Mechanical metamaterials are engineered materials designed to showcase extraordinary macroscopic properties. These macroscopic properties are determined by the mechanical phenomena of the microstructure rather than the physical properties of the constituent materials at the microscopic level. The microstructure is often defined within fundamental building blocks known as unit cells, which are replicated to compose the material. Thus, designing the unit cells allows for precise control and manipulation of mechanical characteristics. This presentation studies unit cell design concepts based on self-contact mechanisms. The variation in the topology of contacts at the microscopic level results in a variation of the stiffness properties of the macroscopic material. Consequently, attaining a mechanical metamaterial with programmable (or tuneable) stiffness. We employ nonlinear finite element models from computational contact mechanics to illustrate that progressive, degressive, and discontinuous stiffness characteristics are achievable as programmable stiffness effects. As a result, mechanical metamaterials founded on microscopic-level contact mechanisms can be used to design on-demand materials where the stiffness is programmed precisely to the engineering task at hand, thus exhibiting superior performance to standard mechanical materials.