We study the buckling of a one fiber composite whose matrix stiffness is slightly dependent on the compressive force. We show that the equilibrium curves of the system exhibit a limit load when the induced stiffness parameter gets bigger than a threshold. This limit load increases when increasing the stiffness parameter and is related to a possible localized path in the post-buckling domain. Such a change in the maximum load may be very desirable from a structural stand point.
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