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The MAX phases and hexagonal metals, among many other plastically anisotropic solids with c/a ratios 1.5, have been recently classified as kinking nonlinear elastic (KNE) solids the signature of which is the formation of fully reversible, hysteretic stress-strain loops during cyclic loadings. Herein, a unique and novel class of Mg matrix composites reinforced with Ti2AlC was fabricated, for the first time, by spontaneous melt infiltration. The ~ 35 nm Mg grains that constituted the matrix of these composites were exceptionally stable: repeatedly heating the composite to 700 °C 50 °C above the melting point of Mg remarkably did not lead to any coarsening. To make these composites, all one needs to do is melt bulk Mg above a porous preform of Ti2AlC; nature does the rest. Because kinking is a form of plastic instability, orienting the Ti2AlC grains, prior to infiltration, with their basal planes parallel to the loading direction led to exceptionally high values of dissipated energy per unit volume per cycle, Wd. At 450 MPa, Wd of these composites with this texture was found to be 0.6 MJ/m3, believed to be the highest ever reported for a crystalline solid.