Title – Enriched Finite Element and Meshfree Methods for Dynamic Crack Propagation Problems

Extended meshfree methods for dynamic crack propagation are reviewed. One class of methods enforces crack path continuity while the other class of method treats the crack as set of cracked particles. In the first method, crack path continuity is enforced either by use of a crack tip enrichment or by use of Lagrange multipliers. All methods are implemented in two and three dimensions and are compared to experimental results

A simple circular cell method for multilevel finite element analysis

A simple multiscale analysis framework for heterogeneous solids based on a computational homogenization technique is presented. The macroscopic strain is linked kinematically to the boundary displacement of a circular or spherical representative volume which contains the microscopic information of the material. The macroscopic stress is obtained from the energy principle between the macroscopic scale and the microscopic scale. This new method is applied to several standard examples to show its accuracy and consistency of the method proposed

A Simple Circular Cell Method for Multilevel Finite Element Analysis

A simple multiscale analysis framework for heterogeneous solids based on a computational homogenization technique is presented. The macroscopic strain is linked kinematically to the boundary displacement of a circular or spherical representative volume which contains the microscopic information of the material. The macroscopic stress is obtained from the energy principle between the macroscopic scale and the microscopic scale. This new method is applied to several standard examples to show its accuracy and consistency of the method proposed

A phantom-node method with edge-based strain smoothing for linear elastic fracture mechanics

This paper presents a novel numerical procedure based on the combination of an edge-based smoothed finite element (ES-FEM) with a phantom-node method for 2D linear elastic fracture mechanics. In the standard phantom-node method, the cracks are formulated by adding phantom nodes, and the cracked element is replaced by two new superimposed elements. This approach is quite simple to implement into existing explicit finite element programs. The shape functions associated with discontinuous elements are similar to those of the standard finite elements, which leads to certain simplification with implementing in the existing codes. The phantom-node method allows modeling discontinuities at an arbitrary location in the mesh. The ES-FEM model owns a close-to-exact stiffness that is much softer than lower-order finite element methods (FEM). Taking advantage of both the ES-FEM and the phantom-node method, we introduce an edge-based strain smoothing technique for the phantom-node method. Numerical results show that the proposed method achieves high accuracy compared with the extended finite element method (XFEM) and other reference solutions

Asymptotic Stress Intensity Factor Density Profiles for Smeared-Tip Method for Cohesive Fracture

Abstract. The paper presents a computational approach and numerical data which facilitate the use of the smeared-tip method for cohesive fracture in large enough structures. In the recently developed K-version of the smeared tip method, the large-size asymptotic profile of the stress intensity factor density along a cohesive crack is considered as a material characteristic, which is uniquely related to the softening stress-displacement law of the cohesive crack. After reviewing the K-version, an accurate and efficient numerical algorithm for the computation of this asymptotic profile is presented. The algorithm is based on solving a singular Abel's integral equation. The profiles corresponding to various typical softening stress-displacement laws of the cohesive crack model are computed, tabulated and plotted. The profiles for a certain range of other typical softening laws can be approximately obtained by interpolation from the tables. Knowing the profile, one can obtain with the smeared-tip method an analytical expression for the large-size solution to fracture problems, including the first two asymptotic terms of the size effect law. Consequently, numerical solutions of the integral equations of the cohesive crack model as well as finite element simulations of the cohesive crack are made superfluous. However, when the fracture process zone is attached to a notch or to the body surface and the cohesive zone ends with a stress jump, the solution is expected to be accurate only for large-enough structures

Meshfree 3D Crack initiation, propagation, junction in non-linear materials: large strains, statics and dynamics without front enrichment A Lagrange multiplier method

International audienceWe present in this paper a technique based on Lagrange multipliers to close the cracks along their fronts when analyzing three-dimensional fracture mechanics problems in statics and dynamics with the enriched element-free Galerkin (EFG) method. This Lagrange multiplier field avoids the use of near-tip enrichment, thereby only requiring discontinuous enrichment to account for the presence of the cracks. We show that the methodology performs quite well, even for very large strains and fragmentation

On three-dimensional modelling of crack growth using partition of unity methods

This paper reviews different crack tracking techniques in three-dimensions applicable in the context of partition of unity methods, especially meshfree methods. Issues such as describing and tracking the crack surface are addressed. A crack tracking procedure is proposed in detail and implemented in the context of the extended element-free Galerkin method (XEFG). Several three-dimensional cracking examples are compared to other results from the literature or the experimental data and show good agreement

Mechanical Behavior of Coupled Elastoplastic Damage of Clastic Sandstone of Different Burial Depths

Clastic sandstone is widely distributed in oil and gas reservoirs; its internal structure has many micro-defects. Under different stress environments of burial depth, significant damage evolution and plastic deformation easily occur. A series of triaxial compression tests were performed to study the coupled elastoplastic damage mechanical behavior of clastic sandstone samples at different burial depths ranging from 581.28 m to 979.82 m. Results reveal that the stress-strain responses of clastic sandstone samples exhibit significant nonlinear and softening characteristics. The mechanical behavior is due to the coupling of plastic deformation and mechanical damage. Plastic and damage internal variables cause damage stiffness degradation and plastic flow. Considering the coupling of elastoplastic damage in the loading process, an elastoplastic damage coupling model is proposed to study the mechanical behavior of different burial depth clastic sandstones. The model can effectively describe the mechanical behavior of clastic sandstone, such as the volume compression and dilatancy transformation, plastic hardening and damage softening, which are in good agreement with the experimental results. Furthermore, the mechanical behavior of the clastic sandstone shows a dependency on the confining pressure and burial depth. The load-bearing capacity and the ability to resist deformation of the clastic sandstone are improved as the confining pressure and burial depth increase. Relevant results can provide reliable basis for the safe exploitation of oil and gas engineering

Hydrology: Glaciology (1863); 1863 Hydrology: Snow and ice (1827)

[1] A size effect law for fracture triggering in dry snow slabs of high enough length-tothickness ratio is formulated, based on simplified one-dimensional analysis by equivalent linear elastic fracture mechanics. Viscoelastic effects during fracture are neglected. The derived law, which is analogous to Bažant's energetic size effect law developed for concrete and later for sea ice, fiber composites, rocks, and ceramics, is shown to agree with two-dimensional finite element analysis of mode II cohesive crack model with a finite residual shear stress. Fitting the proposed size effect law to fracture data for various slab thicknesses permits identifying the material fracture parameters. The value of preexisting shear stress in a thin weak zone of finite length is shown to have significant effect. There exists a certain critical snow depth, depending on the preexisting stress value, below which the size effect disappears. Practical applications require considering that the material properties (particularly the mode II fracture toughness or fracture energy) at the snow slab base are not constant but depend strongly on the slab thickness. This means that one must distinguish the material size effect from the structural size effect, and the combined size effect law must be obtained by introducing into the structural size effect law dependence of its parameters on snow thickness. The thickness dependence of these parameters can be obtained by matching the combined law to avalanche observations. Matching Perla's field data on 116 avalanches suggests that the mode II fracture toughness is approximately proportional to 1.8 power of snow thickness