{'fraction_non_alphanumeric': 0.03175895765472313, 'fraction_numerical': 0.012214983713355049, 'mean_word_length': 5.715846994535519, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
A Numerical Parametric Investigation of Localization and Forming Limits

The ability of a theoretical model to accurately predict localization and failure strains, which characterize the formability of materials, has been a controversial subject as researchers have tried various analytical methods over the years to predict forming limit diagrams. In this work, we analyze various aspects of finite element modeling in which large deformation plasticity is coupled with continuum damage evolution. In the context of the Bammann-Chiesa-Johnson (BCJ) internal state variable model, we examine different finite element codes (DYNA3D, PRONTO3D, and JAC3D), sheet thicknesses (1.0 cm and 0.1 cm), types of instabilities (geometric perturbation and various initial void volume fraction mismatches), element types [solid continuum, Hughes and Liu (1980), and Belytschko and Tsay (1983)], mesh refinement, and two-stage nonproportional straining conditions. By varying these parameters in finite element calculations for determining forming limits, we ascertain not only the forming limit diagrams in a short time but an understanding of parametric effects that have been issues of concern for the auto, steel, and aircraft industries.