---------The development of stress-induced morphing materials which are described as piezomorphic materials is reported. The development of a piezomorphic material is achieved by introducing spatial dependency into the compliance matrix describing the elastic response of a material capable of undergoing large strain deformation. In other words, it is necessary to produce an elastically gradient material. This is achieved through modification of the microstructure of the compliant material to display gradient topology. Examples of polymeric (polyurethane) foam and microporous polymer (expanded polytetrafluoroethylene) piezomorphic materials

The development of longitudinally and radially gradient open-cell polyurethane foams is reported. Local and global mechanical properties and pore structure have been characterized using video extensometry with x−y strain-mapping capability, and x-ray microtomography (CT) and scanning electron microscopy (SEM), respectively. The local axial Poisson’s ratio varies in a smoothly continuous manner along the length of the longitudinally gradient foam from large negative (auxetic), through zero, to positive (conventional) values. The production of radially gradient foams having a coaxial core–sheath structure is reported for the first time. Two radially gradient foams have been produced, each displaying similar global negative axial Poisson’s ratio responses but with markedly different local axial Poisson’s ratio and local axial Young’s modulus behaviours. One of the radially gradient foams displays a positive Poisson’s ratio core and an auxetic sheath resulting from conventional and higher density re-entrant open-cell pore structures, respectively.

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