Material Property Functions and Their Characterization
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This chapter examines four topics of practical importance. It begins with an introduction to material characterization testing, covering stress relaxation, creep, constant rate, and dynamic tests. The chapter then introduces two types of analytical forms, typically used to describe mechanical constitutive property functions. One type, usually referred to as a Dirichlet-Prony series, is expressed as a finite sum of exponentials; the other form is a power law in time. This treatment is followed by a discussion of methods of inversion of material property functions given in Prony series form; both exact and approximate methods of inversion are presented. The chapter is completed with a discussion of practical ways to establish the numerical coefficients entering the analytical forms used to represent the WLF shift relation, the relaxation modulus, and the creep compliance. The use of a computer application available with the book, which was specifically developed to obtain the exact convolution inverse of function in a Prony series form, is also presented and its use is illustrated by means of some examples.
KeywordsCharacterization Test Constitutive Kernel Numerical Inversion Analytical Parameter Prony Dirichlet Power Law Hereditary Logarithmic Transition Property function Relaxation Creep Compliance Complex Laplace Transform Convolution Retardation Time Volterra Polynomial Equation Roots Shift function Least squares
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