A three-dimensional plasticity-damage constitutive model for timber under cyclic loads

The performance of timber structures is governed by the nonlinear response at their connections, where high deformation levels and stress concentrations are developed, particularly when subjected to load reversals. To date, no constitutive model for wood under cyclic load exists which is able to incorporate its most important failure modes while considering plastic deformations and cyclic stiffness and strength degradation simultaneously. This paper presents the formulation and implementation of a plasticity-damage model with these characteristics within a continuum mechanics approach. The theoretical framework of both plasticity and damage models is described, and a detailed derivation of the constitutive equations required for their computational implementation and coupling as well as the return mapping and iterative algorithms for their integration are presented. The damage evolution process is handled by two independent scalar variables for tension and compression. A general orthotropic plasticity yield surface with isotropic hardening is employed to incorporate timber plastic flow in compression. A closed-form expression for the plasticity-damage consistent tangent operator is derived. It is demonstrated that the proposed constitutive model captures all the key characteristics required for an accurate modelling of timber under large deformation levels until failure

Dynamic response of post-tensioned rocking structures with inerters

Post-tensioned rocking systems have proved to be highly effective in controlling structural damage during strong ground motions. However, recent events have highlighted the importance of looking at both the structural and non-structural components within a holistic framework. In this context, the high rotations and accelerations associated with the rocking motion can cause significant non-structural damage and affect the performance and functionality of the entire system. In this paper, we examine analytically the fundamental dynamics of post-tensioned rocking structures and investigate the bene fits of using supplemental rotational inertia to reduce their seismic demands and improve their overall performance. The newly proposed strategy employs inerters, a mechanical device that develops a resisting force proportional to the relative acceleration between its terminals. Analyses conducted for a wide range of acceleration pulses and real pulse-like ground motions show that post-tensioned structures equipped with inerters consistently experience lower demands and have reduced probabilities of exceeding limit states typically associated with damage. Importantly, the new vibration control strategy advanced in this paper opens the door for an expedient modification of the fundamental dynamic response of rocking systems without altering their geometry

Impact and clutch nonlinearities in the seismic response of inerto-rocking systems

Rocking bodies can be found at all structural scales, from small museum exhibits to uplifting buildings. These structures, whose dynamic stability springs from the difficulty of mobilizing their rotational inertia, are ideal candidates for benefiting from the supplemental inertia provided by inerters. This benefit can be limited, however, if the inerter drives the structural response towards potentially undesirable motions by transferring back the kinetic energy accumulated within it at inconvenient times. To control this phenomenon, a clutching system can be employed to direct the interaction between the interter and the structure improving further its dynamic behaviour. To date, however, most of the studies dealing with clutching inerto-elastic or inerto-rocking systems under seismic excitation have adopted a rather simplistic idealisation of the clutch engagement-disengagement response. In this paper, we re-visit the impact effects on inerto-rocking structures and propose an improved mechanistic model of the clutching system. First, the effects of the inerter on the transition upon impact and the impact effects on the acceleration response of rocking blocks are analysed. Then, a set of original analytical expressions for rigid and flexible rocking structures equipped with a pair of clutched inerters are derived. The newly proposed models are used to examine the evolution of the energy dissipation in the device and the influence of key parameters like the clutch stiffness, gears play, viscous damping and dry friction on its response. We conclude by evaluating the behaviour of the detailed rocking model with clutched inerters to a set of realistic earthquake ground motions. Although important differences are observed in the evolution of energy dissipation and engagement response depending on the type and characteristics of the clutch model, largely comparable peak values of displacement are obtained. On the other hand, a more accurate representation of the clutch behaviour leads to potentially larger acceleration demands. Our analyses also show that, in general, the inclusion of the inerter results in higher coefficients of restitution, indicating lower energy dissipation during impact and that the infinite acceleration spikes predicted by Housner’s model can be ignored if impact forces are sufficiently distributed over time as to cause continuous velocity transitions, but sharp enough not to appreciably affect the rotation response

OpenArch: An open-source package for determining the minimum-thickness of arches under seismic loads

Arches are elegant and efficient structural forms that can be used in a wide variety of applications, from bridges to extraterrestrial shielding structures. Oftentimes their design hinges around the identification of the minimum-thickness required to ensure their stability when subjected to gravity and lateral (inertial) loading. This work presents a MATLAB-based code called OpenArch developed within a procedural programming framework for the preliminary design and assessment of optimal arch forms of minimum thickness when subjected to combined self-weight and seismically induced loads. The code, which is based on limit thrust-line analysis can handle any classical or non-classical no-tension arch form and the results compare excellently with the few available analytical solutions

Limit-state analysis of parabolic arches subjected to inertial loading in different gravitational fields using a variational formulation

For thousands of years, arches have been used as durable structures that are easy to build and that rely on gravity for their inherent stability. Since then, many researchers and engineers have studied their stability either when subjected to gravity or inertial loading. Currently, given the Insight mission to Mars and the ambitious Artemis program to the Moon, it has become apparent that there will soon be the need to design and build the first resilient extraterrestrial structures and arches represent an ideal option for such structures. This paper focuses on the stability of parabolic arches with different embrace angles subjected to different levels of equivalent inertial loading in low-gravity conditions. The results are contrasted with the well-studied circular arches. More specifically, this investigation employs variational principles to identify the imminent mechanisms and numerical methods based on the limit thrust line concept in order to estimate the minimum required thickness of parabolic arches for a given loading and in different gravitational fields. The paper shows that although parabolic arches can be much more efficient than their circular counterparts for gravitational-only loading, this is not the case for different combinations of inertial loading and embrace angles where the opposite can be true. It highlights the dominant effect of low-gravity conditions on the minimum thickness requirements for both types of arches and considers the effect of a potential additional infill for shielding from radiation. Furthermore, this study reveals a self-similar behaviour, introduces a “universal” inertial loading and showcases through the use of master curves the areas where the parabolic arches are more efficient than the circular and the opposite. These areas can be used for the preliminary design of such structures. Additionally, the paper identifies hidden patterns associated with the developed mechanisms between the two different geometries for the different gravitational fields. Finally, it presents a case study where the need to optimise the structural form of extraterrestrial structures becomes evident

Optimal arch forms under in‐plane seismic loading in different gravitational environments

This paper is motivated by the renewed interest in space exploration and the need to provide structurally sound and resource-efficient shielding solutions for valuable assets and future habitable modules. We present, implement and test a methodology for the preliminary design and assessment of optimal arch forms subjected to self-weight as well as seismically induced loads. The numerical framework, built around a limit thrust-line analysis, previously published by the authors, is summarized first. This is followed by a detailed account of the form-finding algorithm for arches of variable thickness. Special attention is placed on the physical feasibility of our assumptions and the justification of the engineering inputs adopted. The newly form-found arches achieve material efficiencies between 10% and 50% in comparison with their constant minimum-thickness circular or elliptical counterparts, depending on the relative intensity of the seismic action. The influence of the initial input geometry and the stabilising presence of additional shielding material against extreme radiation are also evaluated with emphasis on the effects of low-gravity conditions. Finally, a case study is presented and Discrete Element Models of constant and varying thickness arches (VTAs) are assessed under a set of representative ground-motions on a lunar setting. The significant over-conservatism of constant thickness arches (CTAs) is made manifest and potential improvements of the optimally found arch shape are highlighted. Although developed with extraterrestrial applications in mind, the results and methods we present herein are also applicable to terrestrial conditions when material efficiency is of utmost concern

Innovations in earthquake risk reduction for resilience: Recent advances and challenges

The Sendai Framework for Disaster Risk Reduction 2015-2030 (SFDRR) highlights the importance of scientific research, supporting the ‘availability and application of science and technology to decision making’ in disaster risk reduction (DRR). Science and technology can play a crucial role in the world’s ability to reduce casualties, physical damage, and interruption to critical infrastructure due to natural hazards and their complex interactions. The SFDRR encourages better access to technological innovations combined with increased DRR investments in developing cost-effective approaches and tackling global challenges. To this aim, it is essential to link multi- and interdisciplinary research and technological innovations with policy and engineering/DRR practice. To share knowledge and promote discussion on recent advances, challenges, and future directions on ‘Innovations in Earthquake Risk Reduction for Resilience’, a group of experts from academia and industry met in London, UK, in July 2019. The workshop focused on both cutting-edge ‘soft’ (e.g., novel modelling methods/frameworks, early warning systems, disaster financing and parametric insurance) and ‘hard’ (e.g., novel structural systems/devices for new structures and retrofitting of existing structures, sensors) risk-reduction strategies for the enhancement of structural and infrastructural earthquake safety and resilience. The workshop highlighted emerging trends and lessons from recent earthquake events and pinpointed critical issues for future research and policy interventions. This paper summarises some of the key aspects identified and discussed during the workshop to inform other researchers worldwide and extend the conversation to a broader audience, with the ultimate aim of driving change in how seismic risk is quantified and mitigated