  Many stiff biological materials exhibiting outstanding compressive
strength/weight ratio are characterized by high porosity, spanning different
size-scales, typical examples being bone and wood. A successful bio-mimicking
of these materials is provided by a recently-obtained apatite, directly
produced through a biomorphic transformation of natural wood and thus
inheriting its highly hierarchical structure. This unique apatite (but also
wood and bone) is characterized by two major distinct populations of
differently-sized cylindrical voids, a porosity shown in the present paper to
influence failure, both in terms of damage growth and fracture nucleation and
propagation. This statement follows from failure analysis, developed through
in-silico generation of artificial samples (reproducing the two-scale porosity
of the material) and subsequent finite element modelling of damage, implemented
with phase-field treatment for fracture growth. It is found that small voids
promote damage nucleation and enhance bridging of macro-pores by micro-crack
formation, while macro-pores influence the overall material response and drive
the propagation of large fractures. Our results explain the important role of
multiscale porosity characterizing stiff biological materials and lead to a new
design paradigm, by introducing an in-silico tool to implement bio-mimicking in
new artificial materials with brittle behaviour, such as carbide or ceramic
foams.
