Generalized Bond-based Peridynamic Theories And The Applications

Material failure has always been the focus of engineers and scientists.Experimental studies show that microstructure has a greater impact on material failure.However,the traditional fracture mechanics theory is developed based on the Cauchy continuum theory,which does not consider the influence of material microstructure and cannot accurately reflect the size effect of materials.In this paper,three generalized bond-based peridynamic models are developed based on the generalized continuum theories to investigate the influence of the microstructure on material failure.Generalized continuum theories are a group of continuum theories that take into account the effect of microstructure,which includes the Cosserat continuum and micromorphic continuum.Generalized continuum theories use the additional degrees of freedom to represent the microstructure deformation and use the internal length scale to represent the size of the microstructure.The development of a fracture mechanics model based on the generalized continuum theories can take into account the influence of microstructure on the crack propagation and better predict the failure behavior.Applying the experimental method to study the fracture behavior is time-consuming and high cost.Especially when the size effect of the material is apparent and the structure size is large,an accurate prediction of structure strength needs a sizeable experimental space.In addition,the fracture test is dispersive,and it requires multiple groups of experiments to accurately measure the fracture parameters.Considering the above limitations of the experiment,the numerical simulation can be used to study the fracture behavior of materials.Peridynamics,which is developed in recent 20 years,applies the spatial integral equilibrium equations.The continuity requirement of peridynamic spatial integral equilibrium equations is lower than the one of spatial differential equilibrium equations of the traditional continuum mechanics,and the peridynamics is suitable for describing the fracture behavior.But at present,most peridynamic models are developed based on the Cauchy continuum and lack the consideration of microstructure.It’s necessary to develop the peridynamic model that takes into account the effect of microstructure.In this thesis,three generalized bond-based peridynamic models are developed,which include the bond-based correspondence model,Cosserat peridynamic model and the micromorphic peridynamic model.And they are applied to study the fracture phenomenon of fiber-reinforced concrete and other materials.The proposed models are applied to investigate the influence of the microstructure parameters such as the internal length scale on crack propagation.The specific contents are as follows:(1)To solve the limitation of Poisson’s ratio of traditional bond-based peridynamics,the bond-based correspondence model is developed,where the bond deformation is defined according to the line element deformation of classical continuum mechanics.The bondbased correspondence model applies the traditional constitutive equations to obtain the peridynamic pair-wise force and solve the limitation of Poisson’s ratio.Besides,the plastic bond-based correspondence model is developed by applying the von Mises yield criterion and the influences of plastic parameters on the crack propagation are investigated.(2)The Cosserat peridynamic model is developed,where the material particle has independent rotation.The internal length scale and Cosserat shear modulus are applied to represent the effect of the microstructure.The unequal relationship between the internal length scale and the horizon size is derived,and the value of the horizon size is suggested.In the numerical examples,the Cosserat peridynamic model is compared to the finite element method to validate the proposed model.The influences of grid space,internal length scale and Cosserat shear modulus on crack propagation are investigated.(3)Two peridynamic fiber-reinforced concrete models are developed based on the Cosserat peridynamic model,where the semi-discrete method and fully-discrete method are applied in fiber modeling.The linear congruential generator is applied to obtain the random numbers.The numerical results of the proposed models are compared to the experimental results and numerical results of other peridynamic models to show the validation.The influences of the fiber content,fiber parameters and other parameters on the strength and crack propagation are investigated.(4)The micromorphic peridynamic model is developed,where the material particle is assumed as a deformable micro-volume.The deformation of the microstructure is represented by the additional degrees of freedom.The bond failure criterion considers the influence of microstructure.And the limitations of micromorphic parameters are discussed.In the numerical examples,the micromorphic peridynamic model is compared to the finite element method to validate the proposed model.And the influences of the micromorphic parameters on the crack propagation are investigated.