The mechanical properties - such as strength, of materials depends on their structure at various length scales - macro (what shape is it?), micro (grains, domains etc.), atomic (atomic defects, crystallinity, bonding: metallic Vs ionic Vs covalent).

This is an incredibly complex topic. We have to take a different perspective on all these aspects depending on the materials we're studying - a metal, plastic or ceramic, bio.

Sadly there's no silver bullet! This is why a large part of Materials Science is dedicated to this very topic.

Perhaps interestingly the answer is basically never as simple as how strong are the atomic bonds.