In the present paper, the problem of a collision of a bullet with a membrane is studied under the following assumptions: (i) the armor is an intact membrane of zero flexural rigidity and very high tensile Young's modulus, (ii) the bullet has a shape of a paraboloid on the front part, (iii) the contact problem for the bullet meeting the membrane is quasi-static, and (iv) the rupture of the vest occurs at some limiting tension of the membrane at the apex of the paraboloid. The final result of this modeling study can be formulated as follows: the armor is safe if the kinetic energy of the bullet does not exceed a certain critical maximum for this armor determined theoretically or experimentally.
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