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On the strong discontinuity approach in finite deformation settings. (English) Zbl 1031.74010
Summary: Taking the strong discontinuity approach as a framework for modelling displacement discontinuities and strain localization phenomena, this work extends previous results in infinitesimal strain settings to finite deformation scenarios. By means of the strong discontinuity analysis, and taking isotropic damage models as target continuum (stress-strain) constitutive equation, we derive projected discrete (tractions-displacement jumps) constitutive models, together with strong discontinuity conditions that restrict the stress states at the discontinuous regime. 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. The large strain counterpart of a non-symmetric finite element with embedded discontinuities, frequently considered in the strong discontinuity approach for infinitesimal strains, is then presented. Finally, some numerical experiments display the theoretical issues and emphasize the role of large strain kinematics in the obtained results.
MSC:
74A45Theories of fracture and damage
74S05Finite element methods in solid mechanics