Mechanics of hierarchical materials

In this paper the simplest mathematical model to design nano-bio-inspired hierarchical materials is proposed. Simple formulas describing the dependence of strength, toughness and stiffness on the considered size-scale are derived, taking into account the toughening biomechanisms.     

Mechanics of porous elastic materials containing multiphase fluid

A continuum theory of mixtures for a porous elastic solid saturated by immiscible viscous fluids is presented. The theory includes micro-inertial effects for the local fluctuation in volume fractions of the solid and fluid constituents. Gradients of volume fraction of both the elastic solid and fluid constituents are included in the constitutive variables. Equations governing the macroscopic motion are developed and show that the present theory contains both Biot's equations and multiphase Darcy flow through porous media as special cases.     

Mechanics of small damage in fiber-reinforced composite materials

In this work the new concept of small damage is examined within the framework of continuum damage mechanics. In particular, special emphasis is given to a new damage variable that is defined in terms of the elastic stiffness of the material. Only the scalar case is studied in this work. The scalar definition of the new damage variable was used recently by many researchers. The investigation of the new scalar damage variable and the new concept of small damage is carried out on fiber-reinforced composite materials.     

Mechanics of tunnelling cracks in trilayer elastic materials in tension

In this work, the crack driving force for a tunnelling crack in a thin brittle layer confined by dissimilar thick, and more compliant, elastic layers is considered at tensile loading. The steady-state energy release rate is evaluated using distributed dislocation technique and series representation of the complex potentials for an isotropic trimaterial. Evolution of the energy release rate with the crack length is studied by means of FEM. The 3D FEM simulations for tunnel cracks suggest that the ERR can represented by a universal relation (mastercurve) in suitably normalised co-ordinates. An analytical approximation of the ERR mastercurve is obtained as a function of crack length, cracking layer thickness, and a non-dimensional steady-state ERR.     

Mechanics of extended continua: modeling and simulation of elastic microstretch materials

The investigation of microstretch and micromorphic continua (which are prominent examples of so-called extended continua) dates back to Eringens pioneering works in the mid 1960, cf. (Eringen in Mechanics of micromorphic materials. Springer, Berlin Heidelberg New York, pp 131–138, 1966; Eringen in Int J Eng Sci 8:819–828; Eringen in Microcontinuum field theories. Springer, Berlin Heidelberg New York, 1999). Here, we re-derive the governing equations of microstretch continua in a variational setting, providing a natural framework within which numerical implementations of the model equations by means of the finite element method can be obtained straightforwardly. In the application of Dirichlets principle, the postulation of an appropriate form of the Helmholtz free energy turns out to be crucial to the derivation of the balance laws and constitutive relations for microstretch continua. At present, the material parameters involved in the free energy have been assigned fixed values throughout all numerical simulations—this simplification is addressed in detail as the influence of those parameters must not be underestimated. Since only few numerical results demonstrating elastic microstretch material behavior in engineering applications are available, the focus is here on the presentation of numerical results for simple twodimensional test specimens subjected to a plane strain condition and uniaxial tension. Confidence in the simulations for microstretch materials is gained by showing that they exhibit a “downward-compatibility” to Cosserat continuum formulation: by switching off all stretch-related effects, the governing set of equations reduces to the one used for polar materials. Further, certain material parameters can be chosen to act as penalty parameters, forcing stretch-related contributions to an almost negligible range in a full microstretch model so that numerical results obtained for a polar model can be obtained as a limiting case from the full microstretch model.     

Mechanics at the interfaces of 2D materials: Challenges and opportunities

At the interfaces of 2D materials, the solid-state condensed matter physics is closely intertwined with the mechanics in terms of adhesion/separation and friction as well as deformation of 2D materials. With atomically thin 2D layers in atomically close proximity, the chemical, physical, and mechanical interactions simultaneously evolve and influence each other, leading to a wide range of topological structures and properties across nano- and micro-scales. Can the study on the mechanics of interfaces help to understand the physics and chemistry at the interfaces of 2D materials or vice versa? This Opinion aims to highlight the recent mechanics research on such material interfaces, where a multiscale, multidisciplinary effort is most effective moving forward with plenty of challenges and opportunities.     

Correction to: Mechanics of the small punch test: a review and qualification of additive manufacturing materials

Journal of Materials Science - A correction to this paper has been published: https://doi.org/10.1007/s10853-021-06081-z     

Mechanics of three-dimensional braided structures for composite materials – Part II: prediction of the elastic moduli

In the first part of this series of paper [Z.X. Zang, R. Postle, Mechanics of three-dimensional braided structures for composite materials – Part I: fabric structure and fibre volume fraction, Comp. Struct. 49 (2000) 451–459], it was demonstrated that the braiding angles and fibre volume fraction can be represented as functions of the normalized pitch length introduced as a key parameter of three-dimensional braided reinforced composite materials. In the present paper, the models for the prediction of the tensile and shear moduli of three-dimensional braided composites are established by numerical simulation and mathematical modelling. Three-dimensional braided preforms are produced from the material system comprising glass/polypropylene and their moduli are measured. The results predicted from the braided composite models are supported by the experimental data.     

Mechanics of form closure

Summary The minimum requirements for the form closure of a rigid body are investigated. This necessarily involves the use of point contacts. The requirements are reduced to a conceptually simple and powerful form: the contacts should be applied in the senses in which the equilibrating forces act along the contact normals in the absence of any applied forces. The number of contacts necessary, the number of unloaded contacts and their identification, the case where the problem is solved in stages and the condition for the determinacy of the reactions are effectively dealt with. Illustrative examples are included.With 6 Figures     

Mechanics of fibre fragmentation

A fragmentation specimen consists of a single fibre embedded along the axis of a long narrow resin block. When the fibre is broken by a tensile load, either a lateral crack runs outwards into the resin, initiated by the break, or a debond (or equivalently a cylindrical crack in the resin) propagates along the fibre. Debonding always occurs with thin fibres. Strain energy release rates have now been calculated, analytically for long debonds and by FEA for short ones. The force to propagate a debond is found to increase as the debond grows, reaching a final value, termed pull-out force, that is higher for softer fibres. If this force exceeds the strength of the fibre, then the fibre breaks again. This is the proposed mechanism of fibre fragmentation. For weakly-bonded, stiff fibres, the inferred minimum distance between breaks, i.e. the critical fragment length, is deduced to be of the order of the geometric mean of the radii of fibre and resin block, about 0.1–0.5 mm for typical fragmentation specimens, and it increases as the ratio of fibre stiffness to resin block stiffness increases, in agreement with observation.     

Mechanics of stretchable electronics

Recent advances in mechanics and materials provide routes to develop stretchable electronics that offer performance of conventional wafer-based devices but with the ability to be deformed to arbitrary shape. Many new applications become possible ranging from electronic eye cameras to wearable electronics, to bio-integrated therapeutic devices. This paper reviews mechanics of stretchable electronics in terms of two main forms of stretchable designs. One is wavy design, which can provide one-dimensional stretchability. The other is island-bridge design, which can be stretched in all directions. Mechanics models and their comparisons to experiments and finite element simulations are reviewed for these two designs. The results provide design guidelines for the development of stretchable electronics.     

Mechanics of Elastomer--Shim Laminates

The mechanics of laminates of elastomer and shims of high modulus material are reviewed. Such structures are often built to provide engineering components with specified, and quite different, stiffnesses in different modes of deformation. The shims may either be rigid or flexible, flat or curved, but are usually close to inextensible, being made of a high modulus material such as steel. On the other hand, rubber has an exceptionally low shear modulus, about one thousandth of its bulk modulus, so that shear of the rubber layers and flexure of the high modulus layers (if thin) are the dominant mechanisms of deformation of the composite. In comparison, extension of the layers and changes to their separation are highly constrained.
Modes of failure are addressed as well as force-deformation behaviour. For compression normal to the laminations, the shear in the rubber results in in-plane tension in the shims, possibly leading to tensile failure. For tension normal to the laminations, the elastomer can cavitate, which would relieve the shear in it and hence the in-plane compressive stress applied to the shim. In flexure, shear in the rubber can apply in-plane compressive stress to the shims and cause buckling failure.     

Mechanics of the onager

Summary A mathematical model is proposed, apparently for the first time, for the onager, a late Roman catapult. The elastic energy of the machine is contained in a cylindrical bundle of twisted elastic cords, and, although each cord satisfies a linear stress-strain law, the geometry of the entire bundle causes a torque to be exerted on the moving arm of the onager which is a nonlinear function of the angular deflection of the arm. This torque is used in the nonlinear differential equations of motion which are integrated numerically. Experimental work is described which assists in determining the torque, and in addition supplies ranges for the projectiles for various masses, sling lengths and finger angles (parts of the release mechanism). Predictions from the mathematics are in reasonable agreement with experiment. A new calibration rule for the onager is proposed, based on the numerical integrations, which complements that known since classical times for the two-armed Greek palintone. Finally an appendix contains a discussion of the effect of a buffer on the motion.     

Mechanics of three-dimensional braided structures for composite materials – part I: fabric structure and fibre volume fraction

This paper is the first part of a series on the mechanics of three-dimensional braided structures for composite materials which include fabric structure and fibre volume fraction models, prediction of mechanical properties, finite element analysis and simulation of deformations. In the present paper, the normalized pitch length is introduced as a key parameter of three-dimensional braided structures. It is demonstrated that the braiding angles and fibre volume fractions can be represented as functions of this key parameter. The structures of three-dimensional braids were simulated and the braided fabrics and preforms were designed and produced. Fibre volume fraction models were established. The predictions from the fibre volume fraction models are supported by experimental results.     

Applied Quantum Mechanics

It is shown that the first-order correlation function connected with a scalar wave field, can be determined from a set of intensity distributions in the image plane, generated by different settings of the defocusing and the moment of axial astigmatism. Estimates of the error with which the coherence function can be determined are derived.