There was a very interesting talk at Google Next in March that described a way in which the Kubernetes open source team is bringing this sidecar architecture to Kub. In fact I think they are working with the Lyft team. The whole talk is interesting but I've added a time offset to skip to the bit where they talk about sidecar/service mesh.

https://www.youtube.com/watch?v=3quCoi5YHz4#t=27m59s

Also, there is https://istio.io/ but it's a placeholder site at the moment.