Pressure-dampening casing to reduce stress load on cement sheath

A casing string comprising:

• a first casing coupled to a second casing, wherein the first casing is axially below the second casing,
• wherein the first casing comprises:
• a first tubular body formed by a first wall extending axially from a first end to a second end, the first tubular body having a first bore therein throughout,
• the first wall radially extends from a first inner surface of the first tubular body to a first outer surface of the first tubular body, wherein the first wall comprises:
• a first base layer;
• and
• one or more first secondary layers embedded within a void of the first base layer, wherein the one or more first secondary layers is a rubber or smart foam,
• wherein the one or more secondary layers is attached to a first interior surface of the base layer and a gap is formed between the one or more secondary layers and a second interior surface of the base layer, or wherein the one or more secondary layers is attached to the second interior surface and the gap is formed between the one or more secondary layers and the first interior surface,
• wherein the second casing comprises:
• a second tubular body formed by a second wall extending axially from a third end to a fourth end, the second tubular body having a second bore therein throughout,
• the second wall radially extends from a second inner surface of the second tubular body to a second outer surface of the second tubular body, wherein the second wall comprises:
• a second base layer;
• and
• one or more second secondary layers embedded within a second void of the second base layer, wherein the one or more second secondary layers is a rubber or smart foam,
• wherein the one or more second secondary layers is attached to a third interior surface of the second base layer and a second gap is formed between the one or more second secondary layers and a fourth interior surface of the second base layer, or wherein the one or more second secondary layers is attached to the fourth interior surface and the second gap is formed between the one or more second secondary layers and the third interior surface;
• and
• a collar or coupling configured to couple the second end of the first casing to the third end of the second casing.

A method comprising:

• forming a base layer of a tubular body extending axially from a first end to a second end;
• providing one or more voids within the base layer, wherein the one or more voids is an empty space extending a radially distance between a first interior surface of the base layer and a second interior surface of the base layer;
• embedding one or more secondary layers within the one or more voids, wherein the one or more secondary layers is a rubber or smart foam,
• wherein embedding the one or more secondary layers comprises attaching the one or more secondary layers to the first interior surface to form a gap between the one or more secondary layers and the second interior surface or attaching the one or more secondary layers to the second interior surface to form the gap between the one or more secondary layers and the first interior surface.