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In this paper, experimental testing and numerical analysis were used to investigate the effect of tube thickness on the face bending for concrete filled hollow sections connected to other structural members using Extended Hollobolts. Six samples were tested experimentally by applying pull-out load on the bolts. These samples were designed to fail by column face bending. The main variable in all tests is the column face thickness. Finite element analyses were also performed using ABAQUS 6.11 to extend the experimental results and to quantify the effect of column face thickness. Results show that, the column face thickness has a clear impact on the connection strength and stiffness. However, the amount of improvement in the connection stiffness by changing the column face thickness from 5mm to 6.3mm seems to be higher than that when increasing it from 6.3mm to 8mm. The displacement at which the bolts start pulling-out from their holes increased with the use of thinner column face due to the high flexibility of the section. At the ultimate strength, the yielding of the column face propagated to the column corner and there was no yielding in its walls. After the ultimate resistance is reached, the propagation of the yielding was mainly in the column face with a miner yielding in the walls., {"references":["E. Mourad, Behaviour of Blind Bolted Moment Connections for Square HSS Columns. School of Graduated Studies, 1993. PhD Thesis. McMaster University.","T. Barnett, The Behaviour of a Blind Bolt for Moment Resisting Connections in Hollow Steel Sections. Civil Engineering, 2001. Ph. D. Thesis. University of Nottingham.","J.E. France, Bolted Connections between Open Section Beams and Box Columns. Department of Civil and Structural Engineering, 1997. PhD Thesis. University of Sheffield.","J. Lee, H.M. Goldsworthy, and E.F. Gad, Blind Bolted T-Stub Connections to Unfilled Hollow Section Columns in Low Rise Structures. Journal of Constructional Steel Research, 2010. 66(8–9): p. 981-992.","L. Silva, L. Neves, and F. Gomes, Rotational Stiffness of Rectangular Hollow Sections Composite Joints. Journal of Structural Engineering, 2003. 129: p. 487-494.","J.E. France, J. Buick Davison, and P. A. Kirby, Moment-Capacity and Rotational Stiffness of Endplate Connections to Concrete-Filled Tubular Columns with Flowdrilled Connectors. Journal of Constructional Steel Research, 1999. 50(1): p. 35-48.","S. Ellison and W. Tizani, Behaviour of Blind Bolted Connections to Concrete Filled Hollow Sections. The Structural Engineer, 2004. 16: p. 16-17.","W. Tizani, A. Al-Mughairi, J.S. Owen, and T. Pitrakkos, Rotational Stiffness of a Blind-Bolted Connection to Concrete-Filled Tubes Using Modified Hollo-Bolt. Journal of Constructional Steel Research, 2013. 80: p. 317-331.","T. Pitrakkos and W. Tizani, Experimental Behaviour of a Novel Anchored Blind-Bolt in Tension. Engineering Structures, 2013. 49: p. 905-919. \n[10]\tA. Elamin, The Face Bending Behaviour of Blind-Bolted Connections to Concrete-Filled Hollow Sections. Department of Civil Engineering 2013. PhD Thesis. University of Nottingham.\n[11]\tCEN, Eurocode 4: Design of Composite Steel and Concrete Structures: Part 1-1: General Rules and Rules for Buildings, in EN 1994-1-1. 2004. \n[12]\tBSI, Metallic Materials -Tensile Testing, Part 1: Method of Test at Ambient Temperature, in EN 10002-1. 2001, British Standards Institution: London. \n[13]\tDassault, Abaqus v. 6.11 (Software), Dassault Systèmes Simulia Corp. 2011, Providence, RI: Dassault Systèmes Simulia Corp. \n[14]\tAbaqus, ABAQUS Analysis User's Manual: Volume IV: Elements, in Abaqus, Inc. 2011, Dassault Systèmes. \n[15]\tA. Elremaily and A. Azizinamini, Design Provisions for Connections between Steel Beams and Concrete Filled Tube Columns. Journal of Constructional Steel Research, 2001. 57(9): p. 971-995. \n[16]\tH.T. Hu, C.S. Huang, M.H. Wu, and Y.M. Wu, Nonlinear Analysis of Axially Loaded Concrete-Filled Tube Columns with Confinement Effect. Journal of Structural Engineering, 2003. 129(10): p. 1322-1329. \n[17]\tE. Ellobody, B. Young, and D. Lam, Behaviour of Normal and High Strength Concrete-Filled Compact Steel Tube Circular Stub Columns. Journal of Constructional Steel Research, 2006. 62(7): p. 706-715. \n[18]\tZ. Wang, Hysteretic Response of an Innovative Blind bolted Endplate Connection to Concrete Filled Tubular Columns. Department of Civil Engineering, 2012. PhD Thesis. University of Nottingham.\n[19]\tBSI, Eurocode 2: Design of Concrete Structures: Part 1-1: General Rules and Rules for Buildings, in EN 1992-1-1. 2004, British Standards Institution."]}

The paper is concerned with the nonlinear dynamics of geometrically exact shells and spatial rods with an SO(3)-valued configuration space. Energy conserving/energy dissipating methods are to be discussed and dimension reduction and post-processing methods will be presented. An energy-momentum integration scheme is constructed which is designed so as to be independent of the configuration space, preserve, by design, specific features of the continuous system such as conservation of momentum, angular momentum, when the applied forces allow to, and conservation of total energy in case of a Hamiltonian system. The application of such methods is of importance since they allow for stable integration in long term dynamics and ensures that the dissipation is of a purely physical source, in case of dissipative systems. However, in certain cases high frequency dissipation is desirable and can be achieved by adding material viscosity-like terms to the dynamic equations. We discuss a dimension reduction method based on the Proper Orthogonal Decomposition Method. The method allows the deduction of the energetically dominating modes of the motion and reduces the motion to these essential modes. Further a post- processed Galerkin finite element method based on hierarchical interpolations is presented. The method makes use of two stress hybrid or, alternatively, enhanced strain finite element formulations; a low-dimensional four-node and a high-dimensional nine- node one. The results of the four-node element are projected on the nine-node ones using a specific projection operator. Altogether the method provides means for a very low-cost improvement of low-dimensional solutions. The kinematical fields are improved to higher orders which makes the method effective in handling large scale problems in structural dynamics.

This contribution deals with the development of a hyperelastic and thermodynamically consistent model for soft tissue that is able to describe the reorientation of collagen fibres during a deformation process. To be specific, we are examining only the continuum scale of reorientation of the collagen fibres under constant mass. A uniform distribution of fibres in the tissue matrix is assumed. We assume a uniform distribution of fibrils (fibres as well) in the matrix. Their dimension is measured in  m, therefore at continuum level we consider only the orientation at continuum points. We are taking into consideration two independent groups of the collagen fibres. The framework of the formulation is inspired by a material model developed in [1]. In the formulation of the anisotropic behaviour of soft tissue we use a popular form for the strain energy function that can be found e.g. in [2, 3], among others. The anisotropic response is described by isotropic expressions modelling the matrix and two groups of the fibres separately. Thus, the strain energy function is decomposed into parts which are related to the matrix, and to the collagen fibres. The collagen architectures are assumed to tend to align with the stress field within the tissue. The initial fibres orientations are defined by structural tensors that are reoriented according to the loading by means of the rotation tensor. The change of the rotation tensor is described using a well known exponential map procedure. The reorientation function is introduced which is assumed to be a linear function of the thermodynamical force derived from the dissipation inequality given by the second law of thermodynamics. However, a more accurate reorientation function should be proposed in the future work which should be verified with appropriate experimental results. Efficiency of the proposed formulation is demonstrated using a uniaxially loaded soft tissue strip, Figure 1. The strip is loaded in the y direction on the upper edge, while at the lower edge it has suppressed displacements in the y-direction. The collagen fibres have initial position of 15° with respect to the y axis. Two calculations are performed, with and without reorientation mechanism, Figure 1 a) and b). As well, the change of the fibre orientation by applying the load is shown by figure 2. In future work the function is to be verified with experimental results as to its appropriate form.

The paper is concerned with the numerical formulation of the anisotropic behaviour of shell structures at large strain elastoplasticity. The material model is based on the multiplicative decomposition of deformation gradient. The orthotropic elastic responses as well as the yield function employing the nonlinear isotropic hardening are described by using the appropriate invariants. The anisotropic deformation responses are demonstrated by numerical example.

Ponašanje mekih tkiva može se modelirati pomoću hiperelastičnog konstitutivnog modela temeljenog na eksponencijalnoj slobodnoj energiji. Usmjerenost vlakana određena je preko strukturalnog tenzora. Takav način formulacije slobodne energije omogućuje opisivanje anizotropne strukture mekih tkiva pomoću izotropnih izraza. Izvedena formulacija po prvi put donosi mehanizam kojim se može numerički modelirati zakretanje kolagenskih vlakana ovisno o veličini i smjeru djelovanja opterećenja.

In this paper a hyperelastic and a thermodynamically consistent model for soft tissue is developed that is able to describe the change of the initial collagen fibres orientation. The collagen architecture is assumed to align with the stress field within the tissue. The anisotropy is described by a strain energy function which is decomposed into a part related to the matrix, and a part related to the fibres. The initial fibre orientation is defined by a structural tensor while the current orientation is described by the time dependent structural tensor. Accordingly, the change of rotation tensor is obtained by exponential map and it is dependent on rate of thermodynamical force. Efficiency of the proposed formulation is demonstrated using some numerical examples.

Within the framework of linear plasticity, based on additive decomposition of the linear strain tensor, kinematical hardening can be described by means of extended potentials. The method is elegant and avoids the need for evolution equations. The extension of small-strain formulations to the finite strain case, which is based on the multiplicative decomposition of the deformation gradient into elastic and inelastic parts, proved not straight forward. Specifically, the symmetry of the resulting back stress remained elusive. In this paper, a free energy-based formulation incorporating the effect of kinematic hardening is proposed. The formulation is able to reproduce symmetric expressions for the back stress while incorporating the multiplicative decomposition of the deformation gradient. Kinematic hardening is combined with isotropic hardening where an associative flow rule and von Mises yield criterion are applied. It is shown that the symmetry of the back stress is strongly related to its treatment as a truly spatial tensor, where contraction operations are to be conducted using the current metric. The latter depends naturally on the deformation gradient itself. Various numerical examples are presented.

Formulation of large strain elastoplastic model for anisotropic materials based on multiplicative decomposition of deformation gradient is considered. In order to achieve formulation invariant to finite rotations, is assumed to be material-like tensor. An anisotropic elastic constitutive law is described by means of free energy that is function of elastic right Cauchy-Green tensor and structural invariants defining material orientation. This dependency is formulated by using so called integrity basis. An anisotropic yield function, described by non-symmetric Eshelby-like stress tensor and further structural tensors, is developed. In order to obtain yield function as an isotropic function of material invariants, integrity basis are made by using theorems for functions with non-symmetric arguments. The model considers non-linear isotropic hardening, as well. An accurate integration algorithm employing exponential map is developed. In order to ensure a high convergence rate in the global iteration approach, an algorithmic tangent operator for anisotropic multiplicative inelasticity is for the first time derived. Various numerical examples show robustness and efficiency of the proposed algorithm. The influence of anisotropy on finite elastoplastic deformation responses is also considered.