| The failure of engineering structures and engineering materials during the construction seriously threatened the safety of people’s lives and led to inestimable economic losses.As a primary means of failure,the fracture has long been the focus of the basic science research field.It is also the goal of researchers to propose a numerical method suitable for fracture problems.As a non-local theory,peridynamic employs the integro-differential equation without partial derivatives to dictate the motion of each material point.In this way,it can effectively circumvent the singular problems that beset the conventional differential equation while modeling discontinuous issues.Therefore,peridynamic is identified as one of the practical solutions to fracture problems.However,classical peridynamic formulations have their own advantages and disadvantages.Given this,this paper aims to incorporate the concept of non-local continuum kinematic elements into peridynamic formulations to eliminate the intrinsic defects of conventional peridynamic formulations.After that,these modified peridynamic formulations are extended for anisotropic linearly elastic material,viscoelastic material,visco-elastic-plastic material,and non-linear viscoplastic material.The main works of this paper are as follows:(1)By introducing specific expressions for one-neighbor,two-neighbor,and three-neighbor interaction potentials of continuum-kinematic-inspired peridynamic(CPD),defining three types of micromodulus,and relating these micromodulus to conventional elastic constants,a linear elastic isotropic constitutive model is proposed for the novel CPD formulation.The proposed linear elastic isotropic CPD formulation can remove the restriction of the fixed Poisson’s ratio in classical bond-based peridynamics and reproduce the elastic deformation of solids subjected to heterogeneous deformation fields.(2)The linear elastic isotropic CPD formulation is generalized to linear elastic anisotropic CPD formulation,where the anisotropy is achieved by changing the material properties,including the micromodulus,critical stretch,and critical micropotential energy of basic finite kinematic elements with their direction in the principal material axes in terms of eight-order double Fourier expansion.The resulting 2D orthotropic CPD formulation is characterized by three independent elastic moduli,and the 3D transversely isotropic CPD formulation is characterized by four independent elastic moduli.(3)The kinematic constraint imposed by non-local continuum kinematic elements is introduced to the conventional bond-associated non-ordinary state-based peridynamic model to endow the explicit mathematical and physical meaning to the bond-associated horizon.In this way,a continuum-kinematic-inspired non-ordinary state-based peridynamic(C-NOSBPD)model is proposed.The linear and angular momentum conservation is firstly and rigorously proved.The novel proposed model is proved capable of avoiding unphysical deformation modes that typically beset conventional formulation through several analytical examples.(4)A viscoelastic C-NOSBPD model is proposed,where the viscoelasticity is generated by directly incorporating the classical viscoelastic constitutive relation in the form of the Generalized Maxwell Model into the C-NOSBPD framework.Equipped with the progressive damage criteria based on the maximum principal strain component of the bond-associated strain tensor,the viscoelastic C-NOSBPD model can reproduce the mechanical responses and rate-dependent fracture behaviors of viscoelastic materials.(5)A visco-elastic-plastic and fractional nonlinear viscoplastic C-NOSBPD model is proposed,where the visco-elastic-plastic constitutive are generated by directly incorporating the classical Burgers-creep viscoplastic constitutive relation and fractional nonlinear viscoplastic relation into the C-NOSBPD framework.Equipped with the progressive damage criteria based on the bond-associated strain tensor,the visco-elastic-plastic C-NOSBPD model can reproduce the complete creep behavior of rock material,including primary creep,steady-state creep,and acceleration creep. |
