Impact of mathematical requirements on the invariant-based anisotropic constitutive models for non-linear biomaterials

doi:10.1016/j.ijnonlinmec.2022.104188

CORC > 金属研究所 > 中国科学院金属研究所

	Impact of mathematical requirements on the invariant-based anisotropic constitutive models for non-linear biomaterials
	Jin, Tao 3; Chams, Aya 3; Zhang, Xing 1,2
刊名	INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS
	2022-12-01
卷号	147 页码:14
关键词	Constitutive modeling Biomaterials Incompressibility Strong ellipticity Polyconvexity
ISSN号	0020-7462
DOI	10.1016/j.ijnonlinmec.2022.104188
通讯作者	Jin, Tao(tao.jin@uottawa.ca)
英文摘要	Finite element simulations are widely used to study the non-linear mechanical behavior of various biomaterials. Constructing an anisotropic strain energy function within the framework of hyperelasticity is an effective approach to describe the material constitutive behavior. The constructed strain energy function needs to satisfy several mathematical requirements to ensure the framework indifference, the material (near) incompressibility, and the material stability. While the framework indifference, or objectivity, can be naturally satisfied by the invariant-based constitutive formulation, how to enforce the material incompressibility and stability requires detailed discussions and careful treatments. The scope of this paper is to examine in detail the impacts of the mathematical requirements on the constitutive formulation for non-linear anisotropic biomaterials. Particularly, theoretical analyses and numerical simulations are combined to investigate the influences of the material incompressibility as a mathematical constraint and various convexity conditions on the invariant -based constitutive modeling. Through a constructed boundary value problem, analytical solutions are derived via the energy minimization and further used to quantify the influences of the material anisotropic and isotropic components on the material responses. The impact of the volumetric-deviatoric split is demonstrated separately for the strictly incompressible and nearly incompressible materials. In order to ensure the material stability, two commonly used convexity conditions, including the strong ellipticity condition and the polyconvexity condition, are discussed in detail. Several numerical examples are provided to demonstrate their impacts on the material stability under different loading conditions. These discussions are particularly relevant to model biomaterials that exhibit non-linear and anisotropic behaviors under complex loading conditions.
资助项目	Natural Sciences and Engineering Research Council of Canada (NSERC) under the Discovery Grants Program[RGPIN-2021-02561] ; Liao Ning Revitalization Talents Program[XLYC2007112]
WOS研究方向	Mechanics
语种	英语
出版者	PERGAMON-ELSEVIER SCIENCE LTD
WOS记录号	WOS:000852142300001
资助机构	Natural Sciences and Engineering Research Council of Canada (NSERC) under the Discovery Grants Program ; Liao Ning Revitalization Talents Program
内容类型	期刊论文
源URL	[http://ir.imr.ac.cn/handle/321006/175091]
专题	金属研究所_中国科学院金属研究所
通讯作者	Jin, Tao
作者单位	1.Univ Sci & Technol China, Sch Mat Sci & Engn, Hefei 230026, Peoples R China 2.Chinese Acad Sci, Inst Met Res, Shenyang 110016, Peoples R China 3.Univ Ottawa, Dept Mech Engn, Ottawa, ON K1N 6N5, Canada
推荐引用方式 GB/T 7714	Jin, Tao,Chams, Aya,Zhang, Xing. Impact of mathematical requirements on the invariant-based anisotropic constitutive models for non-linear biomaterials[J]. INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS,2022,147:14.
APA	Jin, Tao,Chams, Aya,&Zhang, Xing.(2022).Impact of mathematical requirements on the invariant-based anisotropic constitutive models for non-linear biomaterials.INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS,147,14.
MLA	Jin, Tao,et al."Impact of mathematical requirements on the invariant-based anisotropic constitutive models for non-linear biomaterials".INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS 147(2022):14.