On the strong discontinuity approach in finite deformation settings. Theoretical aspects and numerical simulation

Taking the strong discontinuity approach as a framework for modeling displacement discontinuities and strain localization phenomena, this Part 1 extends previous results of the authors, for infinitesimal strain settings, to finite deformation scenarios. By means of the strong discontinuity analysis, and for both damage and elastoplasticity continuum (stress-strain) constitutive models, projected discrete (tractions-displacement jumps) constitutive models are derived, together with the strong discontinuity conditions that restrict the stress states at the discontinuous regime. Also a variable bandwidth model, to automatically induce those strong discontinuity conditions, and a discontinuous bifurcation procedure, to determine the initiation and propagation of the discontinuity, are briefly sketched. Numerical simulation issues are tackled in Part 2 of the work.