梯度弹性的虚拟单元公式  

Virtual element formulation for gradient elasticity

作　　者：Peter Wriggers Blaž Hudobivnik 

机构地区：[1]Institute for Continuum Mechanics,Leibniz Universität Hannover,Hannover,Germany

出　　处：《Acta Mechanica Sinica》2023年第4期84-96,共13页力学学报（英文版）

基　　金：supported by the Deutsche Forschungsgemeinschaft(DFG,German Research Foundation)under Germany’s Excellence Strategy within the Cluster of Excellence PhoenixD,EXC 2122(Grant No.390833453).

摘　　要：虚拟单元法在过去十年中得到了发展,并应用于固体力学中的问题.目前已使用了不同的公式来解释该方法的顺序和稳定性,并应用到包括弹性和非弹性材料以及压裂过程的多种问题中.本文利用虚拟单元法固有的可能性,以简单有效的方式,建立C^(1)连续的弹性函数,研究固体高梯度弹性理论的虚拟单元公式.The virtual element method has been developed over the last decade and applied to problems in solid mechanics.Different formulations have been used regarding the order of ansatz,stabilization of the method and applied to a wide range of problems including elastic and inelastic materials and fracturing processes.This paper is concerned with formulations of virtual elements for higher gradient elastic theories of solids using the possibility,inherent in virtual element methods,of formulating C^(1)-continuous ansatz functions in a simple and efficient way.

关 键 词：虚拟单元 弹性理论 弹性材料 弹性函数 固体力学 高梯度 

分 类 号：O3[理学—力学]