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

doi:10.1016/j.ijnonlinmec.2022.104188

IMR OpenIR

	Impact of mathematical requirements on the invariant-based anisotropic constitutive models for non-linear biomaterials
	Jin, Tao 1; Chams, Aya 1; Zhang, Xing 2,3
通讯作者	Jin, Tao(tao.jin@uottawa.ca)
	2022-12-01
发表期刊	INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS
ISSN	0020-7462
卷号	147 页码:14
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.
关键词	Constitutive modeling Biomaterials Incompressibility Strong ellipticity Polyconvexity
资助者	Natural Sciences and Engineering Research Council of Canada (NSERC) under the Discovery Grants Program ; Liao Ning Revitalization Talents Program
DOI	10.1016/j.ijnonlinmec.2022.104188
收录类别	SCI
语种	英语
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
WOS类目	Mechanics
WOS记录号	WOS:000852142300001
出版者	PERGAMON-ELSEVIER SCIENCE LTD
引用统计	被引频次：1[WOS] [WOS记录] [WOS相关记录]
文献类型	期刊论文
条目标识符	http://ir.imr.ac.cn/handle/321006/175092
专题	中国科学院金属研究所
通讯作者	Jin, Tao
作者单位	1.Univ Ottawa, Dept Mech Engn, Ottawa, ON K1N 6N5, Canada 2.Chinese Acad Sci, Inst Met Res, Shenyang 110016, Peoples R China 3.Univ Sci & Technol China, Sch Mat Sci & Engn, Hefei 230026, Peoples R China
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.