Modeling and simulation of anisotropic linear viscoelasticity
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Modeling and simulation of anisotropic linear viscoelasticity Direction dependent time–temperature-shift functions Heinz E. Pettermann1 Antonio DeSimone2
· Camille Cheyrou1 ·
Received: 9 September 2019 / Accepted: 28 August 2020 © The Author(s) 2020
Abstract A constitutive material law for linear viscoelasticity in the time domain is presented. It does not only allow for anisotropic elastic behavior but also for anisotropic (i.e. direction dependent) relaxation response. Under the assumption of thermo–rheological simple material behavior, the model is capable to account for direction dependent time– temperature-shift functions. The application is demonstrated for a linear viscoelastic matrix material reinforced by linear viscoelastic continuous fibers. The effective orthotropic linear viscoelastic response of the composite is computed by means of a periodic unit cell approach. These data, evaluated at different temperatures, are used to calibrate the input for the developed material law. Predictions from the latter are compared to the results from the unit cell simulations. Keywords Linear viscoelasticity · Orthotropic relaxation · Time–temperature shift · Constitutive law · Finite Element Method · Composite materials
1 Introduction The apparent effects of viscoelasticity manifest itself in a time dependent response to loading and accompanying energy dissipation. Relaxation or creep occurs when a material is exposed to quasi-static loads and load changes. Viscoelastic effects are widespread in natural and in engineering materials. Among them are almost all biological tissues and most polymers, in particular thermoplastic materials. As fiber reinforced plastics, they have gained importance in lightweight design and for industrial applications. Such composites often have elongated reinforcements with preferred orientation. Consequently, their properties are direction depended and the consideration of anisotropy becomes inevitable. In engineering
B H.E. Pettermann
[email protected]
1
Institute of Lightweight Design and Structural Biomechanics, Vienna University of Technology, Vienna, Austria
2
Scuola Internazionale Superiore di Studi Avanzati — SISSA, Trieste, Italy
Mech Time-Depend Mater
composites, composition and spatial arrangement allow for the tailoring of the properties to meet certain demands arising from service loads of composites parts. For the design process, computational tools are desired which are capable to predict the response of composite materials. There are two groups of models which serve for this purpose. First, micromechanical approaches which are based on a detailed representation of the geometry of the composite’s constituents, and second, constitutive material laws which describe the homogenized behavior of the composite. The latter are well suited for structural analyses of large scale components and parts made from composites, because they can handle general multi-axial time varying loading scenarios. A general introduction into viscoelasticity can be found, e.g. in
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