A new multi-scale dispersive gradient elasticity modelwith micro-inertia: Formulation and C0-finiteelement implementation

Motivated by nano-scale experimental evidence on the dispersion characteristics of materials with a lattice structure, a new multi-scale gradient elasticity model is developed. In the framework of gradient elasticity, the simultaneous presence of acceleration and strain gradients has been denoted as dynamic consistency. This model represents an extension of an earlier dynamically consistent model with an additional micro-inertia contribution to improve the dispersion behaviour. The model can therefore be seen as an enhanced dynamic extension of the Aifantis' 1992 strain-gradient theory for statics obtained by including two acceleration gradients in addition to the strain gradient. Compared with the previous dynamically consistent model, the additional micro-inertia term is found to improve the prediction of wave dispersion significantly and, more importantly, requires no extra computational cost. The fourth-order equations are rewritten in two sets of symmetric second-order equations so that C0-continuity is sufficient in the finite element implementation. Two sets of unknowns are identified as the microstructural and macrostructural displacements, thus highlighting the multi-scale nature of the present formulation. The associated energy functionals and variationally consistent boundary conditions are presented, after which the finite element equations are derived. Considerable improvements over previous gradient models are observed as confirmed by two numerical examples

Adaptive Element-Free Galerkin method applied to the limit analysis of plates

The implementation of an h-adaptive Element-Free Galerkin (EFG) method in the framework of limit analysis is described. The naturally conforming property of mesh- free approximations (with no nodal connectivity required) facilitates the implementation of h-adaptivity. Nodes may be moved, discarded or introduced without the need for complex manipulation of the data structures involved. With the use of the Taylor expansion technique, the error in the computed displacement field and its derivatives can be estimated throughout the problem domain with high accuracy. A stabilized conforming nodal integration scheme is extended to error estimators and results in an efficient and truly meshfree adaptive method. To demonstrate its effectiveness the procedure is then applied to plates with various boundary conditions

On the multiaxial fatigue assessment of complex three-dimensional stress concentrators

This paper assesses and quantifies the detrimental effects of complex tri-dimensional notches subjected to uniaxial and multiaxial fatigue loading. A number of experimental results taken from the technical literature and generated by testing specimens containing complex geometrical features were reanalysed using a critical distance/plane method. The investigated notched samples were tested under uniaxial and multiaxial constant amplitude load histories, considering also the effects of non-zero mean stresses as well as non-proportional loading. The common feature of the considered notched geometries was that the position of the critical location changed as the degree of multiaxiality of the applied loading varied. The relevant linear-elastic stress fields in the vicinity of the crack initiation points were calculated by the Finite Element method and subsequently post-processed using the Modified Wöhler Curve Method in conjunction with the Theory of Critical Distances (the latter theory being applied in the form of the Point Method). This validation exercise confirms the accuracy and reliability of our multiaxial fatigue life assessment technique, which can be efficiently used in situations of practical interest by directly post-processing the relevant linear-elastic stress fields calculated with commercial Finite Element software packages.Safe Technology Limite

Gradient enriched linear-elastic crack tip stresses to estimate the static strength of cracked engineering ceramics

According to Gradient Mechanics (GM), stress fields have to be determined by directlyincorporating into the stress analysis a length scale which that takes into account the material microstructuralfeatures. This peculiar modus operandi results in stress fields in the vicinity of sharp cracks which are no longersingular, even though the assessed material is assumed to obey a linear-elastic constitutive law. Given both thegeometry of the cracked component being assessed and the value of the material length scale, the magnitude ofthe corresponding gradient enriched linear-elastic crack tip stress is then finite and it can be calculated by takingfull advantage of those computational methods specifically devised to numerically implement gradient elasticity.In the present investigation, it is first shown that GM’s length scale can directly be estimated from the materialultimate tensile strength and the plane strain fracture toughness through the critical distance value calculatedaccording to the Theory of Critical Distances. Next, by post-processing a large number of experimental resultstaken from the literature and generated by testing cracked ceramics, it is shown that gradient enriched linearelasticcrack tip stresses can successfully be used to model the transition from the short- to the long-crackregime under Mode I static loading

Reducible and irreducible forms of stabilised gradient elasticity in dynamics

The continualisation of discrete particle models has been a popular tool to formulate higher-order gradient elasticity models. However, a straightforward continualisation leads to unstable continuum models. Pade approximations can be used to stabilise ´ the model, but the resulting formulation depends on the particular equation that is transformed with the Pade approximation. In this contribution, we study two different stabilised ´ gradient elasticity models; one is an irreducible form with displacement degrees of freedom only, and the other is a reducible form where the primary unknowns are not only displacements but also the Cauchy stresses — this turns out to be Eringen’s theory of gradient elasticity. Although they are derived from the same discrete model, there are significant differences in variationally consistent boundary conditions and resulting finite element implementations, with implications for the capability (or otherwise) to suppress crack tip singularitie

Ultrafast Thermal Imprinting of Plasmonic Hotspots

Plasmonic photochemistry is driven by a rich collection of near-field, hot charge carrier, energy transfer, and thermal effects, most often accomplished by continuous wave illumination. Heat generation is usually considered undesirable, because noble metal nanoparticles heat up isotropically, losing the extreme energy confinement of the optical resonance. Here it is demonstrated through optical and heat-transfer modelling that the judicious choice of nanoreactor geometry and material enables the direct thermal imprint of plasmonic optical absorption hotspots onto the lattice with high fidelity. Transition metal nitrides (TMNs, e.g., TiN/HfN) embody the ideal material requirements, where ultrafast electron–phonon coupling prevents fast electronic heat dissipation and low thermal conductivity prolongs the heat confinement. The extreme energy confinement leads to unprecedented peak temperatures and internal heat gradients (>10 K nm−1) that cannot be achieved using noble metals or any current heating method. TMN nanoreactors consequently yield up to ten thousand times more product in pulsed photothermal chemical conversion compared with noble metals (Ag, Au, Cu). These findings open up a completely unexplored realm of nano-photochemistry, where adjacent reaction centers experience substantially different temperatures for hundreds of picoseconds, long enough for bond breaking to occur

Microstructural length scale parameters to model the high-cycle fatigue behaviour of notched plain concrete

The present paper investigates the importance and relevance of using microstructural length scale parameters in estimating the high-cycle fatigue strength of notched plain concrete. In particular, the accuracy and reliability of the Theory of Critical Distances and Gradient Elasticity are checked against a number of experimental results generated by testing, under cyclic bending, square section beams of plain concrete containing stress concentrators of different sharpness. The common feature of these two modelling approaches is that the required effective stress is calculated by using a length scale which depends on the microstructural material morphology. The performed validation exercise demonstrates that microstructural length scale parameters are successful in modelling the behaviour of notched plain concrete in the high-cycle fatigue regime

The gauge theory of dislocations: a nonuniformly moving screw dislocation

We investigate the nonuniform motion of a straight screw dislocation in infinite media in the framework of the translational gauge theory of dislocations. The equations of motion are derived for an arbitrary moving screw dislocation. The fields of the elastic velocity, elastic distortion, dislocation density and dislocation current surrounding the arbitrarily moving screw dislocation are derived explicitely in the form of integral representations. We calculate the radiation fields and the fields depending on the dislocation velocities.Comment: 12 page

Mass matrices for elastic continua with micro-inertia

In this paper, the finite element discretization of non-classical continuum models with micro-inertia is analysed. The focus is on micro-inertia extensions of the one-dimensional rod model, the beam bending theories of Euler-Bernoulli and Rayleigh, and the two-dimensional membrane model. The performance of a variety of mass matrices is assessed by comparing the natural frequencies and their modes with those of the associated discrete systems, and it is demonstrated that the use of higher-order mass matrices reduces errors and improves convergence rates. Furthermore, finite element sizes larger than the corresponding physical length scale are shown to be sufficient to capture the natural frequencies, thus facilitating numerical models that are not only reliable but also computationally efficient.The authors acknowledge support from MCIN/ AEI/10.13039/501100011033 under Grants numbers PGC2018-098218-B-I00 and PRE2019-088002. FEDER: A way to make Europe. ESF invests in your future