The Finite Element Computation Method With Varying Multi-scale Domains For Structural Damage Evolution Analysis

In the failure analysis of material and structure,deterioration initiates from micro defects,finally leads to failure of structures in macro-scale.In order to investigate the mechanism of structure failure numerically,vulnerable parts should be modelled in small scale considering voids initiation,damage evolution and crack propagation.While the rest part with low stress level should be modelled in large scale without damage evolution.During service life of the structures,damage could evolve across the trans-scale boundary.However the computational precision of current multi-scale could not hold when cross-scale damage evolution occurs.The aim of the work is to develop a finite element method with varying scale domains.The formation and transformation of finite element equation is obtained from variational analysis,the computation precision and effectiveness of the method is investigated.The element connection method in multi-scale modelling is improved to make its application more universal.A Shear-enhanced Beam Lattice(SBL)model is established to simulate fracture process in material micro structure.The mechanism of wing crack propagation and coalescence is analyzed with micropolar theory.Finally the finite element method with varying scale domains is applied in analysis of engineering failure problem.The main accomplishments and results are listed as following:(1)The computational precision of consistent multi-scale model is investigated during cross-scale damage evolution process.The model shows large error after damage evolves across the trans-scale boundary.Therefore this work proposes the varying scale domain mechanism,the domain division and trans-scale boundary position could be movable to ensure elasticity of the trans-scale boundary.(2)The framework of the finite element method with varying scale domains is established with variational analysis.The transformation method of finite element equation is obtained with varying scale domain mechanism.The inheriting computation strategy is adopted with reconstruction and transferring of previous computation results to avoid re-computation.Results show that the finite element method with varying scale domains could improve computation efficiency without losing precision.(3)The connection method of beam element-solid element and beam element-shell element is improved with numerical integration strategy.The computation precision and element size dependency of the improved method is investigated.Results show that this method has enough computation precision and stability for engineering analysis.(4)The SBL model is established for modelling of material micro structure,quasi-static iteration method is applied.By using random polygonal mesh and Timoshenko beam element,the SBL model could capture accurate path of crack propagation.Meanwhile the element size should be less than the characteristic size of the material.The SBL model is calibrated though a notched three point bending test.(5)The propagation and coalescence process of wing crack is simulated with SBL model.Different stages in crack propagation and coalescence are obtained and different fracture patters are discussed with different initial crack positions.The computation of Chauchy stress and couple stress is derived and verified.The relationships between micopolar effect and crack propagation,crack coalescence and shear crack are revealed.(6)Fracture,damage and fatigue failure process of engineering components and structures are analyzed.1.The tensile fracture process of a weld component is simulated,the damage accumulation and micro crack propagation processes are obtained.2.The damage evolution and failure process of a steel frame is analyzed with the finite element method with varying scale domains,the damage evolution process in material level,component level and structure level are obtained,meanwhile their relationships are discussed.3.The fatigue failure process of a steel plant due to crane load is simulated with the finite element method with varying scale domains,the accumulation process of fatigue damage is analyzed.