Historic monuments, drywall structures, and graphite blocks in AGR nuclear power plants are block‐like structures that have to withstand rocking when subject to seismic excitation of their base, ...which can lead to overturning of some of their components and results in the collapse of the whole structure. We revisit the known nonlinear equations of motion for a dual‐block stack and present the conditions for transition between the eight possible rocking configurations (due to initiation of rocking, opening of new contacts, and collisions between blocks). An algorithm for the numerical simulation of rocking of the dual‐block stack is developed using the Newmark integration method, the Newton‐Raphson iteration method, and a novel contact detection and resolution procedure. The algorithm is used to evaluate rocking stability of five dual‐block stacks, one of which is compared to the results available in the literature. In parallel, a novel experimental program is designed and implemented, to validate the numerically obtained results using a shaking table. While most of the excitation conditions leading to stable rocking and limit values leading to overturning have been successfully validated, some discrepancies between the numerically and experimentally obtained results still exist and point to the need for improvement of the algorithm used, possibly through a more realistic energy‐loss mechanism. Most importantly, we have confirmed the known theoretical prediction that splitting a single block into two half‐size blocks benefits its rocking stability.
A single rigid prismatic block is analysed for free rocking behaviour without sliding and jumping. A numerical procedure based on a precise contact detection is developed and tested. An extensive ...experimental study of free rocking for blocks of different slenderness and size is conducted, with the emphasis on the post-impact behaviour and energy loss mechanism in the existing impact models. The experiments conducted strongly support the definition of the restitution coefficient proposed both by Kalliontzis et al. (J Struct Eng 142(12):06016002,
2016
) and by Chatzis et al. (J Eng Mech 143(5):04017013,
2017
). A method is proposed to determine the extra parameter present in this model.
This paper reports a study to assess nanoindentation mapping of mechanical properties of cement paste and natural rocks. Initial work seems to show that mechanical property mapping by nanoindentation ...is feasible and can be related to microscopic information. Further work is however required on the effect of indent size and spacing. Such a testing technique can be very useful for materials with different phases to study the intrinsic properties of each component, and also the interaction and properties of the interfacial regions of different phases. The values of Young's modulus and hardness of the individual mineral phases were also determined by statistically analysing a large number of experimental data.
•A new hybrid force-based solution method is followed.•A general beam element is proposed.•Quasi-hinge and refined hinge element are compared.
This paper describes a new force-based hinge element ...implemented in the framework of the Large Increment Method (LIM). The element can be of arbitrary cross section and is capable of including inelastic behaviour close to structural hinges. The element formulation can accommodate elasto-plastic strain hardening material behaviour. The solution procedure involves the analysis of elastic and inelastic deformations separately facilitated by splitting of the element length into elastic and inelastic zones. Deformation is calculated by considering inelastic behaviour in the element volume close to both ends of the structural member using an optimum number of integration points in order to achieve good accuracy while maintaining computational efficiency. The predictions of both conventional- and quasi-hinge elements are compared against predictions from Abaqus™. Predictions of the quasi-hinge element show significant improvements over the conventional-hinge method and are shown to converge on the Abaqus™ prediction as the number of monitoring sections in the element is increased.
A detailed and fully generalised (3D) hygro-thermo-mechanical model for concrete is presented. The model captures the complex behaviour of this composite material through the adoption of a ...multi-phase material description which captures the strong coupling between the separately considered solid, liquid and gas fields. Heat and mass transport of the fluid phases are modelled in a coupled manner such that an accurate description of the fluid transport processes in concrete is possible, illustrating in particular the redistribution of liquid and the increases in vapour content and pore pressure associated with the application of elevated temperatures. The mechanical behaviour of the solid skeleton is modelled by way of an isotropic thermo-mechanical damage model in which the degradation of the material due to both mechanical and thermal loading is taken into account. Coupling with the hygro-thermal components of the model allows for the effects of material degradation on mass transport to be captured. The model is validated over a wide range of capability through the reproduction of two sets of separate and differing experimental results concerning isothermal drying and high temperature problems. For these two problems, the model is shown to reproduce accurately values for total moisture mass losses, moisture distributions, temperatures and pore pressures developed in both time and space in various types of both ordinary and high performance concrete materials. A further parametric study is then presented where the model is used to investigate the roles of various mechanical behaviours in the overall hygro-thermo-mechanical response of the concrete under high temperature conditions. The implications of the results are discussed in detail.
Two examples illustrating microstructural size effect and higher-order deformation are considered within the context of second-order computational homogenization. Governing equations and appropriate ...discretization are briefly reviewed, including the scale transition equations and the enforcement of generalised boundary conditions for the RVE (representative volume element). The first example serves as a means of validation for second-order computational homogenization and highlights the difference in terms of higher-order deformation of the RVE between the first and second-order schemes. The second example (indentation test) focuses on microstructural size effect, whereby the result is shown to be dependent on the intrinsic length of the RVE.
Recently developed semismooth Newton approach is adopted in the context of the frictional contact between three-dimensional pseudo-rigid bodies. The Signorini–Coulomb problem is formulated according ...to the formalism of the Contact Dynamics method. Hybrid linearisation, penalty scaling and line search techniques are combined as the global convergence enhancements of the Newton algorithm. Quasi-static simulations of dry masonry assemblies exemplify performance of the presented framework.
A novel finite element method (FEM) based direct method is developed for the material reconstruction inverse problem in soft tissue elastography. The solution is obtained by minimising an objective ...function, defined as the sum of the square of the residual norms at all nodes, where the nodal residual norm is defined as a linear function of elasticity parameters of the associated elements. The measured deformation is enforced directly and satisfying the equilibrium at every node is utilised as the optimisation objective. As a result, the soft tissue elastography can be obtained directly by solving the resulting set of linear equations.
This paper presents a numerical multiscale modelling strategy for simulating fracturing in materials where the fine-scale heterogeneities are fully resolved, with a particular focus on concrete. The ...fine-scale is modelled using a hybrid-Trefftz stress formulation for modelling propagating cohesive cracks. The very large system of algebraic equations that emerges from detailed resolution of the fine-scale structure requires an efficient iterative solver with a preconditioner that is appropriate for fracturing heterogeneous materials. This paper proposes a two-grid strategy for construction of the preconditioner that utilizes scale transition techniques derived for computational homogenization and represents an adaptation of the work of Miehe and Bayreuther
2 and its extension to fracturing heterogeneous materials. For the coarse scale, this paper investigates both classical
C
0
-continuous displacement-based finite elements as well as
C
1
-continuous elements. The preconditioned GMRES Krylov iterative solver with dynamic convergence tolerance is integrated with a constrained Newton method with local arc-length control and line searches. The convergence properties and performance of the parallel implementation of the proposed solution strategy is illustrated on two numerical examples.
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