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Free Energies For Nonlinear Materials With Memory, John Murrough Golden

Articles

An exploration of representations of free energies and associated rates of dissipation for a broad class of nonlinear viscoelastic materials is presented in this work. Also included are expressions for the stress functions and work functions derivable from such free energies. For simplicity, only the scalar case is considered. Certain standard formulae are generalized to include higher power terms.

It is shown that the correct initial procedure in this context is to specify the rate of dissipation as a positive semi-definite functional and then to determine the free energy from this, rather than the other way around, which would be …

Unique Characterization Of Materials With Memory, John Murrough Golden

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In general, materials with linear memory constitutive relations are characterized by a relaxation function. This leads to a situation where the free energy for most materials with memory is not unique. There is a convex set of free energy functionals with a minimum and a maximum element. An alternative procedure is proposed which characterizes a material by the kernel of the rate of dissipation functional. Using some recent results, we find that a unique free energy and relaxation function may then be deduced. An example is given for discrete spectrum materials. Also, the new results are used to show that …

Free Energies And Minimal States For Scalar Linear Viscoelasticity, John Murrough Golden

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The concept of a minimal state was introduced in recent decades, based on earlier work by Noll. The property that a given quantity is a functional of the minimal state is of central interest in the present work. Using a standard representation of a free energy associated with a linear memory constitutive relation, a new condition, involving linear functionals, is derived which, if satisfied, ensures that the free energy is a functional of the minimal state. Using this result and recent work on constructing free energy functionals, it is shown that if the kernel of the rate of dissipation functional …

Free Energies For Materials With Memory In Terms Of State Functionals, John Murrough Golden

Articles

Abstract The aim of thiswork is to determinewhat free energy functionals are expressible as quadratic forms of the state functional It which is discussed in earlier papers. The single integral form is shown to include the functional wF proposed a few years ago, and also a further category of functionals which are easily described but more complicated to construct. These latter examples exist only for certain types of materials. The double integral case is examined in detail, against the background of a newsystematic approach developed recently for double integral quadratic forms in terms of strain history, which was used to …