In this paper, a new microarchitectured material is introduced that consists of a large periodic lattice of small compliant unit cells (i.e., <5 mm) that are independently controlled using piezo actuators, sensors, and microprocessors embedded within each cell. This material exhibits desired bulk properties according to control instructions that are programmed and uploaded to the material's microprocessors. Analytical methods are used to identify optimal design instantiations of the material that achieve programmable properties over ranges of strain as high as 9.1% or achieve any desired stiffness over ranges of externally applied stresses as high as 10.6 MPa without failing. A macro‐scale 2D version of the material's cell is fabricated and controlled to achieve desired stiffness values.