Topological changes in birods and loops

We develop a new theoretical framework for birods—a model for 2-braids and intertwined molecules such as DNA—grounded in continuum mechanics and built upon invariance principles. We represent birods as Cosserat curves enriched by additional phase fields. We look at large strain setting and consider virtually varying reference configurations as a tool for describing structural mutations like those induced by the helicase in DNA. Actions are associated with each independent mechanism that changes the birod shape. We deduce pertinent balance equations by requiring objectivity to the power of external actions relatively to virtually varying reference configurations and a power of disarrangement. We do not postulate the expression of the inner power of actions, which is instead derived. In other words, we deliberately avoid the principle of virtual power, that is, we do not postulate a weak form of the balance equations in dynamical setting. Then, by looking at loops, we find closed form expressions of the energy changes due to variations of the loop writhe number. The results pertain to a class of mechanisms that includes DNA supercoiling.