The microstructure of the materials constituting a metallic frictional contact strongly influences tribological performance. Being able to tailor friction and wear is challenging due to the complex microstructure evolution associated with tribological loading. Here, we investigate the effect of the strain distribution on these processes. High-purity copper plates were morphologically surface textured with two parallel rectangles—referred to as membranes—over the entire sample length by micro-milling. By keeping the width of these membranes constant and only varying their height, reciprocating tribological loading against sapphire discs resulted in different elastic and plastic strains. Finite element simulations were carried out to evaluate the strain distribution in the membranes. It was found that the maximum elastic strain increases with decreasing membrane stiffness. The coefficient of friction decreases with increasing membrane aspect ratio. By analyzing the microstructure and local crystallographic orientation, we found that both show less change with decreasing membrane stiffness.