Structural devices for energy dissipation can be designed to provide asymmetrical responses to cyclic axial loading. The energy dissipation devices can be designed to provide a known or predictable response to tensile loading, along with a different known or predictable response to compressive loading. The devices may include a filament which bears a portion of both tensile and compressive loads and a bracing device which provides lateral support to the filament to prevent buckling. Interlocks or a similar restraining mechanism can be used to resist part of either a compressive or tensile load. These components can be configured in such a manner as to provide an asymmetric response.