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H. E. Pettermann:
"Direction Dependent Time-Temperature-Shift Functions and Energy Considerations in Viscoelasticity";
Berichts-Nr. ILSB-Report 301, 2018; 24 S.

The present report documents the activities of the author during the stay at the Scuola Internazionale Superiore di Studi Avanzati - SISSA in Trieste, Italy, as visiting scientist in summer 2018, in course of a sabbatical leave from the Vienna University of Technology. The work is a continuation and extension of the developments elaborated in 2015 where the author was at SISSA in an equivalent setup.
Starting point is the constitutive material law for linear thermo-viscoelasticity in the time domain with orthotropic material symmetry under plane stress assumption as developed in 2015. It has been implemented into the commercial FEM package ABAQUS/Standard using the interfaces "user supplied material routine" and "user supplied expansion".
The current work concern the time-temperature-shift functions, as typically applied in the case of thermo-rheological simple materials. In addition to the already available WLF function an Arrhenius-type function is implemented. As an extension of the orthotropic considerations, also the shift functions (i.e. the reduced times) are treated to be direction dependent. Corresponding modifications to the "user supplied material routine" and the input data description are implemented.
In addition, the development of the strain energy and the dissipated energy in linear viscoelasticity is treated. Theoretical considerations and corresponding implementations are carried out to provide energy output in course of FEM simulations.
Various tests on isotropic and orthotropic problems are carried out for verification.
The developments are exemplified on a continuous fiber reinforced composite with dissimilar generic material data of the constituents. Both fiber and matrix material are linear viscoelastic, however, possessing different time-temperature-shift functions. A periodic unit cell approach is employed to compute a set of homogenized responses of the composite. These are used to calibrate the input parameters for the developed material law. The predicted behavior of the latter is compared to the unit cell simulations and the concept of direction dependent time-temperature-shift functions is discussed.
Moreover, the elastically stored energy and the dissipated energy are evaluated. Corresponding results from unit cell simulations and the predictions form the calibrated constitutive model are compared and discussed.