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Novel techniques for modeling 3D cracks and their evolution in solids are presented.Cracks are modeled in terms of signed distance functions (level sets).Stress, strain and displacement field are determined using the extended finite elements method (X-FEM).

This paper presents the development of a new prismatic solid-shell finite element, denoted SHB6, obtained using a purely three-dimensional approach. This element has six nodes with displacements as the only degrees of freedom, and only requires two integration points distributed along a preferential direction, designated as the “thickness”. Although geometrically three-dimensional, this element can be conveniently used to model thin structures while taking into account the various phenomena occurring across the thickness. A reduced integration scheme and specific projections of the strains are introduced, based on the assumed-strain method, in order to improve performance and to eliminate most locking effects. It is first shown that the adopted in-plane reduced integration does not generate “hourglass” modes, but the resulting SHB6 element exhibits some shear and thickness-type locking. This is common in linear triangular elements, in which the strain is constant. The paper details the formulation of this element and illustrates its capabilities through a set of various benchmark problems commonly used in the literature. In particular, it is shown that this new element plays a useful role as a complement to the SHB8PS hexahedral element, which enables one to mesh arbitrary geometries. Examples using both SHB6 and SHB8PS elements demonstrate the advantage of mixing these two solid-shell elements.

We propose a non-intrusive numerical coupling method for transient fluid-structure interaction (FSI) problems simulated by means of different discretization methods: smoothed particle hydrodynamics (SPH) and finite element (FE) methods for the fluid and the solid sub-domains, respectively. As a partitioned coupling method, the present algorithm can ensure a zero interface energy during the whole period of numerical simulation, even in the presence of large interface motion. In other words, the time integrations of the two sub-domains (second order Runge–Kutta scheme for fluid and Newmark integrator for solid) are synchronized. Thanks to this energy-conserving feature, one can preserve the minimal order of accuracy in time and the numerical stability of the FSI simulations, which are validated with a 1D and a 2D trivial numerical test cases. Additionally, some other 2D FSI simulations involving large interface motion have also been carried out with the proposed SPH–FE coupling method. Finally, an example of aquaplaning problem is given in order to show the feasibility of such coupling method in multi-dimensional applications with complicated structural geometries.

On the basis of a thermomechanical phenomenological model, we analyze the thermomechanical behavior of polycrystalline NiTi. Pseudoelastic response and strain-temperature response under fixed stress are studied by using finite element simulation. Calculated mechanical and thermal hysteresis behaviors of NiTi sheet are in good agreement with those observed experimentally. Hardening in stress–strain hysteresis loop and sharp change of strain in strain-temperature hysteresis loop are described by numerical simulation. The result from thermomechanically coupled calculation shows the phenomenon that phase transition occurs by nucleation and propagation of transformation fronts.

This work deals with the development of 2D solid shell non-uniform rational B-spline elements. We address a static problem, that can be solved with a 2D model, involving a thin slender structure under small perturbations. The plane stress, plane strain and axisymmetric assumption can be made. B ¯ projection and reduced integration techniques are considered to deal with the locking phenomenon. The use of the B ¯ approach leads to the implementation of two strategies insensitive to locking: the first strategy is based on a 1D projection of the mean strain across the thickness; the second strategy undertakes to project all the strains onto a suitably chosen 2D space. Conversely, the reduced integration approach based on Gauss points is less expensive, but only alleviates locking and is limited to quadratic approximations. The performance of the various 2D elements developed is assessed through several numerical examples. Simple extensions of these techniques to 3D are finally performed.

The work presented in this publication can be categorized among domain decomposition methods of the dual Schur type applied to structural dynamics. This approach leads to lower CPU times and better control of the accuracy of the time discretization and allows to take into account multi-time-scale effects which arise in transient structural dynamics. In order to consider incompatible time scales, one has to enforce continuity at the interfaces between the subdomains. Here, we propose a general formalism which enables the coupling of subdomains with their own numerical time integration scheme. The proposed method enables one to take into account possible nonlinearities which may present different time scale between the subdomains in a general manner for a wide range of time numerical scheme. This method also offers an important improvement for industrial software with easy implementation. Linear and nonlinear numerical examples are proposed in order to show the efficiency and the robustness of the method.

This paper presents the robust implementation of a cohesive zone model based on extrinsic cohesive laws (i.e. laws involving an infinite initial stiffness). To this end, a two-field Lagrangian weak formulation in which cohesive tractions are chosen as the field variables along the crack’s path is presented. Unfortunately, this formulation cannot model the infinite compliance of the broken elements accurately, and no simple criterion can be defined to determine the loading–unloading change of state at the integration points of the cohesive elements. Therefore, a modified Lagrangian formulation using a fictitious cohesive traction instead of the classical cohesive traction as the field variable is proposed. Thanks to this change of variable, the cohesive law becomes an increasing function of the equivalent displacement jump, which eliminates the problems mentioned previously. The ability of the proposed formulations to simulate fracture accurately and without field oscillations is investigated through three numerical test examples.

This paper presents a technique for the experimental measurement of stress intensity factors in cracked specimens under mixed-mode loading. This technique is based on full-field measurement using digital image correlation and an interaction integral. Such domain-independent integrals are often used in the finite element method to calculate stress intensity factors. The main advantage of this technique is that the errors made in the estimation of the measured displacement field near the crack’s tip do not affect the measurement of the stress intensity factors. The capabilities of the method are illustrated through fracture measurements on compact tension specimens made of maraging steel. Another test under mixed-mode loading is presented.

We propose an approach to the simulation of the shear-tensile transition in dynamic crack growth based on two points: a new crack propagation criterion which is suitable for shear, and an algorithm which is capable of handling the transition from shear mode to tensile mode and back in the same simulation. The new crack propagation criterion for brittle crack growth is based on the maximum shear stress rather than the maximum hoop stress. The shear stress direction becomes the new crack’s direction in which propagation is initiated for shear-type failure. The stress state at the crack’s tip is obtained through a local approach which can be used even in the case of extensive plasticity. Additionally, we propose to control the transition from shear mode to tensile mode during the simulation of crack propagation using an equivalent strain estimated at the crack’s tip. Depending on a threshold strain, the propagation direction is predicted using the maximum shear stress (in the shear case) or the maximum hoop stress (in the tensile case).

This paper is concerned with the development of a new family of solid–shell finite elements. This concept of solid–shell elements is shown to have a number of attractive computational properties as compared to conventional three-dimensional elements. More specifically, two new solid–shell elements are formulated in this work (a fifteen-node and a twenty-node element) on the basis of a purely three-dimensional approach. The performance of these elements is shown through the analysis of various structural problems. Note that one of their main advantages is to allow complex structural shapes to be simulated without classical problems of connecting zones meshed with different element types. These solid–shell elements have a special direction denoted as the “thickness”, along which a set of integration points are located. Reduced integration is also used to prevent some locking phenomena and to increase computational efficiency. Focus will be placed here on linear benchmark problems, where it is shown that these solid–shell elements perform much better than their counterparts, conventional solid elements.