In layered systems with porous substrates and a dense solid surface, stiffness and strength are inherently coupled through porosity-dependent relations, influencing their load-bearing behaviour. This work presents a systematic methodology for the assessment and design of such layer-substrate systems based on a criterion of balanced material utilization. A dimensionless parameter is defined to characterize the stress state in both components relative to their admissible limits, from which the optimal layer thickness is determined at equal stress levels in both constituents. Stress distributions are calculated using a numerical half-space model for layered contacts and evaluated through material-dependent equivalent stress criteria. The relationship between material utilization and load-carrying capacity is reduced to a scaling factor that combines the influence of porosity-dependent parameters. The approach establishes a direct link between the governing material parameters and structural design variables. Across the investigated parameter range, the utilization rate scales linearly with optimal layer thickness, whereas the load-carrying capacity follows a cubic relation. For a representative Ashby strength scaling coefficient of 𝐶𝜎 = 0.3, for example, a substrate porosity of 90% leads to a scaling factor of 1.6, corresponding to a possible load amplification of 60% relative to the homogeneous reference.
Grutza et al. (Thu,) studied this question.