  There has been significant recent interest in the mechanics community to
design structures that can either violate reciprocity, or exhibit elastic
asymmetry or odd elasticity. While these properties are highly desirable to
enable mechanical metamaterials to exhibit novel wave propagation phenomena, it
remains an open question as to how to design passive structures that exhibit
both significant non-reciprocity and elastic asymmetry. In this paper, we first
define several design spaces for chiral metamaterials leveraging specific
design parameters, including the ligament contact angles, the ligament shape,
and circle radius. Having defined the design spaces, we then leverage machine
learning approaches, and specifically Bayesian optimization, to determine
optimally performing designs within each design space satisfying maximal
non-reciprocity or stiffness asymmetry. Finally, we perform multi-objective
optimization by determining the Pareto optimum and find chiral metamaterials
that simultaneously exhibit high non-reciprocity and stiffness asymmetry. Our
analysis of the underlying mechanisms reveals that chiral metamaterials that
can display multiple different contact states under loading in different
directions are able to simultaneously exhibit both high non-reciprocity and
stiffness asymmetry. Overall, this work demonstrates the effectiveness of
employing ML to bring insights to a novel domain with limited prior
information, and more generally will pave the way for metamaterials with unique
properties and functionality in directing and guiding mechanical wave energy.
