Pet door asembly and flap

A flap for use in a pet door, the flap comprising:

• two or more rigid segments extending vertically, wherein gaps are provided between the two or more rigid segments;
• and
• elastic material connecting adjacent rigid segments of the two or more rigid segments,
• wherein elastic stretch zones are provided in the gaps, wherein the flap resists horizontal and vertical bending in locations where a rigid segment is provided, wherein the elastic stretch zones are configured to permit vertical bending when the flap is opened.

A pet door comprising:

• a flap having a flap magnet proximate to a bottom of the flap;
• and
• a frame that is configured to hold the flap, the frame having a sill assembly with one or more pistons that are configured to shift within one or more corresponding cavities,
• wherein the sill assembly includes a sill magnet that is configured to attract the flap magnet, wherein magnetic attraction between the sill magnet and the flap magnet is configured to urge the one or more pistons into the one or more corresponding cavities to seal the flap regardless of an amount of thermal expansion or contraction in the flap, wherein the sill assembly includes viscous material in the one or more corresponding cavities, and wherein the pistons are configured to block viscous material from exiting the one or more corresponding cavities.