Modelling finite deformation and progressive failure of hyperelastic solid with implicit BA-NOSB-PD

• Published in: Computer methods in applied mechanics and engineering Vol. 431; p. 117260
• Main Authors: Wang, Luyu, Yin, Zhen-Yu
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.11.2024
• Subjects: Finite deformation; Hyperelastic material; Non-ordinary state-based peridynamics; Progressive failure; Quasi-static condition; Progressive failure; Finite deformation; Non-ordinary state-based peridynamics; Quasi-static condition; Hyperelastic material
• ISSN: 0045-7825
• DOI: 10.1016/j.cma.2024.117260

•A hyperelastic non-ordinary state-based peridynamics (NOSB-PD) is proposed.•A bond-associated (BA) scheme is integrated into the hyperelastic NOSB-PD to improve numerical stability in calculating deformation gradient.•An implicit scheme is developed to discretize the BA-NOSB-PD equations, enabling damage simulation under quasi-static conditions.•Effects of crack patterns, loading conditions, and material properties on damage evolution are thoroughly analysed. Deformation and failure in hyperelastic materials exhibit unique characteristics that are absent in purely elastic materials. The presence of pre-existing cracks and holes further increases these complications. To study this phenomenon, an implicit hyperelastic non-ordinary state-based peridynamics (NOSB-PD) is developed for modelling finite deformation and damage under quasi-static conditions. Highlights in the present work include: (1) integration of a bond-associated (BA) scheme to improve numerical stability in calculation of the deformation gradient; (2) development of an implicit scheme to discretize PD equations, facilitating simulation of quasi-static damage process; (3) implementation of an equivalent strain-based criterion to accurately determine PD bond breakage; and (4) comprehensive analysis of the effects of crack patterns, loading conditions, and material properties on damage evolution. Next, the proposed implicit BA-NOSB-PD is validated through benchmark tests to examine its convergence performance and accuracy. Comparative analysis is conducted to explore deformation and damage characteristics in failure under shear and tensile loadings. Then, the proposed method is applied to study more complex scenarios involving multiple holes and edge crack. Simulation results provide insights into underlying mechanisms that govern the failure process under large deformation condition.