The book covers all basic ingredients of contact and computational contact mechanics: from efficient contact detection algorithms and classical optimization methods to new developments in contact ...kinematics and resolution schemes both for sequential and parallel computer architectures. The book is self-consistent and is intended for people working on implementation and improvement of contact algorithms in a finite element software. The book contains numerous examples and figures to make the material accessible for a broad audience. The book combines extended introductory parts with new developments, so it is accessible for freshmen in computational contact and is of interest for established researchers. Using a new tensor algebra, we introduce some original notions in contact kinematics and extend the classical formulation of contact elements. We discuss robust and efficient contact detection algorithms both for sequential and parallel computer architectures. Some classical and new resolution methods for contact problems and associated ready-to-implement expressions are given. Many validation problems and tests are presented.
In this contribution we address the issue of efficient finite element treatment for phase-field modeling of brittle fracture. We start by providing an overview of the existing quasi-static and ...dynamic phase-field fracture formulations from the physics and the mechanics communities. Within the formulations stemming from Griffith’s theory, we focus on quasi-static models featuring a tension-compression split, which prevent cracking in compression and interpenetration of the crack faces upon closure, and on the staggered algorithmic implementation due to its proved robustness. In this paper, we establish an appropriate stopping criterion for the staggered scheme. Moreover, we propose and test the so-called hybrid formulation, which leads within a staggered implementation to an incrementally linear problem. This enables a significant reduction of computational cost—about one order of magnitude—with respect to the available (non-linear) models. The conceptual and structural similarities of the hybrid formulation to gradient-enhanced continuum damage mechanics are outlined as well. Several benchmark problems are solved, including one with own experimental verification.
In the present paper a new additive manufacturing processing route is introduced for ultra-high performance concrete. Interdisciplinary work involving materials science, computation, robotics, ...architecture and design resulted in the development of an innovative way of 3D printing cementitious materials. The 3D printing process involved is based on a FDM-like technique, in the sense that a material is deposited layer by layer through an extrusion printhead mounted on a 6-axis robotic arm. The mechanical properties of 3D printed materials are assessed. The proposed technology succeeds in solving many of the problems that can be found in the literature. Most notably, this process allows the production of 3D large-scale complex geometries, without the use of temporary supports, as opposed to 2.5D examples found in the literature for concrete 3D printing. Architectural cases of application are used as examples in order to demonstrate the potentialities of the technology. Two structural elements were produced and constitute some of the largest 3D printed concrete parts available until now. Multi-functionality was enabled for both structural elements by taking advantage of the complex geometry which can be achieved using our technology for large-scale additive manufacturing.
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•A novel large-scale 3D printing process is proposed for cementitious materials.•Structures with complex geometry are produced without temporary supports.•The tangential continuity method for slicing is used, providing mechanical stability.•3D-printed concrete structures produced are some of the largest available today.•Geometric complexity enables multifunctionality and multiscale architecturation.
Rigorous coupling of fracture–porous medium fluid flow and topologically complex fracture propagation is of great scientific interest in geotechnical and biomechanical applications. In this paper, we ...derive a unified fracture–porous medium hydraulic fracturing model, leveraging the inherent ability of the variational phase-field approach to fracture to handle multiple cracks interacting and evolving along complex yet, critically, unspecified paths. The fundamental principle driving the crack evolution is an energetic criterion derived from Griffith’s theory. The originality of this approach is that the crack path itself is derived from energy minimization instead of additional branching criterion. The numerical implementation is based on a regularization approach similar to a phase-field model, where the cracks location is represented by a smooth function defined on a fixed mesh. The derived model shows how the smooth fracture field can be used to model fluid flow in a fractured porous medium. We verify the proposed approach in a simple idealized scenario where closed form solutions exist in the literature. We then demonstrate the new method’s capabilities in more realistic situations where multiple fractures turn, interact, and in some cases, merge with other fractures.
•A unified fracture - porous medium flow model has been proposed, which is regularized with a phase-field variable consistent with the fracture mechanics regularization without defining extra variables or level set functions.•The methodology to compute the crack opening displacement using the gradient of the phase-field variable has been derived using the Gamma-convergence approximation.•Additionally, we point out erroneous crack opening displacement computation under deformed domain, which has not been discussed before, and propose an approach to mitigate this error.•The proposed model has been verified in the toughness dominated regime of hydraulic fracturing.
Category:
Ankle, Arthroscopy, Trauma
Introduction/Purpose:
Background: A shift and increase in mean tibiotalar contact pressure has been demonstrated in simulated syndesmotic injuries. The effect of ...screw fixation and/or suspensory fixation on restoration of pressure mechanics in the setting of a syndesmotic injury remains largely unknown.
Hypothesis/Purpose:
The purpose of this study is to examine the contact mechanics of the tibiotalar joint following syndesmosis fixation with screws versus a flexible fixation device for complete syndesmotic injury.
Methods:
Six matched pairs of cadaveric below knee specimens were randomly assigned fixation with either two 3.5 mm cortical screws or two TightRopes™ (Arthrex). Motion capture trackers were fixed to the tibia, fibula, and talus and a pressure sensor was placed in the tibiotalar joint. Each specimen was first tested intact with an axial compressive load followed by external rotation torque while maintaining axial compression. The syndesmosic ligaments were then completely sectioned and subsequently repaired with either two TightRopes™ or two screws and the protocol was repeated. Mean contact pressure (MCP), peak pressure (PP), reduction in contact area (CA), translation of the center of pressure (COP), and relative talar and fibular motion were calculated. Specimens were then cyclically loaded in external rotation to failure. Comparisons were made using paired t-tests and/or Welch’s t-tests.
Results:
No differences in MCP, PP, or CA were observed between the intact and instrumented states during AL alone for either group. MCP relative to intact testing was increased in the screw group at 5 Nm (4.8±4.1 MPa vs 3.6±0.8 MPa, p=0.033) and 7.5 Nm torque (6.2±1.4 MPa vs 4.2±1.2 MPa, p=0.024). Likewise, PP was increased in TightRope™ group at 7.5 Nm torque (14.4±3.1 MPa vs 10.8±1.6 MPa, p=0.046). There was no change in COP in the TightRope™ group at any threshold; however, at every threshold tested there was significant medial and anterior COP translation in the screw group relative to the intact state.
Conclusion:
Either screws or TightRope™ fixation is adequate with AL alone. With lower amounts of torque, the TightRope™ group exhibits contact and pressure mechanics that more closely match native mechanics.
Fracture mechanics concepts are applied to gain some understanding of the hierarchical nanocomposite structures of hard biological tissues such as bone, tooth and shells. At the most elementary level ...of structural hierarchy, bone and bone-like materials exhibit a generic structure on the nanometer length scale consisting of hard mineral platelets arranged in a parallel staggered pattern in a soft protein matrix. The discussions in this paper are organized around the following questions: (1) The length scale question: why is nanoscale important to biological materials? (2) The stiffness question: how does nature create a stiff composite containing a high volume fraction of a soft material? (3) The toughness question: how does nature build a tough composite containing a high volume fraction of a brittle material? (4) The strength question: how does nature balance the widely different strengths of protein and mineral? (5) The optimization question: Can the generic nanostructure of bone and bone-like materials be understood from a structural optimization point of view? If so, what is being optimized? What is the objective function? (6) The buckling question: how does nature prevent the slender mineral platelets in bone from buckling under compression? (7) The hierarchy question: why does nature always design hierarchical structures? What is the role of structural hierarchy? A complete analysis of these questions taking into account the full biological complexities is far beyond the scope of this paper. The intention here is only to illustrate some of the basic mechanical design principles of bone-like materials using simple analytical and numerical models. With this objective in mind, the length scale question is addressed based on the principle of flaw tolerance which, in analogy with related concepts in fracture mechanics, indicates that the nanometer size makes the normally brittle mineral crystals insensitive to cracks-like flaws. Below a critical size on the nanometer length scale, the mineral crystals fail no longer by propagation of pre-existing cracks, but by uniform rupture near their limiting strength. The robust design of bone-like materials against brittle fracture provides an interesting analogy between Darwinian competition for survivability and engineering design for notch insensitivity. The follow-up analysis with respect to the questions on stiffness, strength, toughness, stability and optimization of the biological nanostructure provides further insights into the basic design principles of bone and bone-like materials. The staggered nanostructure is shown to be an optimized structure with the hard mineral crystals providing structural rigidity and the soft protein matrix dissipating fracture energy. Finally, the question on structural hierarchy is discussed via a model hierarchical material consisting of multiple levels of self-similar composite structures mimicking the nanostructure of bone. We show that the resulting 'fractal bone', a model hierarchical material with different properties at different length scales, can be designed to tolerate crack-like flaws of multiple length scales.
A phase-field model for cohesive fracture Verhoosel, Clemens V.; de Borst, René
International journal for numerical methods in engineering,
5 October 2013, Letnik:
96, Številka:
1
Journal Article
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