A Parametric Finite-Volume Formulation for Linear Viscoelasticity
This chapter of contribution presents a new numerical model for the analysis of structures of heterogeneous materials with linear viscoelastic constituents. The model is based on the recently developed parametric finite-volume theory. The use of quadrilat
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Abstract This chapter of contribution presents a new numerical model for the analysis of structures of heterogeneous materials with linear viscoelastic constituents. The model is based on the recently developed parametric finite-volume theory. The use of quadrilateral subvolumes made possible by the mapping facilitates efficient modeling of microstructures with arbitrarily shaped heterogeneities, and eliminates artificial stress concentrations produced by the rectangular subvolumes employed in the standard version. The parametric formulation is here extended to model viscoelastic behavior. Several examples, including both homogeneous and heterogeneous situations, are analyzed. Comparison between numerical and analytical results has shown an excellent performance of the proposed model.
1 Introduction The application of heterogeneous materials to fill the needs of diverse industrial sectors has significantly increased in the last years [1]. Some of these composites are constituted by high performance fibers (carbon, glass, metal, ceramic, etc.) embedded in a polymeric matrix. Due to the time-dependent behavior of polymers,
S. P. C. Marques (&) R. S. Escarpini Filho LCCV/Center of Technology Federal University of Alagoas, Campus AC Simoes, Maceio-AL, Brazil e-mail: [email protected] R. S. Escarpini Filho e-mail: [email protected] G. J. Creus CEMACOM-UFRGS, Porto Alegre-RS, Brazil e-mail: [email protected]
A. Öchsner et al. (eds.), Design and Analysis of Materials and Engineering Structures, Advanced Structured Materials 32, DOI: 10.1007/978-3-642-32295-2_6, Ó Springer-Verlag Berlin Heidelberg 2013
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the composites exhibit an effective viscoelastic response that is affected by environmental agents, particularly temperature, humidity and age [2–4]. On the other hand, composites show a heterogeneous texture on the microlevel, determined by the constitutive behavior of the matrix material and the embedded fibers. Approximate constitutive relations may be obtained using micromechanical models [5, 6]. Traditionally, the finite element method is the numerical technique most employed to analyse composites, particularly to understand their macro-level behavior [7, 8]. To have a more complete understanding of the viscoelastic behavior of a composite, the influence of the heterogeneous nature at the microscale on the macroscale response must be examined in detail. Lately, computational tools other than finite elements have been proposed to model heterogeneities and their effects under a variety of thermo-mechanical conditions [9–11]. An attractive alternative technique is the recently developed parametric formulation of the finite-volume theory [12], which incorporates a parametric mapping capability into the Finite-Volume Direct Averaging Method (FVDAM) [11]. The use of quadrilateral subvolumes made possible by the parametric mapping facilitates the modeling of heterogeneities and eliminates artificial stress concentrations produced by the rectangular subvolumes employed in the sta
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