SUMMARYDisplacement and mixed finite element formulations of shear localization in materials are presented. The formulations are based on hypoplastic constitutive laws for soils and the mixed enhanced treatment involving displacement, strain and stress rates as independently varied fields. Included in these formulations are the standard displacement method, the three-field mixed formulation, the enhanced assumed strain method and the mixed enhanced strain method. Several numerical examples demonstrating the capability and performance of the different finite element formulations are presented. The numerical results are compared with available experimental data for Hostun RF sand and numerical results for Karlsruhe sand on biaxial tests.
A new approach for the treatment of strain localization in inelastic material is proposed. It is based on energy minimization principles associated with micro-structure developments. Shear bands are treated as micro-shearing of rank-one laminates. It is assumed that the thickness of the shear band represented by its volume fraction tends to zero, and the energy inside the shear band is a function of the norm of the strain field. The existence of shear bands in the structure leads to an ill-posed problem which can be solved by means of energy relaxation. The performance of the proposed concept is demonstrated through numerical simulation of tension test under plane strain conditions. Numerical results show that mesh sensitivity can be completely removed.
EN] In this work, a nonlocal damage model is proposed for dynamic analysis of viscoplastic shell structures using the phasefield approach. A phase-field variable on the mid surface is introduced to characterize the nonlocal damage as well as the transition between undamaged and damaged phase. The total free energy in [1] is modified as a sum of Helmholtz free-energy and Ginzburg-Landau one. The latter is defined as a function of the phase-field variable and its corresponding gradient. This enhancement gives rise to an introduction of gradient parameters in terms of a substructure-related intrinsic length-scale. The evolution of the phase-field based damage variable can be found from the minimum principle of the dissipation potential [3]. The performance of the proposed model is demonstrated through numerical results of a plate with a circular hole.
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