Encrypting (large) files in PHP with openSSL

I'm trying to encrypt (big) files in PHP using AES and have looked into using Mcrypt and OpenSSL, the problem is all solutions I have found so far only encrypt strings, and the files I'm trying to encrypt would trigger the max memory limit for PHP (which unfortunately can't be set higher), how would I go about achieving this?

You could use CBC encryption using Mcrypt and then encrypt a segment of data at a time. Make sure that the segment is x times the block size of the used cipher (e.g. 16 bytes for AES). Encrypt the segment and take the last block of the generated ciphertext and use it as IV for the next segment. The final segment should be PKCS#7 padded (plenty of examples out there including in the mcrypt_encrypt comments).

By chaining the segments together you get a ciphertext indistinguishable from a single encrypt (test your code using this information). Decryption is identical, using the ciphertext as IV. To see how it works, look at the CBC encryption method:

EDIT: if possible you should use the OpenSSL equivalent functionality. That's not (well) documented, but you should be able to do the same using the code found in the link within the comment that Scott mentioned. Note that you should first perform everything without padding, and then for the final segment with padding.