Experimental investigations of uniaxial and biaxial cold stretching within PC‐films and bars using optical measurements - Hamdoun, Ayoub; Mahnken, Rolf (PAMM)
Abstract Polycarbonate (PC) is an amorphous polymer that is an extremely robust material with a high tenacity, and thus suitable for a lightweight construction with glass‐like transparency. Due to these advantageous properties, PC is often used in industry for example in medical devices, automotive headlamps, sporting equipment, electronics, and a variety of other products. PC is often subjected to uniaxial and biaxial loading conditions. Therefore, reliable material models have to take into account the various resulting experimental effects. For those reasons, we investigate PC specimens under uniaxial and biaxial loading by using different stretch rates and loading scenarios. In addition to that, we propose methods for optical measurement of local stretches to obtain the approximated local true stress. In future work, the displacement fields and the resulting reaction forces will be used for parameter identification of constitutive equations.
Keywords: Electrical and Electronic Engineering; Atomic and Molecular Physics; and Optics

Multiscale simulation of polymer curing of composites combined mean-field homogenisation methods at large strains - Lenz, Peter; Mahnken, Rolf (International Journal of Solids and Structures)
Keywords: Applied Mathematics; Mechanical Engineering; Mechanics of Materials; Condensed Matter Physics; General Materials Science; Modeling and Simulation

Construction of A-stable explicit last-stage diagonal implicit Runge–Kutta (ELDIRK) methods - Mahnken, Rolf; Westermann, Hendrik (Computational Mechanics)
ELDIRK methods are defined to have an Explicit Last stage in the general Butcher array of Diagonal Implicit Runge-Kutta methods, with the consequence, that no additional system of equations must be solved, compared to the embedded RK method. Two general formulations for second- and third-order ELDIRK methods have been obtained recently in Mahnken [21] with specific schemes, e.g. for the embedded implicit Euler method, the embedded trapezoidal-rule and the embedded Ellsiepen method. In the first part of this paper, we investigate some general stability characteristics of ELDIRK methods, and it will be shown that the above specific RK schemes are not A-stable. Therefore, in the second part, the above-mentioned general formulations are used for further stability investigations, with the aim to construct new second- and third-order ELDIRK methods which simultaneously are A-stable. Two numerical examples are concerned with the curing for a thermosetting material and phase-field RVE modeling for crystallinity and orientation. The numerical results confirm the theoretical results on convergence order and stability.
Keywords: Applied Mathematics; Computational Mathematics; Computational Theory and Mathematics; Mechanical Engineering; Ocean Engineering; Computational Mechanics

A large deformation gradient theory for glassy polymers by means of micromorphic regularization - Hamdoun, Ayoub; Mahnken, Rolf (Archive of Applied Mechanics)
Abstract Cold forming of polycarbonate films results in the formation of shear bands in the necking zone. The numerical results obtained from standard viscoplastic material models exhibit mesh size dependency, requiring mathematical regularization. For this purpose, we present in this work a large deformation gradient theory for a viscoplastic isotropic material model published before. We extend our model to a micromorphic model by introducing a new micromorphic variable as an additional degree of freedom along with its first gradient. This variable represents a microequivalent plastic strain. The relation between the macroequivalent plastic strain and the micromorphic variable is accomplished by a micromorphic coupling modulus. This coupling forces proximity between the macro- and microvariables, leading to the targeted regularization effect. The micromorphic model is implemented as a three-dimensional initial boundary value problem in an in-house finite element tool. The analysis is performed for both uniaxial and biaxial specimens. The provided numerical examples show the ability of our model to regularize shear bands within the specimens and address the issue of localization.

Uniaxial and biaxial experimental investigation of glassy polymers - Hamdoun, Ayoub; Mahnken, Rolf (Polymer)