Special Issue “Extreme Mechanics in Multiscale Analyses of Materials”

EditorialThe responses and behaviour of engineering structures and materials subjected to various types of loading, particularly those under extreme loading such as earthquakes, explosions, and impacts, as well as under exposure to environmental elements, are of critical significance for the safety and integrity of said structures to fulfil their intended functions [...

Numerical simulation of the dynamic response in pulse-loaded fibre-metal-laminated plates

This article presents a three-dimensional constitutive model to replicate the dynamic response of blastloaded fibre–metal laminates made of 2024-0 aluminium alloy and woven composite (glass fibre–reinforced polypropylene). Simulation of the dynamic response is challenging when extreme localised loads are of concern and requires reliable material constitutive models as well as accurate modelling techniques. It is well known that back layers in a fibre–metal laminate provide structural support for front layers; thus, proper modelling of constituent failure and degradation is essential to understanding structural damage and failure. The improved developed model to analyse damage initiation, progression and failure of the composite is implemented in finite element code ABAQUS, and a good correlation is observed with experimental results for displacements of the back and front faces as presented by other researchers. The model was also able to predict accurately the tearing impulses. Finally, the concepts of the ‘efficiency of the charge’ and ‘effectiveness of the target’ are proposed in the context of localised blast loading on a structure. Dimensionless parameters are introduced to quantify these parameters

Dynamic Performance of Simply Supported Rigid-Plastic Square Plates Subject to Localized Blast Loading

This paper presents the theoretical solution to the response of a square plate undergoing plastic deformation due to a generic localized blast pulse. A localized blast load function was assumed multiplicative of its spatial distribution and temporal pulse shape. The spatial distribution was representative of constant pressure over the central zone, while exponentially decaying outside that zone. Considering an appropriate moment function and ignoring the membrane, transverse shear, and rotary inertia effects, the static plastic collapse was found, whereby the analysis was extended to the dynamic case by assuming a kinematically admissible, time-dependent velocity profile. The analytical model, which was validated against the numerical results obtained through ABAQUS hydrocode, showed close correlation in terms of the permanent transverse deflection profile. In order to consider the effect of temporal pulse shape, the results were formulated for rectangular as well as exponentially and linearly decaying pulses. For blast loads of high magnitude, the pressure load was replaced by an impulsive velocity. The calculations were simplified by utilizing the dimensionless form, and the results were corroborated with theoretical and experimental results from the literature. The model showed improvements in predicting the final deformation of square plates over previous models of simplified loading function

Inelastic dynamic response of square membranes subjected to localised blast loading

Extensive shock and highly localised blast waves generated by detonation of near field explosives (such as improvised explosive devices (IEDs)) are catastrophic to structures and humans, resulting in injury or death, progressive damage, or perforation through the structure and collapse. Mitigating the effects of such waves is paramount in various aspects of design engineering. A theoretical model is presented here to predict the large inelastic deformation of ductile thin square membranes induced by a generic, short pulse pressure load, comprising a piecewise function of spatial and temporal parts. Using the constitutive framework of limit analysis and incorporating the influence of finite displacements, two patterns of kinematically admissible, time dependent velocity profiles were investigated. These patterns included stationery and moving plastic hinges. The results were investigated in two cases: once with the interaction between bending moment and membrane forces retained in the analyses, and then when the response was solely governed by membrane forces. For blast loads of high magnitude, the pressure was replaced by an impulsive velocity and the results were expressed in terms of dimensionless form of initial kinetic energy. The effects of boundary conditions and visco-plasticity have also been investigated. The theoretical results corroborated well with various experimental results in the literature, on ductile metallic plates such as high strength ARMOX steel and mild steel

State of the art in fatigue modelling of composite wind turbine blades

This paper provides a literature review of the most notable models relevant to the evaluation of the fatigue response of composite wind turbine blades. As wind turbines spread worldwide, ongoing research to maximize their lifetime – and particularly that of wind turbine blades – has increasingly popularized the use of composite materials, which boast attractive mechanical properties. The review first presents the wind turbine blade environment, before distributing fatigue models broadly between three categories: life-based failure criterion models, which are based on S-N curve formulations and constant-life diagrams to introduce failure criteria; residual property calculation models, which evaluate the gradual degradation of material properties; and progressive damage models, which model fatigue via the cycle-by-cycle growth of one or more damage parameters. These are then linked to current testing standards, databases, and experimental campaigns. Among the fatigue modelling approaches covered, progressive damage models appear to be the most promising tool, as they both quantify and qualify physical damage growth to a reasonable extent during fatigue. The lack of consensus and shortcomings of literature are also discussed, with abundant referencing

Coupling XFEM and Peridynamics for Brittle Fracture Simulation - Part II: Adaptive Relocation Strategy

An adaptive relocation strategy for a coupled XFEM–Peridynamic (PD) model is introduced. The motivation is to enhance the efficiency of the coupled model and demonstrate its applicability to complex brittle fracture problems. The XFEM and PD approximation domains can be redefined during the simulation, to ensure that the computationally expensive PD model is applied only where needed. To this end a two-step expansion/contraction process, allowing the PD patch to adaptively change its shape, size and location, following the propagation of the crack, is employed. No a priori knowledge of the crack path or re-meshing is required, and the methodology can automatically switch between PD and XFEM. Three 2D fracture examples are presented to highlight the performance of the methodology and the ability to follow multiple crack tips. Results indicate significant computational savings. Furthermore, the characteristic length scale of PD theory bestows a nonlocal and multiscale component to the methodology

On the computational derivation of bond-based peridynamic stress tensor

The concept of ‘contact stress’, as introduced by Cauchy, is a special case of a nonlocal stress tensor. In this work, the nonlocal stress tensor is derived through implementation of the bond-based formulation of peridynamics that uses an idealised model of interaction between points as bonds. The method is sufficiently general and can be implemented to study stress states in problems containing stress concentration, singularity, or discontinuities. Two case studies are presented, to study stress concentration around a circular hole in a square plate and conventionally singular stress fields in the vicinity of a sharp crack tip. The peridynamic stress tensor is compared with finite element approximations and available analytical solutions. It is shown that peridynamics is capable of capturing both shear and direct stresses and the results obtained correlate well with those obtained using analytical solutions and finite element approximations. A built-in MATLAB code is developed and used to construct a 2D peridynamic grid and subsequently approximate the solution of the peridynamic equation of motion. The stress tensor is then obtained using the tensorial product of bond force projections for bonds that geometrically pass through the point. To evaluate the accuracy of the predicted stresses near a crack tip, the J-integral value is computed using both a direct contour approximation and the equivalent domain integral method. In the formulation of the contour approximation, bond forces are used directly while the proposed peridynamic stress tensor is used for the domain method. The J-integral values computed are compared with those obtained by the commercial finite element package Abaqus 2018. The comparison provides an indication on the accurate prediction of the state of stress near the crack tip

Plastic dynamic response of simply supported thick square plates subject to localised blast loading

Localised blast loads due to proximal charges are encountered in a variety of circumstances. This paper proposes an analytical solution for the dynamic plastic response of a rigid-perfectly plastic thick square plate subject to a localised explosion. The proposed model is an extension of the analytical model proposed by Micallef et al [1] to study circular plates which is adopted and modified in order to study impulsively loaded square plates where the effect of shear deformation is included. A piecewise continuous blast load function was assumed with axisymmetric spatial distribution of constant pressure in the central zone and exponentially decaying beyond it. Using the constitutive framework of limit analysis and incorporating the interactions between bending moment and transverse shear forces in the analyses, transverse displacement and response duration were examined on three classes of plates, classified according to the length to thickness ratio parameter ν. The results were furnished in terms of the impulsive velocity, which is a function of the localised blast load parameters. A theoretical solution for plates with ν > 2 was sought for the non-impulsive blast loads. Parametric studies were performed to elucidate the effect of loading parameters and plate thickness on the permanent deformation. The theoretical solutions have been found generic and can predict, by the correct choice of the load parameters, the dynamic response of most blast load scenarios brought about by proximal or distal charges. It was found that, for proximal impulsive blasts, the effect of transverse shear becomes irrelevant for even moderate values of ν which effect is inconsequential on both central and endpoint displacements at discontinuous interface in the range of ν > 5. Since the short duration pulse is of concern, localised pressure loads affect only a small area of the plated structures. Thus, whilst the theoretical treatments also examine the fully clamped plates, the boundary conditions in such loads do not influence the overall response of the structure compared to the static or global blast loads