. These conditions can be expressed in terms of each viscoelastic response function ranging over a cone. The elements of each cone are completely characterized by an integral representation. The 1:1 correspondence between the viscoelastic response functions is expressed in terms of cone-preserving mappings and their inverses. The theory covers scalar- and tensor-valued viscoelastic response functions.

Keywords:

viscoelasticity, completely monotone function, Herglotz function, relaxation, Bernstein function, Stieltjes function

Affiliations:
Seredyńska M.-IPPT PAN
Hanyga A.-University of Bergen (NO)
4.Hanyga A., Seredyńska M., Hamiltonian and Lagrangian theory of viscoelasticity, CONTINUUM MECHANICS AND THERMODYNAMICS, ISSN: 0935-1175, Vol.19, pp.475-492, 2008
5.Hanyga A., Seredyńska M., A rigorous construction of maximum recoverable work, ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK ZAMP, ISSN: 0044-2275, Vol.59, No.5, pp.722-732, 2008
6.Hanyga A., Seredyńska M., On a mathematical framework for the constitutive equations of anisotropic dielectric relaxation, JOURNAL OF STATISTICAL PHYSICS, ISSN: 0022-4715, Vol.131, No.2, pp.266-303, 2008
7.Hanyga A., Seredyńska M., Multiple-integral viscoelastic constitutive equations, INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS, ISSN: 0020-7462, Vol.42, pp.722-732, 2007
8.Hanyga A., Seredyńska M., Relations between relaxation modulus and creep compliance in anisotropic linear viscoelasticity, JOURNAL OF ELASTICITY, ISSN: 0374-3535, Vol.88, pp.41-46, 2007
9.Hanyga A., Seredyńska M., A dynamic model of capillary hysteresis in immiscible fluid displacement, TRANSPORT IN POROUS MEDIA, ISSN: 0169-3913, Vol.59, No.3, pp.249-265, 2005
10.Seredyńska M., Hanyga A., Nonlinear differential equation with fractional damping with applications to the 1dof and 2dof pendulum, ACTA MECHANICA, ISSN: 0001-5970, Vol.176, pp.169-183, 2005
11.Hanyga A., Rozwiązania problemu Riemanna dla dowolnych hiperbolicznych układów praw zachowania (Praca habilitacyjna), Prace IPPT - IFTR Reports, ISSN: 2299-3657, No.38, pp.1-137, 1975

List of chapters in recent monographs
1.
160
Hanyga A., Seredyńska M., IUTAM Symposium on Theoretical, computational and modelling aspects of inelastic media, IUTAM Bookseries, rozdział: Hamiltonian theory of viscoelasticity, Springer, Reddy B.D. (Ed.), 11(9), pp.373-383, 2008