Felix Mendelssohn The Complete String Quartets Cedille Records 90000 082 (3 CDs) July 10, 2005 By Wynne Delacoma Mendelssohn is certainly a classical music household name, and his quartets are beloved by string ensembles and audiences alike. But not until relatively recently have ensembles rushed to perform cycles of his complete works for string quartet.   For generations, ambitious ensembles have attempted complete cycles of quartets by Beethoven, Haydn and Mozart. Those works are among classical music's epic challenges, ones by which an ensemble tests its mettle. Mendelssohn's string quartets have never quite entered that rarefied realm. But the dynamic young, Illinois-based Pacifica Quartet has taken on the Mendelssohn challenge in a new three-CD set issued by Chicago's Cedille Records. Including the seven quartets and four other chamber pieces, the CDs are an exciting showcase for the Pacifica's brand of exuberant, polished musicmaking.   Now celebrating its 10th season, the Pacifica makes a persuasive argument for Mendelssohn's artistry. There is a sinew as well as gracious delicacy in these performances. The mix of introspection and windswept energy in the opening of the E-minor quartet, Op. 44 No. 2, typifies Pacifica's thoughtful approach to a composer whose reputation too often rests on the airy flights of works like "A Midsummer Night's Dream."   The Pacifica's repertoire is varied, and the ensemble has wrestled memorably with Elliott Carter's knotty quartets. The virtuosity and intense commitment it brings to a contemporary master like Carter give Mendelssohn's music an equally powerful glow.