Analysis and visualization of traceless symmetric tensors. Application to the Hencky strain tensor for large strain tension–torsion
Résumé
Cyclic multiaxial loadings of soft materials are usually studied throughout experiments involving machines that prescribe a combination of uniaxial tension and torsion. Due to the large strain framework, classical kinematic analyses of strain in uniaxial tension–torsion are usually very complex. Based on this observation, the present paper proposes a method to both analyze and visualize a strain measure during a duty cycle of uniaxial tension–torsion in large strain: based on the mathematical properties of the Hencky strain tensor , the method consists in projecting onto a well-chosen tensor basis, whose constituting elements are described in terms of physical meaning. Thanks to this decomposition, the history of reduces to the time evolution of a 3-component vector . This vector history can then be visualized as a path in 3D space, rendering very visual the complex kinematic phenomenon. As a second result, an original definition of the mean and the amplitude of a strain path, based on the theory of the Minimum Circumscribed Spheres, is proposed. This definition could be useful for fatigue studies, for instance.
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