<Dl> <Dd> σ = 2 J F ∂ W ∂ C F T where J: = det F . (\ displaystyle (\ boldsymbol (\ sigma)) = (\ cfrac (2) (J)) ~ (\ boldsymbol (F)) (\ cfrac (\ partial W) (\ partial (\ boldsymbol (C)))) (\ boldsymbol (F)) ^ (T) \ quad (\ text (where)) \ quad J: = \ det (\ boldsymbol (F)) \, .) </Dd> </Dl> <Dd> σ = 2 J F ∂ W ∂ C F T where J: = det F . (\ displaystyle (\ boldsymbol (\ sigma)) = (\ cfrac (2) (J)) ~ (\ boldsymbol (F)) (\ cfrac (\ partial W) (\ partial (\ boldsymbol (C)))) (\ boldsymbol (F)) ^ (T) \ quad (\ text (where)) \ quad J: = \ det (\ boldsymbol (F)) \, .) </Dd> <P> Linear elasticity is used widely in the design and analysis of structures such as beams, plates and shells, and sandwich composites . This theory is also the basis of much of fracture mechanics . </P> <P> Hyperelasticity is primarily used to determine the response of elastomer - based objects such as gaskets and of biological materials such as soft tissues and cell membranes . </P>

Among solids liquids and gases which one can have all the moduli of elasticity