Learn More
This paper formulates the moving least-square interpolation scheme in a framework of the so-called moving least-square reproducing kernel (MLSRK) representation. In this study, the procedure of constructing moving least square interpolation function is facilitated by using the notion of reproducing kernel formulation, which, ‘as a generalization of the(More)
This work is concerned with developing the hierarchical basis for meshless methods. A reproducing kernel hierarchical partition of unity is proposed in the framework of continuous representation as well as its discretized counterpart. To form such hierarchical partition, a class of basic wavelet functions are introduced. Based upon the built-in consistency(More)
The Reproducing Kernel Particle Method (RKPM), which utilizes the fundamental notions of the convolution theorem, multiresolution analysis and meshfree properties, is reviewed. The multiple-scale RKPMs are then proposed as an alternative to commonly used numerical methods such as the ®nite element method. The elimination of a mesh, combined with the(More)
A micro-mechanics damage model is proposed based on homogenization of penny-shaped cohesive micro-cracks (Barenblatt–Dugdale type) in a three dimensional representative volume element. By assuming that macro-hydrostatic stress state has dominant effect on permanent crack opening, a class of pressure sensitive yielding potentials and corresponding damage(More)
This work is concerned with the precise characterization of the elastic fields due to a spherical inclusion embedded within a spherical representative volume element (RVE). The RVE is considered having finite size, with either a prescribed uniform displacement or a prescribed uniform traction boundary condition. Based on symmetry and group theoretic(More)
A computational multiscale method is proposed to simulate coupled, nonequilibrium thermomechanical processes. This multiscale framework couples together thermomechanical equations at the coarse scale with nonequilibrium molecular dynamics at the fine scale. The novel concept of distributed coarse scale thermostats enables subsets of fine scale atoms to be(More)
In this part of the work, the Eshelby tensors of a finite spherical domain are applied to various homogenization procedures estimating the effective material properties of multiphase composites. The Eshelby tensors of a finite domain can capture the boundary effect of a representative volume element as well as the size effect of the different phases.(More)
In this paper, a notion of invariant Galerkin-variational weak forms is proposed. Two speci c invariant variational weak forms, the J -invariant and the L-invariant, are constructed based on the corresponding conservation laws in elasticity, one of which is the conservation of Eshelby’s energy-momentum (Eshelby, Philos. Trans. Roy. Soc. 1951; 87:12; In(More)