Localization of deformation in plane elastic–plastic solids with anisotropic elasticity

Multiple shear band development and related instabilities in granular materials

“…• Analysis of the onset of strain localisation is performed using standard concepts. This reveals the essential role played by induced elastic anisotropy, therefore extending previous results by Bigoni and Loret (1999) and Bigoni et al (2000). • Post-localisation analysis is investigated by developing a speciÿc numerical procedure, based on certain simplifying assumptions (the width and inclination of the band are ÿxed, interaction of shear bands and boundary is neglected, the ÿelds outside and inside the band are uniform).…”

“…We therefore exploit the framework of elastoplastic coupling to describe induced elastic anisotropy, as produced by particle reorientations and modiÿcations of intergranular contacts, an e ect that has been systematically tested in a conventional triaxial apparatus (Gajo et al, 2001;. Although not believed to be important in the description of the global stress-strain response of a soil sample, this becomes essential when the onset of shear banding is analysed (Bigoni and Loret, 1999;Bigoni et al, 2000). …”

“…The maximisation problem (45) was explicitly solved by Rudnicki and Rice (1975) for isotropic elasticity and coaxial yield function and plastic potential gradients. Bigoni and Loret (1999) and Bigoni et al (2000) have analysed the problem of elastic anisotropy relevant to the present paper. Their solutions can be used when tensors P; Q and B are coaxial, a condition which may not be veriÿed in our model for general loading, but it is veriÿed if we refer to the state of stress realized in a biaxial or triaxial test apparatus.…”

“…Their solutions can be used when tensors P; Q and B are coaxial, a condition which may not be veriÿed in our model for general loading, but it is veriÿed if we refer to the state of stress realized in a biaxial or triaxial test apparatus. Therefore, the condition for the onset of strain localisation will be obtained analytically in the examples that follow using formulae taken from Bigoni et al (2000) and not repeated here for conciseness. It is important however to realise that the speciÿc elastic anisotropy evolution introduced in our model is a key feature in determining the onset of strain localisation, particularly for simulation of triaxial tests .…”

Strain Localization in Unsaturated Elastic-Plastic Materials Subjected to Plane Strain Compression

“…He found that the initial homogenous deformation of saturated sand samples was followed by a spontaneous deformation of a persistent shear band. Bigoni et al (2000) found analytical solutions for elastic-plastic solids with anisotropic elasticity. Rudnicki (1983) discussed conditions for the onset of strain localization in the case of partly drained behavior.…”