ArticleMaterials (Basel, Switzerland)2022
Thermodynamic Restrictions in Linear Viscoelasticity.
Article in Materials (Basel, Switzerland), 2022. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 2 papers.
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2 citing papers in PubMed.
- The Thermal Stress Problem of Bimodular Curved Beams under the Action of End-Side Concentrated Shear Force.Materials (Basel, Switzerland) · 2023Article
- A Phase-Field Approach to Continuum Damage Mechanics.Materials (Basel, Switzerland) · 2022Article
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Abstract
The thermodynamic consistency of linear viscoelastic models is investigated. First, the classical Boltzmann law of stress-strain is considered. The kernel (Boltzmann function) is shown to be consistent only if the half-range sine transform is negative definite. The existence of free-energy functionals is shown to place further restrictions. Next, the Boltzmann function is examined in the unbounded power law form. The consistency is found to hold if the stress functional involves the strain history, not the strain-rate history. The stress is next taken to be given by a fractional order derivative of the strain. In addition to the constitutive equations involving strain-rate histories, finding a free-energy functional, consistent with the second law, seems to be an open problem.
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