  Materials with negative Poisson ratio have the counter-intuitive property of
expanding laterally when they are stretched longitudinally. They are
accordingly termed auxetic, from the Greek auxesis meaning to increase.
Experimental studies have demonstrated auxetic materials to have superior
material properties, compared with conventional ones. These include synclastic
curvature, increased acoustic absorption, increased resilience to material
fatigue, and increased resistance to mechanical failure. Until now, the latter
observations have remained poorly understood theoretically. With this
motivation, the contributions of this work are twofold. First, we elucidate
analytically the way in which stress propagates spatially across a material
following a localised plastic failure event, finding a significantly reduced
stress propagation in auxetic materials compared with conventional ones. In
this way, a plastic failure event occurring in one part of a material has a
reduced tendency to trigger knock-on plastic events in neighbouring regions.
Second, via the numerical simulation of a lattice elastoplastic model, we
demonstrate a key consequence of this reduced stress propagation to be an
increased resistance to mechanical failure. This is seen not only via an
increase in the externally measured yield strain, but also via a decreased
tendency for plastic damage to percolate internally across a sample in
catastrophic system-spanning clusters.
