Title: Existence of minimizers for the pure displacement problem in nonlinear elasticity
Abstract: We show that the total energy of the pure displacement problem in nonlinear elasticity possesses a unique global minimizer for a large class of hyperelastic materials, including that of Saint Venant—Kirchhoff, provided the density of the applied forces are small in Lp‐norm. We also establish a nonlinear Korn inequality with boundary showing that the H1‐distance between two deformation fields is bounded, up to a multiplicative constant, by the L2‐distance between their Cauchy‐Green strain tensors.