Since your date is actually text, you must first convert it to a bona fide date using CONVERT. Then, use CONVERT on that date a second time to generate the text output you want.
SELECT CONVERT(varchar(20), CONVERT(datetime, '15.03.18', 4), 120);
Note that it is generally bad practice to store your dates as text. Hopefully you can use my answer to tidy up your table. For example, you could add a new datetime column new_dt and then update it using:
UPDATE yourTable
SET new_dt = CONVERT(datetime, old_dt, 4);
Don't worry about the internal format used by SQL Server. If you still need to display yyyy-mm-dd output, then use CONVERT again, as I did in my first query.
WEEK_DATE, and can you show us sample data?