Quantum mechanical based microscopic description of macroscopic mechanical properties including young's modulus,stress-strain curves …, is an attractive issue in theoretical material science. In the present effort, we tried to shed light on interconnection of macro- and micro- mechanical properties, our main purpose is to show that it is possible to find another way of achieving mechanical characteristics. In order to perform this task properly, we computed mechanical properties of widely applied Cu, Ag and Au from first-principle approach and then analyzed evolution of charge density, which is proven to has a deep connection with mechanical properties (i.e. stress-strain) and is a microscopic observable. In this regard, along with increasing strain in a systematic way , the topological characteristics of charge density was monitored. We observed that elastic-plastic transition in [100] coincides with topological transition of charge density while in [111] direction, elastic-plastic transition has a geometrical character. For the first time, we realized that t he key point in the strain induced evolution of charge density is the important role of cages (charge density minima) . Further investigation showed that variation of curvature of cages can locate Yield point and Ultimate Tensile Strength, which are two important points on stress-strain curves, regardless of tensile direction. Therefore , there would be another method of finding this points, i.e. studying of strain induced charge density evolution. Experimental tensile tests on Cu, Ag and Au in [111] direction showed that they are capable of forming mono-atomic chains [Phys.Rev.B78 115409 ]. In order to finding the theoretical parameter for chain-ability of Au, Ag and Cu, we used universal energy function and topology of charge density to attain more insight into process of elongation to mono- atomic chain . With the aid of stress-strain curves, we found that chaining process starts before ultimate tensile strength, and also we found that critical points of charge density are influential in chain formation. Using above mentioned information, we proved that Au is the most promising metal for ending up to a mono-atomic chain. As stated before, cage critical points are important in the process of chain formation and the amount of charge density in them can predict that which metal is capable of elongation to mono atomic chain. Further investigation lead us to a new conclusion that the cage-ring-cage angle could provide a good reason for formation of A uAg alloy chain. Keywords: First principle study, Quantum stress, Mechanical properties , topology of charge density , mono-atomic chains, Au, Ag, Cu.