  By extending the classical Peyrard-Bishop model, we are able to obtain a
fully analytical description for the mechanical resistance of DNA under
stretching at variable values of temperature, number of base pairs and
intrachains and interchains bonds stiffness. In order to compare elasticity and
temperature effects, we first analyze the system in the zero temperature
mechanical limit, important to describe several experimental effects including
possible hysteresis. We then analyze temperature effects in the framework of
equilibrium statistical mechanics. In particular, we obtain an analytical
expression for the temperature dependent melting force and unzipping assigned
displacement in the thermodynamical limit, also depending on the relative
stability of intra vs inter molecular bonds. Such results coincide with the
purely mechanical model in the limit of zero temperature and with the
denaturation temperature that we obtain with the classical transfer integral
method. Based on our analytical results, explicit analysis of the phase
diagrams and cooperativity parameters are obtained, where also discreteness
effect can be accounted for. The obtained results are successfully applied in
reproducing the thermomechanical experimental melting of DNA and the response
of DNA hairpins. Due to its generality, the proposed approach can be extended
to other thermomechanically induced molecular melting phenomena.
