WHAT IF SPIDERS MADE METAMATERIAL WEBS USING MATERIALS WITH MECHANICAL SIZE-EFFECTS?

Spider’s webs are elegant examples of natural composites that can absorb outof- plane impact energy to capture prey. Different spiders have different methods and structure of webs, and these variations in topologies have a significant effect on the prey catching abilities of the web. Taking inspiration from the spiders, metamaterials that have architectured topology can be fabricated according to end applications such as energy absorbers or impact tolerant materials. In this investigation, we theoretically examined impact loading on various orb-spider webs modeled with metamaterial architecture using materials that show size-dependent behavior. Using the size-dependent properties of nano-reinforced polymer-derived ceramics (PDCs), various metamaterial topologies were evaluated for out-of-plane impact due using ANSYS Ls-Dyna. The material properties capture the size dependency of the ceramics where smaller elements have higher strength due to reduced flaw intensity; the mechanical strength of these elements does not follow the conventional Griffith Theory. In this study, spider web geometries fabricated with PDCs with varying size elements were examined.

Calculations on compact disc cracking

The Griffith equation for brittle cracking has three problems. First, it applies to an infinite sheet whereas a laboratory test sample is typically near 100 × 100 mm. Second, it describes a central crack instead of the more dangerous and easily observable edge crack. Third, the theory assumes a uniform stress field, instead of tensile force application used in the laboratory. The purpose of this paper is to avoid these difficulties by employing Gregory's solution in calculating the crack behaviour of PMMA (Poly Methyl Meth Acrylate) discs, pin loaded in tension. Our calculations showed that axial disc loading gave nominal strengths comparable with Griffith theory, but the force went to zero as the crack fully crossed the disc, fitting experimental results. Off-axis loading was more interesting because the predicted strength was lower than in axial testing, but also gave unexpected behaviour at short crack lengths, where nominal strength did not rise indefinitely but dropped as crack length went below D/10, quite different from Griffith, where strength rose continuously as cracks were shortened. Such off-axis loading leads to a size effect in which larger discs are weaker, reminiscent of the fine fibre strengthening phenomenon reported in Griffith's early paper (Griffith 1921 Phil. Trans. R. Soc. Lond. A 221 , 163–198. ( doi:10.1098/rsta.1921.0006 )). This article is part of a discussion meeting issue ‘A cracking approach to inventing new tough materials: fracture stranger than friction'.

The Use of Peridynamic Virtual Fibres to Simulate Yielding and Brittle Fracture

The forces in the ‘arms’ joining the particles in a peridynamic analysis depend upon the state of stress in the equivalent continuum and the orientation, length and density of the arms. Short and long arms carry less force than medium length arms as controlled by the weighting kernel. We introduce an intermediate step of imagining a mat of long fibres in which the fibre forces only depend upon the stress, the fibre orientation and the length of fibres per unit volume without the added complexity of the arm lengths. The effect of the arm lengths can then be considered as a separate exercise, which does not involve the continuum properties. The arm length is proportional to size of the particles and the separation of length from the state of stress allows for modelling of variable particle density in the discretisation of a problem domain, which enables computationally efficient accurate analysis. We then introduce the concept of arm elongation to fracture in order to model surface energy in fracture mechanics. This means that shorter arms have a larger strain to fracture than longer arms. Numerical implementation demonstrates that this produces a fracture stress that is inversely proportional to the square root of the crack length as predicted by the Griffith theory [1, 2].

Modeling of porous concrete elements under load

It is known that cell concretes are almost immediately destroyed under load, having reached certain critical stresses. Such kind of destruction is called a “catastrophic failure”. Process of crack formation is one of the main factors, influencing process of concrete destruction. Modern theory of crack formation is mainly based on the Griffith theory of destruction. However, the mentioned theory does not completely correspond to the structure of cell concrete with its cell structure, because the theory is intended for a solid body. The article presents one of the possible variants of modelling of the structure of cell concrete and gives some assumptions concerning the process of crack formation in such hollow, not solid environment.

The Reliability of Micro-Spring under Dynamic Circumstances

This article mainly focuses on the reliability of micro-spring, which as a typical component of MEMS device, applies electrodeposited nickel material and is fabricated by LIGA process, being used under the circumstances like transporting and restoring which may induce shock and crash. Griffith theory of brittle fracture and Abaqus FEA simulation software are applied for analyzing the probable failure modes of the micro-spring as overloaded. And the principle of elastic deformation, energy-time and displacement-time variation curves are given by three groups of simulation experiments. It proves to be one novel method to evaluate the reliability and accelerate exposing the failure mode of these MEMS components under dynamic circumstances in short period. After comparison, this method is proved reliable for analyzing and providing evidence for enhancing the reliability of the micro-spring, also improving the performance in micron size.

PHENOMENOLOGICAL MODELING FOR PORE OPENING, CLOSURE AND RUPTURE OF THE GUV MEMBRANE

In this paper, the pore opening and closure on the giant unilamellar vesicle GUV membrane are studied under different theoretical schemes. The opening process is considered as a dynamics process; while the closure process is considered as a quasi-static process. The opening criterion is set based on an energy release rate theory, similar to the Griffith theory for crack initiation. On the other hand, the closure process is described by a non-equilibrium thermodynamic theory. When the size of initial pore is smaller than a critical value, the pore is stable, and followed by the closure process. Otherwise, the pore is unstable, which leads to the rupture of the vesicle.