| 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) |
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| 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 | |
