  Mechanical waves that travel without inertia are often encountered in nature
-- e.g. motion of plants -- yet such waves remain rare in synthetic materials.
Here, we discover the emergence of slow kinks in overdamped metamaterials and
we show that they can be used for applications such as sensing, dynamic pattern
morphing and transport of objects. To do this, we create dissipative kirigami
with suitably patterned viscoelasticity. These kirigami shape-change into
different textures depending on how fast they are stretched. We find that if we
stretch fast and wait, the viscoelastic kirigami can eventually snap from one
texture to another. Crucially, such a snapping instability occurs in a sequence
and a travelling overdamped kink emerges. We demonstrate that such kink
underpins dynamic shape morphing in 2D kirigami and can be used to transport
objects. Our results open avenues for the use of slow kinks in metamaterials,
soft robotics and biomimicry.

Soft Condensed Matter;Materials Science