Polymeric materials referred to herein as PEU include a plurality of linking groups selected from urea and urethane groups, and a plurality of segments located between adjacent linking groups, where at least some of the segments of the PEU are polyoxyalkylene, but other exemplary segments include hydrocarbons, polyesters, polycarbonates and polysiloxanes. The polymeric materials are biocompatible and may be used, for example, to replace or supplement cartilage in an articulated joint.