  We consider a new class of problems in elasticity, referred to as Data-Driven
problems, defined on the space of strain-stress field pairs, or phase space.
The problem consists of minimizing the distance between a given material data
set and the subspace of compatible strain fields and stress fields in
equilibrium. We find that the classical solutions are recovered in the case of
linear elasticity. We identify conditions for convergence of Data-Driven
solutions corresponding to sequences of ap- proximating material data sets.
Specialization to constant material data set sequences in turn establishes an
appropriate notion of relaxation. We find that relaxation within this
Data-Driven framework is fundamentally different from the classical relaxation
of energy functions. For instance, we show that in the Data-Driven framework
the relaxation of a bistable material leads to material data sets that are not
graphs.
