Variational damage model:A new paradigm for fractures  

作　　者：Huilong REN Timon RABCZUK Xiaoying ZHUANG 

机构地区：[1]Institute of Photonics,Department of Mathematics and Physics,Leibniz University Hannover,Hannover 30167,Germany [2]State Key Laboratory of Disaster Reduction in Civil Engineering,College of Civil Engineering,Tongji University,Shanghai 200092,China [3]Institute of Structural Mechanics,Bauhaus-University at Weimar,Weimar 99423,Germany

出　　处：《Frontiers of Structural and Civil Engineering》2025年第1期1-21,共21页结构与土木工程前沿(英文版)

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

摘　　要：The computational modeling of fracture in solids using damage mechanics faces challenges with complex crack topology.This can be addressed by using a variational framework to reformulate the damage mechanics.In this paper,we propose several mathematically elegant variational damage models(VDMs)for fracture mechanics without explicitly using damage variables.Based 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 infinity.These limits demonstrate that the new energy density converges to the Griffith energy release rate at full-damage state.The VDM profoundly modified the energy functional,implicitly incorporating the damage field.As a generalization of previous model,we propose a family of VDMs of varying orders.Additionally,we develop a multidamage model to account for different types of energy densities,such as elastic thin plate and gradient elasticity.Using this functional,it is straightforward to deduce the governing equation for automatically evolving fractures.These formulations can be employed in conventional finite element method or other numerical methods with minimal modifications.Compared to the phase field method with the same mesh density,a sharper crack interface can be achieved.We demonstrate the capabilities of the proposed variational damage formulations using representative numerical examples.

关 键 词：fracture damage mechanics multi-damage variational principle 

分 类 号：TU528[建筑科学—建筑技术科学]