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On the development of direct displacement control method: application to local and nonlocal damage mechanics

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Abstract

The present work deals with development of method called direct displacement control (DDCM) that explicitly imposes the incremental displacement without recourse to pseudo force vector while solving nonlinear problems from solid mechanics. The limitation of the approaches, generalized displacement control method and displacement control method are overcome in DDCM approach while achieving faster inter-element force balance in finite element framework (FEF). The important application of DDCM is proposed to be elasto-plastic damage (EPD), as the damage-induced softening makes internal force balance difficult. The 1D local, and 1D and 2D nonlocal EPD formulations are developed; the derivation of 1D algorithmic tangent modulus is proposed. The applicability and correctness of DDCM approach are successfully demonstrated solving several 1D and 2D local and nonlocal EPD problems within FEF (in-house code and ABAQUS®).

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Acknowledgements

The author gratefully acknowledges the financial support provided by VSSC, ISRO, India, under Project number ICSR/ISRO-IITM/ASE/14-15/SHAT. The author also gratefully acknowledges several technical discussions with Prof. Shyam Keralavarma of the Aerospace engg. dept. of IIT Madras, which helped in the validation of several derived equations in the present work.

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  1. Structural mechanics group, Department of Aerospace Engineering, Indian Institute of Technology Madras, Chennai, TN, 600036, India

    Shantanu Shashikant Mulay & Harini Subramanian

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  1. Shantanu Shashikant Mulay
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  2. Harini Subramanian
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Correspondence to Shantanu Shashikant Mulay.

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Mulay, S.S., Subramanian, H. On the development of direct displacement control method: application to local and nonlocal damage mechanics. Int J Adv Eng Sci Appl Math 12, 101–124 (2020). https://doi.org/10.1007/s12572-020-00274-6

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