All organisms have cell membranes which are composed of lipids. The length of lipids affects the elastic properties of the cell membrane which play an important role in cell's survival. For instance, membrane flexibility controls the amount of stress that a membrane can sustain before pore formation. In the bacterial cell membranes, the pore formation is also induced by naturally occurring peptides and synthetic amphiphilic copolymers. For this reason, they are one of the most anticipated novel antimicrobial materials. Understanding the mechanism of their action is essential for their use against microbes. Using coarse-grained simulations and a mean field model, we study lipid bilayer membranes under the variation of stress and tail length, as well as their interaction with flexible amphiphilic copolymers. We used a polymer brush model to describe the free energy of the membrane in terms of entropic contributions and hydrophobic interactions. As the stress is increased on the membranes, at high stresses, the membrane transits to a stable pore state in agreement with simulation results. The increased hydrophobic interaction energy at the interface at high stresses leads to the formation of a pore. The hydrophobic interactions induce a contraction stress and the entropy of lipid tails induces a repulsive stress on the membrane. The simulations show that the entropic contribution to the stress, at its positive values, decreases as the length of lipid tails is increased. This increases the tendency of the membrane with the longer lipids to withstand larger stresses before rupturing into pores, as the internal repulsive stress is reduced. We show that copolymers can enhance the pore stability by decreasing the line tension due to the weak adsorption along the rim of the pore. The bilayers studied in our simulations do not require high copolymer concentration at the pores nor any self-organization of the copolymers to open the pore. This is in contrast to the commonly known barrel stave model where the copolymers are assumed to be strongly localised at the rim of the pore. In the presence of the copolymers, we observe a meta-stable pore state of membrane. This happens at a specific concentration of copolymers depending upon the stress acting on the membrane. If the concentration is further increased from this value, then, the membrane shifts to a stable pore state. An increase in the probability of pore formation is observed as the length of copolymers or stress on the membrane are increased. Both the solvent and copolymer permeability increase as the pore becomes stable.