Methods and devices are provided for support of a body structure. The devices can be adjusted within the body of a patient in a minimally invasive or non-invasive manner such as by applying energy percutaneously or external to the patient's body. The energy may include, for example, acoustic energy, radio frequency energy, light energy and magnetic energy. Thus, as the body structure changes size and/or shape, the size and/or shape of the annuloplasty rings can be adjusted to provide continued reinforcement. In certain embodiments, the devices include a body member including a shape memory material, and an energy absorption enhancement material configured to absorb energy in response to an activation energy. The energy absorption enhancement material is in thermal communication with said shape memory material. The body member has a first size of a dimension in a first configuration and a second size of the dimension in a second configuration, and is configured to be implanted in the first configuration into a heart. The body member is configured to transform from the first configuration to the second configuration in response to the activation energy. The second configuration is configured to reduce a dimension of a cardiac valve annulus in the heart.