A simple proof of a duality theorem with applications in viscoelasticity
Andrzej Hanyga
TL;DR
This paper presents a concise proof of a duality theorem linking relaxation and creep functions in viscoelasticity, utilizing the theory of Bernstein and Stieltjes functions to establish the relation.
Contribution
The paper introduces a simplified proof of a duality theorem in viscoelasticity using advanced function theory, providing clearer insights into the mathematical relationship.
Findings
Establishes a duality between relaxation and creep functions
Utilizes complete Bernstein and Stieltjes functions in the proof
Simplifies the mathematical understanding of viscoelastic duality
Abstract
A new concise proof is given of a duality theorem connecting completely monotone relaxation functions with Bernstein class creep functions. The proof makes use of the theory of complete Bernstein functions and Stieltjes functions and is based on a relation between these two function classes.
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Taxonomy
TopicsRheology and Fluid Dynamics Studies · Elasticity and Material Modeling · Probabilistic and Robust Engineering Design