本文讨论微势近场动力学模型在模拟结构无限变形和有限变形的一般性与普适性。微势近场动力学模型中键长变化采用二次方作为度量，针对平面应力和应变问题提出了应变的非局部度量形式，与经典连续介质力学一致将键长变化分解为两部分，一部分由体积应变引起，另一部分由偏差应变引起。变形键中产生的微势能假设为2个长度变化分量的函数，物质点处的非局部弹性应变能密度通过该物质点近场内键势的积分获得。物质点间采用指数-指数微势函数，通过非局部弹性应变能密度的Fréchet导数，建立依赖于微势函数的一般本构关系。数值实例进一步说明了所提出的模型能够模拟固体材料中的无限和有限变形。
This work discusses a generality of a recently developed micro-potential-based peridynamics and its applications to infinite and finite deformations. A square measure of the bond length change is applied and a generalized Peridynamic strain for plane stress and strain problems is developed to decompose the bond length change into two parts, one resulting from the volumetric PD strain and the other from the deviatoric PD strain. The micro potential generated in the deformed bond is postulated as a function of both length change components. The nonlocal elastic strain energy density at a material point is computed by the integral of the bond potential over the horizon. Through the Fréchet derivative of the nonlocal elastic strain energy density, a general constitutive relation depending on the micro-potential function is well formulated. Numerical examples further illustrate the ability of the proposed model to model both infinite and finite deformations in solid materials.
2023,45(15): 52-58 收稿日期：2023-02-04
DOI：10.3404/j.issn.1672-7649.2023.15.010
分类号：O343.1
基金项目：国家自然科学基金资助项目（52201323); 江苏省自然科学基金资助项目（BK20200998）
作者简介：刘仁伟(1992-),男,博士,讲师,研究方向为冰区结构物载荷特性
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