Crack kinking at the tip of a mode I crack in an orthotropic solid.

The competition between crack penetration and crack kinking is addressed for a mode I macroscopic crack in an orthotropic elastic solid. Cohesive zones of finite peak strength and finite toughness are placed directly ahead of and orthogonal to the plane of the parent crack. The cohesive zone ahead of the crack tip is tensile in nature and leads to crack penetration, whereas the inclined zones slide without opening under a combined shear and normal traction, and give crack kinking. Thereby, the competition between continued crack growth by penetration ahead of the crack tip versus kinking is determined as a function of the relative strength and relative toughness of the cohesive zones. This competition is plotted in the form of a failure mechanism map, with the role of material orthotropy emphasized. Synergistic toughening is observed, whereby the parent crack tip is shielded by the activation of both the tensile and shear (kinking) cohesive zones, and the macroscopic toughness is elevated. The study is used to assess the degree to which various classes of composite have the tendency to undergo kinking

Valley filtering and spatial maps of coupling between silicon donors and quantum dots

Exchange coupling is a key ingredient for spin-based quantum technologies since it can be used to entangle spin qubits and create logical spin qubits. However, the influence of the electronic valley degree of freedom in silicon on exchange interactions is presently the subject of important open questions. Here we investigate the influence of valleys on exchange in a coupled donor/quantum dot system, a basic building block of recently proposed schemes for robust quantum information processing. Using a scanning tunneling microscope tip to position the quantum dot with sub-nm precision, we find a near monotonic exchange characteristic where lattice-aperiodic modulations associated with valley degrees of freedom comprise less than 2~\% of exchange. From this we conclude that intravalley tunneling processes that preserve the donor's $\pm x$ and $\pm y$ valley index are filtered out of the interaction with the $\pm z$ valley quantum dot, and that the $\pm x$ and $\pm y$ intervalley processes where the electron valley index changes are weak. Complemented by tight-binding calculations of exchange versus donor depth, the demonstrated electrostatic tunability of donor/QD exchange can be used to compensate the remaining intravalley $\pm z$ oscillations to realise uniform interactions in an array of highly coherent donor spins.Comment: 6 pages, 4 figures, 6 pages Supplemental Materia

The crack growth resistance of an elastoplastic lattice

The degree to which the toughness of a lattice material can be enhanced by the suitable placement of multiple phases is explored. To achieve this, the resistance to mode I and mode II crack growth in a two-dimensional (2D), elastoplastic, triangulated lattice is investigated using finite element (FE) simulations. The fully triangulated lattice is idealised as a pin-jointed truss, and each strut has an axial force versus elongation (or shortening) characteristic based on the uniaxial tensile response of an elastoplastic solid with power-law hardening. When the tensile force in the strut attains a critical value, a linear softening law is adopted for the force versus elongation response of the strut to simulate its failure. FE simulations of crack growth in the 2D lattice are performed under small-scale yielding conditions, and the sensitivity of the crack growth resistance curve (curve) to the cell wall strain hardening exponent and cell wall ductility is determined. Three concepts for enhancing the curve of a triangulated lattice are explored: (i) a brittle lattice reinforced by long ductile fibres transverse to the cracking plane, (ii) a bilattice such that a small scale brittle lattice is reinforced by a large scale ductile lattice, and (iii) a 2D version of an interpenetrating lattice wherein a large-scale ductile lattice is bonded at its joints to an underlying small-scale brittle lattice.The authors gratefully acknowledge the financial support from the European Research Council (ERC) in the form of an advanced grant, MULTILAT, GA669764

2013 Koiter Medal Paper: Crack-Tip Fields and Toughness of Two-Dimensional Elastoplastic Lattices

The dependence of the fracture toughness of two-dimensional (2D) elastoplastic lattices upon relative density and ductility of cell wall material is obtained for four topologies: the triangular lattice, kagome lattice, diamond lattice, and the hexagonal lattice. Crack-tip fields are explored, including the plastic zone size and crack opening displacement. The cell walls are treated as beams, with a material response given by the Ramberg-Osgood law. There is choice in the criterion for crack advance, and two extremes are considered: (i) the maximum local tensile strain (LTS) anywhere in the lattice attains the failure strain or (ii) the average tensile strain (ATS) across the cell wall attains the failure strain (which can be identified with the necking strain). The dependence of macroscopic fracture toughness upon failure strain, strain hardening exponent, and relative density is obtained for each lattice, and scaling laws are derived. The role of imperfections in degrading the fracture toughness is assessed by random movement of the nodes. The paper provides a strategy for obtaining lattices of high toughness at low density, thereby filling gaps in material property space

Crack kinking at the tip of a mode I crack in an orthotropic solid

The competition between crack penetration and crack kinking is addressed for a mode I macroscopic crack in an orthotropic elastic solid. Cohesive zones of finite peak strength and finite toughness are placed directly ahead of and orthogonal to the plane of the parent crack. The cohesive zone ahead of the crack tip is tensile in nature and leads to crack penetration, whereas the inclined zones slide without opening under a combined shear and normal traction, and give crack kinking. Thereby, the competition between continued crack growth by penetration ahead of the crack tip versus kinking is determined as a function of the relative strength and relative toughness of the cohesive zones. This competition is plotted in the form of a failure mechanism map, with the role of material orthotropy emphasized. Synergistic toughening is observed, whereby the parent crack tip is shielded by the activation of both the tensile and shear (kinking) cohesive zones, and the macroscopic toughness is elevated. The study is used to assess the degree to which various classes of composite have the tendency to undergo kinking

2019 Proceedings of the 2nd International Conference on Trauma Surgery Technology in Giessen (Germany)

It is now for a second time that we can invite researchers to come to Giessen for an international exchange of the latest research and a discussion of ideas. This year again, the Deutsche Forschungsgemeinschaft (DFG) is sponsoring the event. The main topic for 2019 is 'Vibration in antibacterial and oncological therapy'. Many effects of mechanical vibration on tissue have been discovered so far. Clinical applications relying on vibration exist for a variety of conditions. The intracellular processes, however, are still largely not understood. And reproducibility remains a matter of potential for improvement. DFG funds for the 3rd conference in 2020 have already been approved for a focus on multifunctional trauma surgery implants.Deutsche Forschungsgemeischaft (DFG), German

Notch sensitivity of orthotropic solids: interaction of tensile and shear damage zones.

The macroscopic tensile strength of a panel containing a centre-crack or a centre-hole is predicted, assuming the simultaneous activation of multiple cohesive zones. The panel is made from an orthotropic elastic solid, and the stress raiser has both a tensile cohesive zone ahead of its tip, and shear cohesive zones in an orthogonal direction in order to represent two simultaneous damage mechanisms. These cohesive zones allow for two modes of fracture: (i) crack extension by penetration, and (ii) splitting in an orthogonal direction. The sensitivity of macroscopic tensile strength and failure mode to the degree of orthotropy is explored. The role of notch acuity and notch size are assessed by comparing the response of the pre-crack to that of the circular hole. This study reveals the role of the relative strength and relative toughness of competing damage modes in dictating the macroscopic strength of a notched panel made from an orthotropic elastic solid. Universal failure mechanism maps are constructed for the pre-crack and hole for a wide range of material orthotropies. The maps are useful for predicting whether failure is by penetration or kinking. Case studies are developed to compare the predictions with observations taken from the literature for selected orthotropic solids. It is found that synergistic strengthening occurs: when failure is by crack penetration ahead of the stress raiser, the presence of shear plastic zones leads to an enhancement of macroscopic strength. In contrast, when failure is by crack kinking, the presence of a tensile plastic zone ahead of the stress raiser has only a mild effect upon the macroscopic strength

Valley interference and spin exchange at the atomic scale in silicon

Tunneling is a fundamental quantum process with no classical equivalent, which can compete with Coulomb interactions to give rise to complex phenomena. Phosphorus dopants in silicon can be placed with atomic precision to address the different regimes arising from this competition. However, they exploit wavefunctions relying on crystal band symmetries, which tunneling interactions are inherently sensitive to. Here we directly image lattice-aperiodic valley interference between coupled atoms in silicon using scanning tunneling microscopy. Our atomistic analysis unveils the role of envelope anisotropy, valley interference and dopant placement on the Heisenberg spin exchange interaction. We find that the exchange can become immune to valley interference by engineering in-plane dopant placement along specific crystallographic directions. A vacuum-like behaviour is recovered, where the exchange is maximised to the overlap between the donor orbitals, and pair-to-pair variations limited to a factor of less than 10 considering the accuracy in dopant positioning. This robustness remains over a large range of distances, from the strongly Coulomb interacting regime relevant for high-fidelity quantum computation to strongly coupled donor arrays of interest for quantum simulation in silicon

Spatial metrology of dopants in silicon with exact lattice site precision

Scaling of Si-based nanoelectronics has reached the regime where device function is affected not only by the presence of individual dopants, but also by their positions in the crystal. Determination of the precise dopant location is an unsolved problem in applications from channel doping in ultrascaled transistors to quantum information processing. Here, we establish a metrology combining low-temperature scanning tunnelling microscopy (STM) imaging and a comprehensive quantum treatment of the dopant-STM system to pinpoint the exact coordinates of the dopant in the Si crystal. The technique is underpinned by the observation that STM images contain atomic-sized features in ordered patterns that are highly sensitive to the STM tip orbital and the absolute dopant lattice site. The demonstrated ability to determine the locations of P and As dopants to 5 nm depths will provide critical information for the design and optimization of nanoscale devices for classical and quantum computing applications

Two-electron states of a group-V donor in silicon from atomistic full configuration interactions

Two-electron states bound to donors in silicon are important for both two-qubit gates and spin readout. We present a full configuration interaction technique in the atomistic tight-binding basis to capture multielectron exchange and correlation effects taking into account the full band structure of silicon and the atomic-scale granularity of a nanoscale device. Excited s-like states of A1 symmetry are found to strongly influence the charging energy of a negative donor center. We apply the technique on subsurface dopants subjected to gate electric fields and show that bound triplet states appear in the spectrum as a result of decreased charging energy. The exchange energy, obtained for the two-electron states in various confinement regimes, may enable engineering electrical control of spins in donor-dot hybrid qubits