This is very interesting piece of music, even though there is no "story" to the piece.
Th piece was written for Antoine Tamestit, a frequent collaborator of Widmann’s, and was premiered at the Philharmonie de Paris on 28 October 2015 with the Orchestre de Paris conducted by Paavo Järvi.
From the web site of the publisher Schott:
The audience can expect ‘a unique concerto experience’ with Widmann’s Viola Concerto, where the tradition of the solo concerto genre is tested with characteristic refinement. The work begins without a cue from the conductor — the soloist just starts playing, and without the bow. Inventive playing techniques demonstrate the instrument’s versatility: the imitation of a sitar using a ‘trembling’ vibrato, or percussive use of the viola’s body whilst playing with the other hand. Throughout the piece, the soloist must behave like an actor following detailed stage directions, with a mixture of pride and self-irony. Widmann’s inventiveness is not limited to the solo part; for instance, a scotch glass is used to prepare the piano.
Schott provides a perusal score including all the stage directions (in German).
There's another discussion of the piece in German here.