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Simplified analysis of a generalized bias test for fabrics with two families of inextensible fibres

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Abstract

Two tests for woven fabrics with orthogonal fibres are examined using simplified kinematic assumptions. The aim is to analyse how different constitutive assumptions may affect the response of the specimen. The fibres are considered inextensible, and the kinematics of 2D continua with inextensible chords due to Rivlin is adopted. In addition to two forms of strain energy depending on the shear deformation, also two forms of energy depending on the gradient of shear are examined. It is shown that this energy can account for the bending of the fibres. In addition to the standard bias extension test, a modified test has been examined, in which the head of the specimen is rotated rather than translated. In this case more bending occurs, so that the results of the simulation carried out with the different energy models adopted differ more that what has been found for the BE test.

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Authors and Affiliations

  1. Dipartimento di ingegneria Civile e Architettura (DICAR), Università degli Studi di Catania, Catania, Italy

    M. Cuomo

  2. Dipartimento di Ingegneria Strutturale e Geotecnica (DISG), Università di Roma La Sapienza, Rome, Italy

    F. dell’Isola

  3. International Research Center for the Mathematics and Mechanics of Complex Systems (MeMoCS), Università dell’Aquila, Cisterna di Latina, Italy

    M. Cuomo, F. dell’Isola & L. Greco

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  1. M. Cuomo
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  2. F. dell’Isola
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  3. L. Greco
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Cuomo, M., dell’Isola, F. & Greco, L. Simplified analysis of a generalized bias test for fabrics with two families of inextensible fibres. Z. Angew. Math. Phys. 67, 61 (2016). https://doi.org/10.1007/s00033-016-0653-z

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