Device-to-Device (D2D) communications can offload the traffic and boost the throughput of cellular networks. By caching files at users, content delivery traffic can be offloaded via D2D links, if a helper user are willing to send the cached file to the user who requests the file. Yet it is unclear how much energy needs to be consumed at a helper user to support the traffic offloading. In this paper, we strive to find the minimal energy consumption required at a helper user to maximize the amount of offloaded traffic. To this end, we introduce a user-centric proactive caching policy that can control the energy cost for a helper user to convey a file, and then optimize the caching policy to maximize the offloaded traffic. To reduce the energy during transmission, we optimize the transmit power to minimize the energy consumed by a helper to send a file. We analyze the relationship between traffic offloading and energy cost with the optimized caching policy and transmit power by numerical and simulation results, which demonstrate that a significant amount of traffic can be offloaded with affordable energy costs.