kill -QUIT process_id will cause a core dump from a running process (assuming that resource limits allow it).
Or see man 3 abort for causing a program to dump itself.
Added: From an interactive shell, a running program can be made to abort with the quit key, usually Ctrl+\, which sends a SIGQUIT just as the more common Ctrl+C sends a SIGINT. This is identical to the kill -QUIT… it’s just easier to type if you are on the controlling terminal. See man 1 stty if your default quit key is different.