Variational damage model:A new paradigm for fractures

作     者：Huilong REN Timon RABCZUK Xiaoying ZHUANG 

作者机构：Institute of PhotonicsDepartment of Mathematics and PhysicsLeibniz University HannoverHannover 30167Germany State Key Laboratory of Disaster Reduction in Civil EngineeringCollege of Civil EngineeringTongji UniversityShanghai 200092China Institute of Structural MechanicsBauhaus-University at WeimarWeimar 99423Germany 

出 版 物：《Frontiers of Structural and Civil Engineering》 (结构与土木工程前沿(英文版))

年 卷 期：2025年第19卷第1期

页      面：1-21页

核心收录：

学科分类：08[工学] 081304[工学-建筑技术科学] 0805[工学-材料科学与工程（可授工学、理学学位）] 080502[工学-材料学] 0813[工学-建筑学] 

基　　金：support from ERC Grant COTOFLEXI(No.802205) 

主　　题：fracture damage mechanics multi-damage variational principle 

摘      要：The computational modeling of fracture in solids using damage mechanics faces challenges with complex crack *** can be addressed by using a variational framework to reformulate the damage *** this paper,we propose several mathematically elegant variational damage models(VDMs)for fracture mechanics without explicitly using damage *** on the energy densityϕ,the fracture energy density is formulated as=ϕ/(1+ℓϕ/G_(c))and the damage variable is expressed as s=ϕ/(ϕ+G_(c)/ℓ),which satisfy|_(ϕ→∞)=G_(c)/ℓand s|_(ϕ→∞)=1 asϕapproaches *** limits demonstrate that the new energy density converges to the Griffith energy release rate at full-damage *** VDM profoundly modified the energy functional,implicitly incorporating the damage *** a generalization of previous model,we propose a family of VDMs of varying ***,we develop a multidamage model to account for different types of energy densities,such as elastic thin plate and gradient *** this functional,it is straightforward to deduce the governing equation for automatically evolving *** formulations can be employed in conventional finite element method or other numerical methods with minimal *** to the phase field method with the same mesh density,a sharper crack interface can be *** demonstrate the capabilities of the proposed variational damage formulations using representative numerical examples.