In this article, the authors obtain an integral representation for the relaxation of the functional
F(x, u, Ω):={∫_Ω f(x, u(x), εu(x))dx if u ∈ W^{1, 1}(Ω, R^N), +∞ otherwise,
in the space of functions of bounded deformation, with respect to L¹-convergence. Here εu represents the absolutely continuous part of the symmetrized distributional derivative εu.f(x, p, ξ) satisfying weak convexity assumption.