Energy balance for fractional anti-Zener and Zener models in terms of relaxation modulus and creep compliance
arXiv:2305.06098 · doi:10.1016/j.apm.2023.07.019
Abstract
Relaxation modulus and creep compliance corresponding to fractional anti-Zener and Zener models are calculated and restrictions on model parameters narrowing thermodynamical constraints are posed in order to ensure relaxation modulus and creep compliance to be completely monotone and Bernstein function respectively, that a priori guarantee the positivity of stored energy and dissipated power per unit volume, derived in time domain by considering the power per unit volume. Both relaxation modulus and creep compliance for model parameters obeying thermodynamical constraints, proved that can also be oscillatory functions with decreasing amplitude. Model used in numerical examples of relaxation modulus and creep compliance is also analyzed for the asymptotic behavior near the initial time instant and for large time.
arXiv commentThe manuscript is under review in the Applied Mathematical Modeling
References in corpus (13)
- Creep, Relaxation and Viscosity Properties for Basic Fractional Models in Rheology
- Distributed-order fractional wave equation on a finite domain. Stress relaxation in a rod
- Fractional Burgers models in creep and stress relaxation tests
- A dynamic viscoelastic analogy for fluid-filled elastic tubes
- A class of linear viscoelastic models based on Bessel functions
- On infinite order differential operators in fractional viscoelasticity
- Distributed order fractional constitutive stress-strain relation in wave propagation modeling
- Well-posedness of the fractional Zener wave equation for heterogenous viscoelastic materials
- Restrictions on wave equations for passive media
- The Frequency Response Function of the Creep Compliance
- Fractional Burgers wave equation
- Micro-local and qualitative analysis of the fractional Zener wave equation
- Distributed-order time-fractional wave equations