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The paper presents results on the mechanisms of plastic strain accommodation of Ni-Al laminates composed of concentrically aligned thin foils processed at different conditions undergoing a high strain radial collapse in thick walled cylinder experiments. Numerical simulations were conducted to examine the influence of mesoscale parameters (layer size, defects in mesostructure, and ductility) on the mechanisms of large plastic strain accommodation (high amplitude cooperative buckling; high frequency, low amplitude buckling; and kinking) at high strain rates in pure shear (plane strain) conditions. These mechanisms are dramatically different than observed in solid ductile and brittle homogeneous materials where a pattern of shear bands is the major mode of strain accommodation. It was observed that the layer thickness and ductility greatly influenced the dominant mode of plastic strain accommodation. The number of apices was related to the layer thickness. The presence of defects mainly had a localized area of influence. Numerical simulations showed good qualitative agreement with the experiments and provided the ability to simulate additional mesoscale and material dependencies: the role of friction/bonding, relative layer sizes, and sample thickness.