Computation of dynamic stress intensity factors in cracked functionally graded materials using scaled boundary polygons

Micromechanics determination of effective properties of voided magnetoelectroelastic materials

“…Note that both the macroscale and mesoscale analyses are performed within the theory of continua in contrast to the multiscale modelling when different physical models as well as different computational methods are employed on different length scales [7]. In the present paper, the scaled boundary finite element method (SBFEM) [22][23][24] is developed for magnetoelectroelastic materials. In this method, a scaling center O is selected at a point from which the whole boundary is directly visible.…”

“…In the present paper, the scaled boundary finite element method (SBFEM) is developed for 2D boundary value problem in a porous magnetoelectroelastic solid under stationary boundary conditions. Up to now the SBFEM have been successfully applied to elastostatic, elastodynamic problems and piezoelectric crack problem too [22][23][24]. The SBFEM is applied here on the micro-level (RVE) of the magnetoelectroelastic solids with voids to compute effective material properties.…”

A novel scaled boundary finite element formulation with stabilization and its application to image‐based elastoplastic analysis

“…The compatibility between adjacent polytope elements is guaranteed, as long as their common edges have the same number of nodes and shape functions N u ( η ). The scaled boundary shape functions Φ ( ξ , η ) are conforming and linearly complete. They can reproduce all rigid body translations, rigid body rotations, and constant strain modes The scaled boundary shape functions Φ ( ξ , η ) can describe singularities semianalytically in a cracked polytope element …”

“…They can reproduce all rigid body translations, rigid body rotations, and constant strain modes The scaled boundary shape functions Φ ( ξ , η ) can describe singularities semianalytically in a cracked polytope element The scaled boundary shape functions Φ ( ξ , η ) are comprised of different displacement modes.…”

“…This is achieved by assuming that the elastoplastic constitutive matrix D ep within a polytope element is approximated by a constant value. This constant D ep is evaluated based on the stresses at the scaling center, which are corresponding to the constant stress modes of the scaled boundary polytope element . If the stresses at the scaling center of the element reach the yielding surface, the entire polytope element is considered to be elastoplastic.…”