Problem – The explanation of nuclear properties from the strong force upwards has been elusive. It is not clear how binding energy arises, or why the neutrons are necessary in the nucleus at all. Nor has it been possible to explain, from first principles of the strong force, why any one nuclide is stable, unstable, or non-existent. Approach – Design methods were used to develop a conceptual mechanics for the bonding arrangements between nucleons. This was based on the covert structures for the proton and neutron as defined by the Cordus theory, a type of non-local hidden-variable design with discrete fields. Findings - Nuclear bonding arises from the synchronous interaction between the discrete fields of the proton and neutron. This results in not one but multiple types of bond, cis- and transphasic, and assembly of chains and bridges of nucleons into a nuclear polymer. The synchronous interaction constrains the relative orientation of nucleons, hence the nuclear polymer takes only certain spatial layouts. The stability of nuclides is entirely predicted by morphology of the nuclear polymer and the cis/transphasic nature of the bonds. The theory successfully explains the qualitative stability characteristics of all hydrogen and helium nuclides. Originality – Novel contributions include: the concept of a nuclear polymer and its mechanics; an explanation of the stability, instability, or non-existence of nuclides starting from the strong/synchronous force; explanation of the role of the neutron in the nucleus. The theory opens a new field of mechanics by which nucleon interactions may be understood.