SUMMARYA methodology is developed for switching from a continuum to a discrete discontinuity where the governing partial di erential equation loses hyperbolicity. The approach is limited to rate-independent materials, so that the transition occurs on a set of measure zero. The discrete discontinuity is treated by the extended ÿnite element method (XFEM) whereby arbitrary discontinuities can be incorporated in the model without remeshing. Loss of hyperbolicity is tracked by a hyperbolicity indicator that enables both the crack speed and crack direction to be determined for a given material model. A new method was developed for the case when the discontinuity ends within an element; it facilitates the modelling of crack tips that occur within an element in a dynamic setting. The method is applied to several dynamic crack growth problems including the branching of cracks.

SUMMARYAn extended ÿnite element method scheme for a static cohesive crack is developed with a new formulation for elements containing crack tips. This method can treat arbitrary cracks independent of the mesh and crack growth without remeshing. All cracked elements are enriched by the sign function so that no blending of the local partition of unity is required. This method is able to treat the entire crack with only one type of enrichment function, including the elements containing the crack tip. This scheme is applied to linear 3-node triangular elements and quadratic 6-node triangular elements. To ensure smooth crack closing of the cohesive crack, the stress projection normal to the crack tip is imposed to be equal to the material strength. The equilibrium equation and the traction condition are solved by the Newton-Raphson method to obtain the nodal displacements and the external load simultaneously. The results obtained by the new extended ÿnite element method are compared to reference solutions and show excellent agreement.

We report on the facile fabrication of a stretchable array of highly sensitive pressure sensors. The proposed pressure sensor consists of the top layer of Au-deposited polydimethylsiloxane (PDMS) micropillars and the bottom layer of conductive polyaniline nanofibers on a polyethylene terephthalate substrate. The sensors are operated by the changes in contact resistance between Au-coated micropillars and polyaniline according to the varying pressure. The fabricated pressure sensor exhibits a sensitivity of 2.0 kPa(-1) in the pressure range below 0.22 kPa, a low detection limit of 15 Pa, a fast response time of 50 ms, and high stability over 10000 cycles of pressure loading/unloading with a low operating voltage of 1.0 V. The sensor is also capable of noninvasively detecting human-pulse waveforms from carotid and radial artery. A 5 × 5 array of the pressure sensors on the deformable substrate, which consists of PDMS islands for sensors and the mixed thin film of PDMS and Ecoflex with embedded liquid metal interconnections, shows stable sensing of pressure under biaxial stretching by 15%. The strain distribution obtained by the finite element method confirms that the maximum strain applied to the pressure sensor in the strain-suppressed region is less than 0.04% under a 15% biaxial strain of the unit module. This work demonstrates the potential application of our proposed stretchable pressure sensor array for wearable and artificial electronic skin devices.

A stretchable polyaniline nanofiber temperature sensor array with an active matrix consisting of single-walled carbon nanotube thin-film transistors is demonstrated. The integrated temperature sensor array gives mechanical stability under biaxial stretching of 30%, and the resultant spatial temperature mapping does not show any mechanical or electrical degradation.

[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.