Investigation On Multiscale Mechanical Behavior Of Composite Materials And Structures Based On Self-consistent Clustering Analysis

Composite materials are widely used in fields such as aerospace,transportation,and fundamental research.Especially in the Large Hadron Collider（LHC）project,composite materials are utilized to build superconducting magnets that accelerate particle beams with high magnetic fields and induce high-energy particle collisions,thereby further exploring the fundamental composition of matter.The mechanical behaviors of superconducting magnets,which are directly related to the safety and stability of the overall structure,are affected by the electromagnetic-mechanical-thermal multi-field loading in actual service conditions.However,complex structures such as large superconducting magnets exhibit hierarchical characteristics,and the detailed numerical analysis requires consideration of lower-level components such as superconducting strands and cables,which consume significant computational resources and make it difficult to meet practical engineering needs.Multiscale analysis can efficiently quantify the overall mechanical behavior of composite structures and provide detailed mechanical responses of materials and structures at different levels and scales.In this dissertion,based on the high precision and efficiency of self-consistent clustering analysis（SCA）method,a multiscale mechanical behavior analysis framework is established.Numerical studies are conducted on the mechanical behaviors of composite materials and structures under axial loading,thermal residual stress and strain,and electromagnetic-mechanical-thermal multi-field loading.The main contents are as follows:Firstly,a detailed theoretical derivation is carried out for the SCA method,which is used to solve mechanical problems and steady-state heat transfer problems for representative volume element（RVE）.The algorithm verification is performed by solving two-dimensional and three-dimensional problems with simple inclusion.And the effects of material constitutive relationships,cluster number and mesh resolution on the calculation results are studied.The results show that the SCA method is applicable to different material constitutive relationships,and has high prediction accuracy under reasonable clustering number and grid resolution.Secondly,a FEM-SCA two-scale framework is constructed by combining the SCA method and the finite element method（FEM）,and the multiscale mechanical behaviors of multi-filaments composites under axial loading are studied.Then,the two-scale analyses of cylindrical models with straight and spiral filaments under axial loading are carried out respectively,and the influences of the twist degree of spiral inclusion and the mechanical behavior of the local recovered results of microscopic model are discussed.The results show that the two-scale analysis is in good agreement with the full-size model,and the microscopic model can effectively characterize the local mechanical responses during different loading stages under axial cyclic loading.When the twist degree of the spiral inclusion increases,the bearing capacity of the inclusion decreases and the overall stress of the model is reduced.Then,the random sequence expansion and elimination algorithm is introduced to construct the microscopic RVE of particle reinforced composite.The SCA method is modified to simulate the thermal residual stress-strain during the heat treatment process.The influence of thermal residual stress on the mechanical behavior of particle reinforced composites is investigated within the two-scale analysis framework.The influences of three clustering methods in offline stage are discussed,and the results show that the clustering method based on thermoelastic response is closest to the results of FEM.Thermal residual stresses and strains during the temperature change process will alter the stresses and strains state in the microscale model,thus affecting the overall mechanical behaviors of the macroscopic and microscopic models.Finally,the Nb₃Sn superconducting accelerator MQXFS magnet with a multiscale structure is studied.Building upon the aforementioned two scale analysis framework,the influence of the mesoscale is further considered,and a macro-meso-micro analysis framework is developed.Three-dimensional multiscale nonlinear mechanical behavior analysis is conducted for the assembly,cooldown,and excitation processes of the magnet structure.By comparing the numerical results of the microscopic RVE and the mesoscopic PIT strand with existing experimental results,the reliability of the multiscale model is verified.Furthermore,the stress and strain distributions of the magnet structure is investigated using the multiscale approach,and the effects of material parameters,excitation current,friction coefficient,Bladder pressure,and Nb₃Sn filament stiffness degradation on the mechanical behaviors of macroscopic magnet coil,mesoscopic Rutherford cable,and microscopic Nb₃Sn filament RVE are discussed.Numerical results indicate that the use of homogenized linear elastic material parameters leads to underestimated stresses for the magnet coil.Changes in excitation current lead to significant stress variations in regions with high Lorentz forces.The magnitude of coil stress is negatively correlated with the friction coefficient and positively correlated with the Bladder pressure.