The phrase "impenetrable by" is correct and can be used in written English.
You can use it to describe something that cannot be affected or influenced by something else, or cannot be understood or solved. Example: The walls of the castle were impenetrable by the enemy's arrows, making it impossible for them to conquer it.
Markets dominated by major players with huge promotional budgets and economies of scale can seem impenetrable by small businesses.
He's impenetrable by axe, they discover, and he ends up disgustingly ripping part of somebody's head off.
He was known by the people as "the Donald," and his crown was protected by an enchanted golden helmet said to be impenetrable by any sword.
Announcing his Oscar win, the Academy hailed him for a body of work that can be teasing, provocative and impenetrable by turns.
Overcoming deeply held cultural beliefs and traditions will not be easy, especially in outlying rural districts impenetrable by communications from the capital.
The dogma meant that the genetic message was impenetrable by information from outside the cell, thus excluding the Lamarckian thesis that acquired characteristics could be inherited.
The porky broth is of the thick, impenetrable-by-light milky tonkotsu variety and has an almost gamey flavor to it; it is not for the faint of heart.
The swampland was impenetrable, except by hounds.
The existence of cosmopolitan species is explained by "improbable dispersal," Darwin's term for dispersal across seemingly impenetrable barriers by "occasional means of transport" such as ocean currents, winds, and floating ice.
But with the aid of a collection of "impenetrable" essays by the "wacky French psychoanalyst" Jacques Lacan, Knipfel ambles his way back to relative mental health.
It is a "surreal, shambolic work, to an impenetrable libretto by Paul Haines" and is "more closely related to the nonlinear, associative cinema of avant-garde filmmakers Kenneth Anger, Stan Brakhage... than to any musical parallel..
