The Study Of The Coupling Approach Of Peridynamics With Classical Continuum Mechanics

The simulation of a series of discontinuous problems,such as the failure of materials and the progressive fracture of structures,has been a challenging issue within the framework of solid mechanics as well as the key topic concern to the industry,which is directly related to the reliability life of products and personal safety.The theories and methods of traditional continuum mechanics,that are based on the continuum hypothesis and adding additional discontinuous functions in describing the progressive fracture of structures,not only has great limitations in solving the crack problems,but also need extra relations to govern the initiation of cracks as well as their growth velocities and directions,which leads to the complexity of these methods,especially when tackling the propagation and branching interaction of multiple cracks.Peridynamics is a new non-local continuum method,different from the theory of traditional continuum mechanics based on the differential governing equation,it employs the space integral equation to describe the interaction between the points of material,additionally,it inherits the characteristics of the meshless and molecular and shows natural advantages in solving discontinuous,multiscale and multiphysical coupling problems.However,the computational efficiency and boundary effect greatly restrict the application of peridynamics in engineering,to tackle these two problems,this paper combines the theories of peridynamics and traditional continuum mechanics,and the main works has been done that are listed as follows:(1)An explicit dual-based coupling approach is proposed to couple peridynamics and continuum mechanics for solving the dynamic fracture of structure.Different from the existing local/non-local coupling methods in the literature,no transition regions,additional elements and conservation criteria are introduced in this coupling method,the local and non-local forces are transmitted mutually with simplicity and effectivity,which effectively avoids the spurious forces and stress waves that may exist in the boundary of local and non-local regions,and moreover,the computational cost is significantly reduced and the boundary effect of peridynamics is solved.(2)Based on the linearization theory of peridynamics,the module state of dual-horizon bond-based peridynamics and dual-horizon ordinary state-based peridynamics are derived.And subsequently,the non-local peridynamic stiffnessmatrix is constructed and the dual assembly algorithm of the peridynamic stiffness matrix is developed.At last,the implicit coupling of peridynamics and continuum mechanics is proposed to solve the quasi-static fracture of structures.(3)The peridynamic finite element method is proposed and the definitions of the peridynamic element and node are given in this paper.Additionally,the peridynamic element force vector,element mass matrix and element stiffness matrix are constructed to realize the explicit and implicit calculations of peridynamics in the commercial software Abaqus through the user-defined VUEL and UEL subroutines.Moreover,using the dual-based approach,the authors realize the coupling calculation of peridynamics and finite element method,which provides an effective way for the engineering application of peridynamics.