An apparatus for ultrasonically bonding two or more layers of material , the apparatus comprising: anvil means and horn means for gripping a portion of the layers of material and for ultrasonically bonding the gripped portion; and a pressure device configured to press the horn means downward, wherein the anvil means and the horn means comprise: outer protrusions for gripping an outer region of the gripped portion of the layers , the outer protrusions of the anvil means being arranged to face the outer protrusions of the horn means , respectively; and medial protrusions for gripping an inner region of the gripped portion of the layers , the medial protrusions of the anvil means being arranged to face the medial protrusions of the horn means , respectively; wherein the outer protrusions protrude by an amount less than the medial protrusions ; wherein the pressure device presses the horn means downward to apply a first gripping force on the outer region that is gripped by the outer protrusions of the anvil means and the horn means , and a second gripping force on the inner region that is gripped by the medial protrusions of the anvil means and the horn means ; and wherein the first gripping force is less than the second gripping force. anvil means and horn means for gripping a portion of the layers of material and for ultrasonically bonding the gripped portion; and a pressure device configured to press the horn means downward, wherein the anvil means and the horn means comprise: outer protrusions for gripping an outer region of the gripped portion of the layers , the outer protrusions of the anvil means being arranged to face the outer protrusions of the horn means , respectively; and medial protrusions for gripping an inner region of the gripped portion of the layers , the medial protrusions of the anvil means being arranged to face the medial protrusions of the horn means , respectively; wherein the outer protrusions protrude by an amount less than the medial protrusions ; wherein the pressure device presses the horn means downward to apply a first gripping force on the outer region that is gripped by the outer protrusions of the anvil means and the horn means , and a second gripping force on the inner region that is gripped by the medial protrusions of the anvil means and the horn means ; and wherein the first gripping force is less than the second gripping force. outer protrusions for gripping an outer region of the gripped portion of the layers , the outer protrusions of the anvil means being arranged to face the outer protrusions of the horn means , respectively; and medial protrusions for gripping an inner region of the gripped portion of the layers , the medial protrusions of the anvil means being arranged to face the medial protrusions of the horn means , respectively; wherein the outer protrusions protrude by an amount less than the medial protrusions ; wherein the pressure device presses the horn means downward to apply a first gripping force on the outer region that is gripped by the outer protrusions of the anvil means and the horn means , and a second gripping force on the inner region that is gripped by the medial protrusions of the anvil means and the horn means ; and wherein the first gripping force is less than the second gripping force. <EOS>