A hexahedral-dominant finite element mesh can be easily constructed by cutting regular hexahedral elements with CAD surfaces representing outer surfaces of a geometric model. Polyhedral elements are then generated at the domain boundaries, while regular hexahedral elements remain in the interior region. The polyhedral shape functions have similar properties to conventional finite element shape functions in terms of continuity and completeness within elements, compatibility across inter-element boundaries and the Kronecker-delta property.
Polygonal shell elements
A quadrilateral-dominant mesh can be easily prepared by cutting the quadrilateral mesh generated by a paving method along the boundaries of the geometric surface. Polygonal shell elements can be created by cutting the corners of quadrilateral shell elements at the domain boundaries. Shape functions for pentagonal shell elements are developed, and assumed transverse shear strains and membrane strains are used to avoid the transverse shear locking and the membrane locking of polygonal shell elements.
Material point method
A new contact algorithm is developed to analyze the motion of material particles interacting with finite elements. Contact forces at background grid nodes of material point method (MPM) are computed by using a simple grid-based contact algorithm, and then transferred to the nodal forces acting on the faces of finite elements. A severe penetration of material particles into finite elements when the finite element mesh is coarser than the background grid can be avoided by introducing distributed interaction (DI) nodes on the faces of finite elements interacting with material particles.
Interfacing between dissimilar systems
A new approach to simulate fluid-solid interaction (FSI) problems involving non-matching meshes was developed. The coupling between the fluid and solid domains with dissimilar finite element meshes consisting of 4-node quadrilateral elements is achieved by using the interface element method (IEM). Continuity and compatibility conditions across the interface between fluid and solid meshes are satisfied exactly by introducing the interface elements defined on an interfacing region. Importantly, a consistent transfer of loads through the interface elements guarantees the present method to be an efficient approach of the solution strategy to FSI problems. The fluid equations for velocity and pressure and the solid equations for velocity are strongly coupled in a single computational domain by means of the interface elements.
Extraction of cohesive laws (Field Projection Method)
Previously, a field projection method was established to extract the cohesive zone laws from far-field data using interaction J-integrals between the physical field of interest and auxiliary analytical probing fields. We extend the universality of the field projection method and its ease of numerical implementation by using numerical auxiliary fields. The interaction J– and M-integrals between these auxiliary probing fields and the measurement field are used to reconstruct the traction and separation relationship along the crack faces.
Cohesive laws based on continuum damage mechanics
A continuously-deforming material layer associated with a ductile failure process of void nucleation, growth and coalescence is converted into a separating pair of cohesive crack surfaces resisted by cohesive tractions. Representative volume elements of damaged and undamaged material layers are used to extract the damaged portion of the deformation in the failure process zone, which is reduced to a cohesive law based on continuum damage mechanics.
Inverse estimation of residual stresses
This work is concerned with an inverse approach to determine surface tractions from displacements measured on a remote surface. The influence of measurement location and regularization on the evaluation of boundary tractions is investigated in this study. The finite element method is employed in the inverse process, and the Tikhonov and the truncated singular value decomposition techniques are used to regularize the ill-conditioned system.
Welding residual stresses
The residual stresses in an welded joint are concerned. Transformation Induced Plasticity (TRIP) is considered in finite element analysis by using the constitutive model for the plastic behavior including TRIP. One of the interest is to implement the welding residual stress profile with continuum model into the simply constructed shell model as an initial condition.