SOLID-SHELL FINITE ELEMENT MODELS FOR EXPLICIT SIMULATIONS OF CRACK PROPAGATION IN THIN STRUCTURES

Crack propagation in thin shell structures due to cutting is conveniently simulated using explicit finite element approaches, in view of the high nonlinearity of the problem. Solidshell elements are usually preferred for the discretization in the presence of complex material behavior and degradation phenomena such as delamination, since they allow for a correct representation of the thickness geometry. However, in solid-shell elements the small thickness leads to a very high maximum eigenfrequency, which imply very small stable time-steps. A new selective mass scaling technique is proposed to increase the time-step size without affecting accuracy. New ”directional” cohesive interface elements are used in conjunction with selective mass scaling to account for the interaction with a sharp blade in cutting processes of thin ductile shells

Finite Element Nonlocal Technique Based on Superconvergent Patch Second Derivative Recovery

This dissertation proposes a finite element procedure for evaluating the high order strain derivatives in nonlocal computational mechanics. The superconvergent second derivative recovery methods used are proven to be effective in evaluating the Laplacian of the equivalent strain based on low order (linear) elements. Current nonlocal finite element techniques with linear elements are limited to structured meshes, while the new technique can deal with unstructured meshes with various element types. Other superconvergent patch recovery (SCP) based nonlocal approaches, such as the patch projection techniques only utilize nodal based patches to evaluate the first derivatives of the strain. The SCP technique has not yet been used for recovery of higher order strain derivatives. The proposed technique is capable of evaluating the Laplacian of the equivalent strain and has the potential for even higher order derivative recovery. The same patches can be easily utilized for error estimation and adaptive meshing for nonlocal problems. We employ two super-convergent patch options: the element based patch with all neighbors or only facing neighbors. The nonlocal strain derivatives can be recovered through either a mesh nodal averaging process or directly at the patch element quadrature points after the patch least square fitting problems are solved. Numerical examples for both strain gradient damage mechanics and strain gradient plasticity problems are given. In summary, the new finite element nonlocal computational technique based on the superconvergent second derivative recovery methods is proven to be robust in evaluating the high order strain derivatives with low order element unstructured meshes

Mixed Arlequin method for multiscale poromechanics problems

An Arlequin poromechanics model is introduced to simulate the hydro-mechanical coupling effects of fluid-infiltrated porous media across different spatial scales within a concurrent computational framework. A two-field poromechanics problem is first recast as the twofold saddle point of an incremental energy functional. We then introduce Lagrange multipliers and compatibility energy functionals to enforce the weak compatibility of hydro-mechanical responses in the overlapped domain. To examine the numerical stability of this hydro-mechanical Arlequin model, we derive a necessary condition for stability, the twofold inf–sup condition for multi-field problems, and establish a modified inf–sup test formulated in the product space of the solution field. We verify the implementation of the Arlequin poromechanics model through benchmark problems covering the entire range of drainage conditions. Through these numerical examples, we demonstrate the performance, robustness, and numerical stability of the Arlequin poromechanics model