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 (111, 111a, 111b, 151, 151a, 151b, 157) for gripping an outer region of the gripped portion of the layers, the outer protrusions (111, 111a, 111b, 157) of the anvil means being arranged to face the outer protrusions (151, 151a, 151b, 157) of the horn means, respectively; and medial protrusions (112, 152, 158) for gripping an inner region of the gripped portion of the layers, the medial protrusions (112, 158) of the anvil means being arranged to face the medial protrusions (152, 158) of the horn means, respectively; wherein the outer protrusions (111, 111a, 111b, 151, 151a, 151b, 157) protrude by an amount less than the medial protrusions (112, 152, 158); 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 (111, 111a, 111b, 151, 151a, 151b, 157) of the anvil means and the horn means, and a second gripping force on the inner region that is gripped by the medial protrusions (112, 152, 158) 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 (111, 111a, 111b, 151, 151a, 151b, 157) for gripping an outer region of the gripped portion of the layers, the outer protrusions (111, 111a, 111b, 157) of the anvil means being arranged to face the outer protrusions (151, 151a, 151b, 157) of the horn means, respectively; and medial protrusions (112, 152, 158) for gripping an inner region of the gripped portion of the layers, the medial protrusions (112, 158) of the anvil means being arranged to face the medial protrusions (152, 158) of the horn means, respectively; wherein the outer protrusions (111, 111a, 111b, 151, 151a, 151b, 157) protrude by an amount less than the medial protrusions (112, 152, 158); 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 (111, 111a, 111b, 151, 151a, 151b, 157) of the anvil means and the horn means, and a second gripping force on the inner region that is gripped by the medial protrusions (112, 152, 158) of the anvil means and the horn means; and wherein the first gripping force is less than the second gripping force. outer protrusions (111, 111a, 111b, 151, 151a, 151b, 157) for gripping an outer region of the gripped portion of the layers, the outer protrusions (111, 111a, 111b, 157) of the anvil means being arranged to face the outer protrusions (151, 151a, 151b, 157) of the horn means, respectively; and medial protrusions (112, 152, 158) for gripping an inner region of the gripped portion of the layers, the medial protrusions (112, 158) of the anvil means being arranged to face the medial protrusions (152, 158) of the horn means, respectively; wherein the outer protrusions (111, 111a, 111b, 151, 151a, 151b, 157) protrude by an amount less than the medial protrusions (112, 152, 158); 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 (111, 111a, 111b, 151, 151a, 151b, 157) of the anvil means and the horn means, and a second gripping force on the inner region that is gripped by the medial protrusions (112, 152, 158) of the anvil means and the horn means; and wherein the first gripping force is less than the second gripping force.