An optical method allowing the characterization of melt flow instabilities typically occurring during an extrusion process of polymers and polymer compounds is presented. It is based on a camera‐acquired image of the extruded compound with a reference length scale. Application of image processing and transformation of the calibrated image to the frequency domain yields the magnitude spectrum of the instability. The effectiveness of the before mentioned approach is shown on Styrene‐butadiene rubber (SBR) compounds, covering a wide range of silica filler content, extruded through a Göttfert capillary rheometer. The results of the image‐based analysis are compared with the results from the sharkskin option, a series of highly sensitive pressure transducers installed inside the rheometer. A simplified version of the code used to produce the optical analysis results is included as supplementary material. © 2019 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2020, 137, 48806.

Rigorous analysis of the response of nonlinear materials to step inputs requires one to simultaneously handle the discontinuity, differentiation, and nonlinearity. This task is however beyond the reach of the standard theories such as the classical theory of distributions and presents a considerable mathematical difficulty. New advanced mathematical tools are necessary to handle the challenge. An elegant and relatively easy-to-use framework capable of accomplishing the task is provided by the Colombeau algebra, which is a generalisation of the classical theory of distributions to the nonlinear setting. We use the Colombeau algebra formalism and derive explicit formulae describing the response of incompressible Maxwell viscoelastic fluid subject to step load/deformation in the lubricated squeeze flow setting.

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ABSTRACT. The response of mechanical systems composed of springs and dashpots to a step input is of eminent interest in the applications. If the system is formed by linear elements, then its response is governed by a system of linear ordinary differential equations, and the mathematical method of choice for the analysis of the response of such systems is the classical theory of distributions. However, if the system contains nonlinear elements, then the classical theory of distributions is of no use, since it is strictly limited to the linear setting. Consequently, a question arises whether it is even possible or reasonable to study the response of nonlinear systems to step inputs. The answer is positive. A mathematical theory that can handle the challenge is the so-called Colombeau algebra. Building on the abstract result by (Průša & Rajagopal 2016, Int. J. Non-Linear Mech) we show how to use the theory in the analysis of response of a simple nonlinear mass-spring-dashpot system.