“Practical and Theoretical Ramifications of Rheological Interconversion”
For the material characterization of a linear viscoelastic material both the relaxation modulus G(t)
and creep modulus J(t) are required. Because they are connected theoretically through the convolution
interconversion equation (G*J)(t)=t, only one needs to be measured either G or J. Recent theory has
established that stability is guaranteed only if G is measured and J is determined by solving the
interconversion equation. Interestingly, the concept of interconversion can be extended to first kind
convolution Volterra equations, which has been utilized to derive new theoretical results for such
equations. To guarantee the conservation of energy, G and dJ/dt must be completely monotone. By
invoking the Laplace transform representation of Bernstein for completely monotone functions, the
relationship between G and J can be formalized theoretically using measure theory.
The background research, on which this talk is based, relates to various collaborations with Russell
Davies (University of Cardiff), Frank de Hoog (CSIRO Mathematics, Informatics and Statistics) and
Rick Loy (Australian National University).