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This article presents a vertex-centered finite volume algorithm for the explicit dynamic analysis of large strain contact problems. The methodology exploits the use of a system of first order conservation equations written in terms of the linear momentum and a triplet of geometric deformation measures (comprising the deformation gradient tensor, its co-factor, and its Jacobian) together with their associated jump conditions. The latter can be used to derive several dynamic contact models ensuring the preservation of hyperbolic characteristic structure across solution discontinuities at the contact interface, a clear advantage over the standard quasi-static contact models where the influence of inertial effects at the contact interface is completely neglected. Taking advantage of the conservative nature of the formalism, both kinetic (traction) and kinematic (velocity) contact interface conditions are explicitly enforced at the fluxes through the use of appropriate jump conditions. Specifically, the kinetic condition is enforced in the usual linear momentum equation, whereas the kinematic condition can now be easily enforced in the geometric conservation equations without requiring a computationally demanding iterative algorithm. Additionally, a total variation diminishing shock capturing technique can be suitably incorporated in order to improve dramatically the performance of the algorithm at the vicinity of shocks. Moreover, and to guarantee stability from the spatial discretization standpoint, global entropy production is demonstrated through the satisfaction of semi-discrete version of the classical Coleman–Noll procedure expressed in terms of the time rate of the so-called Hamiltonian energy of the system. Finally, a series of numerical examples is examined in order to assess the performance and applicability of the algorithm suitably implemented in OpenFOAM. The knowledge of the potential contact loci between contact interfaces is assumed to be known a priori., Callum J. Runcie and Chun Hean Lee gratefully acknowledge the support provided by the EPSRC Strategic Support Package: Engineering of Active Materials by Multiscale/Multiphysics Computational Mechanics - EP/R008531/1. Antonio J. Gil and Chun Hean Lee would like to acknowledge the financial support received through the project Marie Skłodowska-Curie ITN-EJD ProTechTion, funded by the European Union Horizon 2020 research and innovation program with Grant number 764636. Callum J. Runcie and Chun Hean Lee would also like to acknowledge the many useful discussions with Dr. Peter Grassl from University of Glasgow., Peer Reviewed, Postprint (published version)

A single layer of voids in a ductile material is considered to study the effect of this material imperfection on the onset of shear band localization, and to study the failure evolution in the void-sheet mechanism. The layer is inclined relative to the main tensile direction, and the initially spherical voids are taken to be uniformly spaced both along the inclined direction and transverse to it. The material is elastic-viscoplastic with isotropic hardening. When the solid is subjected to a prescribed strain-rate and the shear band width is negligible compared to specimen dimensions, an infinite ratio of the strain-rate in the band relative to the overall prescribed strain-rate defines the onset of localization. For each stress-state analyzed a limited number of initial inclinations of the void layer are considered, with an angular spacing of 5 degrees, and the angle of inclination giving the smallest critical strain is used as a good approximation of the critical band orientation. Different initial void sizes, relative to the void spacing, are considered. It is shown that increased void spacing in the transverse direction significantly delays localization. Also the effects of different levels of strain hardening are compared. The evolution of the void shape during shear localization is studied, to be able to follow the void-sheet failure mechanism. The critical strain for the onset of void coalescence is compared with the critical strain for shear bands.

Magnetorheological elastomers (MREs), as one of smart composites, exhibit characteristics of both particle reinforced composites and magnetorheological materials. Their mechanical properties (e.g., stiffness and damping) can be tailored rapidly, continuously and reversibly with applied magnetic field.In this research MREs specimens have been fabricated, with their micro-structures and dynamic properties subsequently characterized via scanning electron microscope (SEM) and dynamic mechanical analysis (DMA). The magneto-viscoelastic behaviors have been systematically studied under different external magnetic fields, excitation frequencies and strain amplitudes.A new linear GMM (Generalized Maxwell model)-based magneto-viscoelastic model of MREs is proposed and investigated under small strain. Further, a nonlinear magneto-viscoelastic constitutive model of MREs is developed under large strain. The model predicts the frequency-, amplitude-, and magneto-dependent behaviors of MREs. The internal damping mechanisms are considered by multiplicative decomposition of the deformation gradient and magnetic induction into elastic and inelastic parts. The energy dissipation is assumed to occur due to the frequency- and amplitude-dependent mechanical viscoelasticity as well as the frequency-, amplitude-, and magneto-dependent magnetic-viscoelasticity. Constitutive laws for material behaviors and evolution equations are derived that agree with the laws of thermodynamics. Both mechanical force-induced Payne effect and magneto-induced Payne effect are considered for the amplitude-induced nonlinearities by the introduction of internal state variables integrated in the model, which are interpreted as phenomenological measures for the current state of the filler network. The parameters of the proposed constitutive model are identified by experimental data. Then the shear storage and loss moduli are analyzed and compared with the experimental results to validate the model’s effectiveness

The viscoelastic properties of rubbers are often investigated under small strain by means of a dynamic mechanical analysis (DMA). In many cases, the performance of rubber products such as tiyes, O-ring and engine mounts is predicted based on the viscoelastic properties obtained under the small strain. On the other hand, the rubber products are practically subjected to cyclic large strain. The effect of strain amplitude on the viscoelastic properties (storage modulus and loss tangent) of rubbers, which are well-known as the Payne effect , shows a nonlinear response]. In order to accurately understand the performance of the rubber products, it is important to capture the viscoelastic responses under the cyclic large strain. In this viewpoint, this paper presented nonlinear viscoelastic responses of a carbon-filled SRB vulcanizate under uniaxial cyclic large strain., The viscoelastic properties of rubbers are often investigated under small strain by means of a dynamic mechanical analysis (DMA). In many cases, the performance of rubber products such as tiyes, O-ring and engine mounts is predicted based on the viscoelastic properties obtained under the small strain. On the other hand, the rubber products are practically subjected to cyclic large strain. The effect of strain amplitude on the viscoelastic properties (storage modulus and loss tangent) of rubbers, which are well-known as the Payne effect , shows a nonlinear response]. In order to accurately understand the performance of the rubber products, it is important to capture the viscoelastic responses under the cyclic large strain. In this viewpoint, this paper presented nonlinear viscoelastic responses of a carbon-filled SRB vulcanizate under uniaxial cyclic large strain.

n this paper, a numerical solution for the electro-osmosis consolidation of clay in multi-dimensional domains at large strains is presented, with the coupling of the soil mechanical behaviour, pore water transport and electrical fields being considered. In particular, the Modified Cam Clay model is employed to describe the elasto-plastic behaviour of clay, and some empirical expressions are used to consider the nonlinear variation of the hydraulic and electrical conductivities of the soil mass during the consolidation processes. The implementation of the theoretical model in a finite element code allows for analysis of the evolution of the transient response of the clay subjected to electro-osmosis treatment. The proposed model is verified via comparison with data from a large strain electro-osmosis laboratory test, to demonstrate its accuracy and effectiveness. Various numerical examples are also investigated to study the deformation characteristics and time-dependent evolution of the excess pore pressure. Finally, a well-documented field application of electro-osmosis is simulated to provide further verification. The results show that the numerical solution is effective in predicting the nonlinear behaviour of clay during electro-osmosis consolidation., Geoscience & Engineering, Civil Engineering and Geosciences

Consolidation of soft clay creates a lot of problems in foundation engineering, because of the very low clay permeability and high compressibility. Primary consolidation takes a long time to complete if the material is left consolidating under atmospheric evaporation, and traditional dewatering techniques, such as surcharge preloading, vacuum preloading or vertical drains, have been used for decades to shorten the consolidation time. Among new soft ground improvement technologies, electro-osmosis consolidation is receiving much attention as a possible time efficient solution. Electro-osmosis is a novel technique to consolidate soft clays, and involves the flow of pore fluid in a soil mass in response to an applied electrical field. The electrodes (positive and negative) are installed in pairs in the soil mass; the direct current then forces ions in the mobile part of the electric double layer (EDL) to move from the anode towards the cathode, causing water flow. Electro-osmosis is found to be more effective in clayey soils because the electro-osmosis permeability is independent of the grain size. This means that electroosmosis can generate flow rates that are 100 to 1000 times greater than hydraulic flows in fine grained soft clays. The purpose of this thesis is to develop a numerical model for simulating multidimensional and fully coupled multi-physics electro-osmosis consolidation, including the elasto-plastic behaviour of soil and time dependent transport parameters at large strain. Special attention is paid to the simulation of complicated geometries and boundary conditions, and to the inclusion of more advanced elasto-plastic constitutive models. The overall goal is to develop a more realistic numerical tool which addresses the main features of electro-osmosis consolidation, and that has potential use in the design and optimization of field applications. In this thesis, numerical models for the electro-osmosis consolidation of soft clays in multi-dimensional dom, Geoscience & Engineering, Civil Engineering and Geosciences

The bearing capacity of displacement piles in clay is usually seen to increase during the days following installation. This phenomenon is referred to as ‘set-up’ and occurs because during installation, the high strains imposed by the pile leave a mark on the state of the soil surrounding the pile (pore pressures, a.o.). Once installation has ended, the pore pressures generated during driving are free to dissipate, which allows the pile capacity to grow. This paper presents a numerical simulation of a plane strain soil disk adjacent to a pile which is being driven. Emphasis is placed on the simulation of the excess pore pressure during pile penetration and afterwards, during consolidation. The soil constitutive model used is hypoplasticity for clays coupled with intergranular strain, which allows capturing the soil small strain behaviour and dilatancy. The driving analysis is performed by using a dynamic integration scheme and the consolidation is coupled.

A thermoelastic-plastic body consisting of two phases, a solid and a fluid, each comprising two constituents is considered where one constituent in one phase is allowed to exchange mass with another constituent (of the same substance) in the other phase. A large strain setting is adopted and the formulation applies to general anisotropy and the existence of residual stresses. Generalized forms of Fourier's, Fick's and Darcy's laws are derived and also the stresses on the constituent, phase and mixture level are established; in addition, the evolution law for general plasticity is given. Finally, and in particular, a general evolution law for the rate of deformation tensor related to mass exchange is proposed and this leads to general absorption and desorption evolution laws for mass exchange between two constituents (of the same substance), one belonging to the solid phase and the other to the fluid phase. Equilibrium curves for absorption and desorption also emerge from the theory.

A thermoelastic-plastic body consisting of two phases, a solid and a fluid, each comprising two constituents is considered where one constituent in one phase is allowed to exchange mass with another constituent (of the same substance) in the other phase. A large strain setting is adopted and the formulation applies to general anisotropy and the existence of residual stresses. Generalized forms of Fourier's, Fick's and Darcy's laws are derived and also the stresses on the constituent, phase and mixture level are established; in addition, the evolution law for general plasticity is given. Finally, and in particular, a general evolution law for the rate of deformation tensor related to mass exchange is proposed and this leads to general absorption and desorption evolution laws for mass exchange between two constituents (of the same substance), one belonging to the solid phase and the other to the fluid phase. Equilibrium curves for absorption and desorption also emerge from the theory.

The idea of designing a `sensing string' is presented in this paper. This,sensing string' is a hand-crocheted textile based strain sensor which can be used to measure the in-plane or out-of-plane large strain (up to 40\%, which depends on the fabric structure) at high temperature (up to 400 degrees C). The sensing mechanism is investigated theoretically by using a circuit network to analyse the key sensing elements contributing to the fabric sensor, and it is then validated experimentally to obtain the guidelines for the design of high performance strain sensors. It is found that the contact resistance between two contacting yams is the key factor dominating the sensing mechanism. The fabric density, which determines the number of contacting points within a given length, is proved to be the most important factor governing the sensitivity, repeatability, hysteresis, linearity and strain range of the sensor. Temperature exhibits a greater effect on the magnitude of the initial resistance of the sensor.

An intrinsically conductive knitted fabric-based electrical resistive strain gauge is developed to measure in-plane or out-of-planar large strain under high temperature. Electro-mechanical properties, which governor the sensitivity of the gauge, are analyzed theoretically by a model of weft plain fabric. The contacting electrical resistance (R-c), resulted from two overlapped yams, is attributed to be the key factor contributing to the resistance-strain response while the fabric structure determines the sensitivity of the gauge. Two structures are fabricated making use of the properties of contacting resistance to find the key factors governing the sensitivity, repeatability and accuracy of the sensors. The effects of strain-rate and temperature on the sensitivity of the gauge are analyzed experimentally. From the experimental results, fabric gauges made from carbon fibers display a higher sensitivity, repeatability and accuracy than those made by stainless steel due to its small internal friction and intrinsic physics properties. Meanwhile, tubular structure has high maximum strain level than single warp structure but exhibits lower sensitivity than the latter. Temperature exhibits greater effect on the sensitivity than the strain-rate. (C) 2005 Elsevier B.V. All rights reserved.

This thesis makes two noteworthy contributions in the are of mesh-free methods: a Pseudo-Divergence-Free (PDF) Element Free Galerkin (EFG) method which alleviates the volumetric locking and a Stabilized Updated Lagrangian formulation which allows to solve fast-transient dynamic problems involving large distortions. The thesis is organized in the following way. First of all, this thesis dedicates one chapter to the state of the art of mesh-free methods. The main reason is because there are many mesh-free methods that can be found in the literature which can be based on different ideas and with different properties. There is a real need of classifying, ordering and comparing these methods: in fact, the same or almost the same method can be found with different names in the literature. Secondly, a novel improved formulation of the (EFG) method is proposed in order to alleviate volumetric locking. It is based on a pseudo-divergence-free interpolation. Using the concept of diffuse derivatives an a convergence theorem of these derivatives to the ones of the exact solution, the new approximation proposed is obtained imposing a zero diffuse divergence. In this way is guaranteed that the method verifies asymptotically the incompressibility condition and in addition the imposition can be done a priori. This means that the main difference between standard EFG and the improved method is how is chosen the interpolation basis. Modal analysis and numerical results for two classical benchmark tests in solids corroborate that, as expected, diffuse derivatives converge to the derivatives of the exact solution when the discretization is refined (for a fixed dilation parameter) and, of course, that diffuse divergence converges to the exact divergence with the expected theoretical rate. For standard EFG the typical convergence rate is degrade as the incompressible limit is approached but with the improved method good results are obtained even for a nearly incompressible case, Postprint (published version)

During a hypothetical break of a BWR feed water line, the feed water distributor (FWD) inside the RPV is subjected to a high pressure load for a short time (10 ms). Because of the sudden coolant release from the inner volume of the FWD there is a pressure difference between the inner and outer surface. It is conservatively assumed that the pressure difference nearly can reach the operating pressure for a few milliseconds. The ring line of the feed water distributor is modelled with shell and volume elements capable of being used for large strain analyses with elastic-plastic material behaviour. It is demonstrated by non-linear static calculations (without consideration of the inertia of the material) that a buckling instability occurs at about 60% of the maximum pressure load. The arc-length method is used for the numerical solution to overcome this point of instability. To evaluate the influence of the dynamics of the process a non-linear transient analysis is done showing that the maximum strain occurs with a time delay to the pressure peak. The maximum plastic strain differs only nsignificantly between static and transient solution. Inspite of the large strains the mechanical integrity is maintained during the hypothetical event.

During a hypothetical break of a BWR feed water line, the feed water distributor (FWD) inside the RPV is subjected to a high pressure load for a short time (10 ms). Because of the sudden coolant release from the inner volume of the FWD there is a pressure difference between the inner and outer surface. It is conservatively assumed that the pressure difference nearly can reach the operating pressure for a few milliseconds. The distributor box and the ring line of the feed water distributor are modelled with shell and volume elements capable of being used for large strain analyses with elastic-plastic material behaviour. It is demonstrated by non-linear static calculations (without consideration of the inertia of the material) that a buckling instability occurs at about 60% and 80% of the maximum pressure load. The arc-length method is used for the numerical solution to overcome these points of instability. To evaluate the influence of the dynamics of the process a non-linear transient analysis is done showing that the maximum strain occurs with a time delay to the pressure peak. The maximum plastic strain differs only insignificantly between static and transient solution. Inspite of the large strains the mechanical integrity is maintained during the hypothetical event.

A dual porosity damage model is developed with the intention for the efficient solving of complex hydrofracture problems. The model is developed by utilising two pre-existing methodologies and adapting them for the purpose of solving hydrofracture problems. The damage model uses a NeoHookean finite deformation elastic constitutive model to calculate internally stored elastic energy. The constitutive model is derived from the three strain invariants so that with volume change, mechanical behaviour maintains consistency, a property that will be discussed in the literature, important to the development of both fracture and hydrofracture framework. The energy required for material breakage is derived from the material property: fracture strength. The two energy values are calculated over the considered model domain and are used with the energy minimisation technique to find the global minimum energy that contains the sum of the two aforementioned energy types. While calculating the domain configuration which has the lowest energy sum, fracture behaviour can be deduced from the required energy releases from the system to achieve the global energy minimum. This fracture methodology is combined with a dual porosity methodology that is derived by considering the fluid interface between interconnected porous and fractured domains. Mass balance and effective stress concepts have been utilised to derive partial differential equations which model fluid flow through these two domains in an interconnected manner. This aspect of the model is used to model the fluid transfers that occur in hydrofractures. The set of equations that govern the coupled porous flow are solved using the finite element method. The Galerkin method of the spatial discretisation is applied and solved using a Eularian scheme to iterate the solution of the governing linearised equations utilising the Newton Raphson approach. The plastic behaviour of rock like materials has been described utilising Mohr Coulom