{'fraction_non_alphanumeric': 0.015080113100848256, 'fraction_numerical': 0.003770028275212064, 'mean_word_length': 5.896103896103896, '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}}
Topology optimization of energy absorbing structures with maximum damage constraint

A novel density‐based topology optimization framework for plastic energy absorbing structural designs with maximum damage constraint is proposed. This framework enables topologies to absorb large amount of energy via plastic work before failure occurs. To account for the plasticity and damage during the energy absorption, a coupled elastoplastic ductile damage model is incorporated with topology optimization. Appropriate material interpolation schemes are proposed to relax the damage in the low‐density regions while still ensuring the convergence of Newton‐Raphson solution process in the nonlinear finite element analyses. An effective method for obtaining path‐dependent sensitivities of the plastic work and maximum damage via adjoint method is presented, and the sensitivities are verified by the central difference method. The effectiveness of the proposed methodology is demonstrated through a series of numerical examples. Copyright © 2017 John Wiley & Sons, Ltd.