We study the formation of localized shear zones during the layer-parallel extension of viscous multi-layers using two-dimensional numerical simulations based on the finite-difference method. For power-law viscous layers and a linear viscous embedding medium, the extended multi-layer develops boudins due to necking. For power-law viscous layers embedded in a power-law viscous medium, the extended multi-layer develops first distributed necks, and subsequently a localized shear zone with a vertical offset (with a size of several layer thicknesses) along the multi-layer. During the extension, the deformation style switches from distributed and symmetric necking to localized and asymmetric shearing. A localized shear zone develops in the viscous multi-layer although the rheology is everywhere strain-rate-hardening (power-law stress exponent >1) and no material softening and/or energy feedback mechanism (e.g., shear heating combined with a temperature-dependent viscosity) is applied. The shear localization is caused by structural softening because the formation of a localized shear zone decreases the bulk resistance and hence the work required to deform the multi-layer. A localized shear zone forms in the multi-layer when the distance between the stiff layers is approximately equal to or less than the layer thickness. The shear localization was observed in multi-layers with nine and with only three stiff layers.

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