Peridynamic Theory And Its Numerical Simulation In The Deformation And Damage Process Of The Rock-like Materials

Peridynamic theory is a nonlocal numerical method,which is both the virtue of molecular dynamics and meshless methods. It is not only applied to the continnul and but also discontinual problem. Especially, it has It has great advantage in modeling the fracture of the material.This theory is devided into the bond-based and state-based peridynamics,and state-based peridynamics is devided into ordinary and nonordinary state-based peridynamics.The corresponding numerical program which is based on three different types of peridynamic theory is done in the paper,Then the numerical simulation for the fracture of rock material is done by using it.The results are comparised and analytized with the experimental results, the conclusion demonstrates the numerical results are consistent with the experimental results. so it supplies a new sight for the numerical simulation of rock material’s fracture by using peridynamics.The main research contents and conclusions are listed as follows:①The expression of peridynamic parameters for a homogeneous and istropic two-dimensional material is deduced by using the relation between the force density and strain energy density tensor of the material points at first in the paper,then the expression is comparised with the expression that is obtained from the classical continuum mechanics,so the relation between the peridynamic parameters and macromaterial constant,such as elastic modulus 、 volumerical modulus and shear modulus,etc is gained. and the relation between the macromechanics and micromechanics is established.②Bond-based peridynamic basic equation is deduced by using the balance of linear momentum,angular momentum, and energy, etc. Then the numerical simulation of the deformation for rock material under tensile loading is done using the bond-based peridynamics. The conclusions demonstrate that the simulation of the displacement field for the rock sample has the high accuracy by using it, and the propagation and coalescence process of multicracks in the brittle rock material under tensile loading is simulated by using it.The conclusions demonstrate that the numerical results that is obtained from the peridynamics are consistent with the experimental results.③The bond-based peridynamics is improved.the tensile fracture for rock material can be simulated by using the traditional bond-based peridynamics,but the shear fracture for the rock material can not be done by using it. the superelastic theory is introduced into the bond-based peridynamics.The shear bond is added to simulate the shear fracture of rock material.The limitation that possion’ratio is a constant in classical bond-based peridynamics in two dimension is break through by using improved peridynamics,then comparison and analysis of several examples is done,it is concluded that the numerical results are consistent with the experimental results.It is also improved that this improved peridynamic theory has great validity.④The damage theory is introduced to ordinary, state-based peridynamic theory to model propagation and coalescence procession of the crack. it breaks through limitation of constant Possion’s ratio in traditional bond-based peridynamic theory,the application range of the peridynamic theory for the fracture simulation of the rock material is extended greatly,and it can also afford to a better understanding for the propagation and coalescence of cracks.⑤the elastic constitutive relation for the rock material and damage are introduced into nonordinary, state-based peridynamics,so the basic equation in nonordinary, state-based elastic brittle peridynamics is derived.The corresponding numerical program is done, the fracture and deformation problems for the rock materials are simulated. The conclusions are drawn that it is reasonable relatively to the bond–based and ordinary,stated-on peridynamics.