The venerable British heavy-metal band Def Leppard is postponing several tour dates, including one locally, due to illness. A posting on the group’s website said all shows from Tuesday’s San Antonio concert to Feb. 17 in Allentown, Pennsylvania, will be rescheduled, with existing tickets honored. The band, which was scheduled to play Brooklyn’s Barclays Center on Feb. 16, is touring in support of its eleventh studio album, the eponymous “Def Leppard,” released in October. Drummer Rick Allen tweeted, “The doctor basically said that if [singer] Joe [Elliott] continues to sing without resting his throat for a month he might do permanent damage.”