A corrugated circular membrane (1) is proposed, in particular for a pump, including a total artificial heart. It comprises at least one corrugated circular segment (2), adjacent to a circular rim portion (3) as well as normally at least three and not more than 15 circular segments. The thickness (t) in the at least one corrugated circular segment (2) varies by less than 20% within the at least one corrugated circular segment (2) and is at least a factor of two smaller than the maximum thickness of the circular rim portion (3), and the radial shape of the at least one corrugated circular segment (2) in the position of no strain is shaped based on a series circular segments, which can at most be semi-circles, the circle centres of which are sequentially positioned along a radial direction, and wherein the circle centre of at least one of the innermost and the outermost circular segment is at a distance from a global membrane mid plane different from the distance the circle centres of the other circular segments from said global membrane mid plane.
