A nonlinear finite element model for the stress analysis of soft solids with a growing mass

INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES

卷:51

Article

Liu, Yin¹  Zhang, Hongwu¹  Zheng, Yonggang¹  Zhang, Sheng¹  Chen, Biaosong¹ 

[1] Dalian Univ Technol, Fac Vehicle Engn & Mech, Dept Engn Mech, State Key Lab Struct Anal Ind Equipment, Dalian 116024, Peoples R China

关键词: Mass growth;    Finite element method;    Soft material;    Multiplicative decomposition;    Free growth;   

DOI  :  10.1016/j.ijsolstr.2014.04.010

来源: Elsevier

【 摘 要 】

The paper presents a new finite element (FE) model for the stress analysis of soft solids with a growing mass based on the work of Lubarda and Hoger (2002). Contrary to the traditional numerical methods emphasizing on the influence of growth on constitutive equations, an equivalent body force is firstly detected, which is resulted from the linearization of the nonlinear equation and acts as the driver for material growth in the numerical aspect. In the algorithm, only minor correction on the traditional tangent modulus is needed to take the growth effects into consideration and its objectivity could be guaranteed comparing with the traditional method. To solve the resulted equation in time domain, both explicit and implicit integration algorithms are developed, where the growth tensor is updated as an internal variable of Gauss point. The explicit updating scheme shows higher efficiency, while the implicit one seems to be more robust and accurate. The algorithm validation and its good performance are demonstrated by several two-dimensional examples, including free growth, constrained growth and stress dependent growth. (C) 2014 Elsevier Ltd. All rights reserved.

【 授权许可】

Free