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This book presents research advances in the field of Continuous Media with Microstructure and considers the three complementary pillars of mechanical sciences: theory, research and computational simulation. It focuses on the following problems: thermodynamic and mathematical modeling of materials with extensions of classical constitutive laws, single and multicomponent media including modern multifunctional materials, wave propagation, multiscale and multiphysics processes, phase transformations, and porous, granular and composite materials. The book presents the proceedings of the 2nd Conference on Continuous Media with Microstructure, which was held in 2015 in Łagów, Poland, in memory of Prof. Krzysztof Wilmański. .

This paper investigates the effectiveness of a new hybrid passive control system on the seismic response of an existing steel cable-stayed bridge considering the pounding effect. The proposed hybrid passive control system comprises a seismic isolator and a metallic damper. The bridge is located in a high seismic zone and has suffered several damages including the earthquake-induced pounding damage during the 1988 earthquake. Thereby, the proposed hybrid passive control system was investigated for seismic retrofitting of the bridge to mitigate the seismic damages due to future earthquakes. The hybrid control system was placed at the bridge ends and the tower–deck connection. A detailed three-dimensional finite element model of the bridge was created and validated with the earlier experimental results. A comparative analysis was performed through a series of nonlinear dynamic time-history analyses on the bridge equipped with the proposed and other control systems. The results showed that the hybrid control system reduced the bridge’s longitudinal seismic displacement, mitigated the pounding of the bridge with abutments and improved the overall seismic performance of the bridge.

This paper provides a novel Finite Element (FE) simulation to estimate the out-of-plane response of masonry prisms retrofitted with Shape Memory Alloy (SMA) stripes. Empirical data were utilized to develop the computational analysis parameters (mechanical parameters for brick, mortar, and SMA materials) as well as the calibration of the computational FE-based models. For this purpose, a complete micro-modeling approach was applied, assuming perfect contact between mortar joints and brick units. A Concrete Damage Plasticity (CDP) model was developed to define the constitutive relation between brick and mortar. SMA stripes were mortar-installed on the surface of the prisms with a perfect connection. The masonry prism’s verified computational model was utilized to generate parametric research to explore the effect of varying SMA stripe thicknesses and different SMA usage (Ni-Ti or Cu-Zn-Al). The FE study findings indicated that, independent of their material type or thickness, using SMA stripes greatly minimizes brick prism deterioration. SMA stripes greatly decreased residual displacement and plastic strains. Parametric tests, however, revealed that employing Ni-Ti SMA and increasing its thickness is more effective with respect to the masonry prism out-of-plane response than Cu-Zn-Al SMA.

Concrete is the most widely used construction material nowadays. We are concerned with the computational modelling and laboratory testing of high-performance concrete (HPC). The idea of HPC is to enhance the functionality and sustainability of normal concrete, especially by its greater ductility as well as higher compressive, tensile, and flexural strengths. In this paper, the influence of three types (linear displacement, uniform traction, and periodic) of boundary conditions used in numerical homogenization on the calculated values of HPC properties is determined and compared with experimental data. We take into account the softening behavior of HPC due to the development of damage (micro-cracks), which finally leads to failure. The results of numerical simulations of the HPC samples were obtained by using the Abaqus package that we supplemented with our in-house finite element method (FEM) computer programs written in Python and the homogenization toolbox Homtools. This has allowed us to better account for the nonlinear response of concrete. In studying the microstructure of HPC, we considered a two-dimensional representative volume element using the finite element method. Because of the random character of the arrangement of concrete’s components, we utilized a stochastic method to generate the representative volume element (RVE) structure. Different constitutive models were used for the components of HPC: quartz sand—linear elastic, steel fibers—ideal elastic-plastic, and cement matrix—concrete damage plasticity. The numerical results obtained are compared with our own experimental data and those from the literature, and a good agreement can be observed.

This paper presents validation and evaluation of usefulness of three non-advanced methods in EN 1992-1-2 used to determine the load-bearing capacity of columns under fire conditions: the method A, the isotherm 500 °C method, and the zone method. To verify the usefulness of these methods, experimental results for columns tested in the fire laboratories in Ottawa, Braunschweig, Liege and Ghent were used. The FDM was used to calculate the cross-section temperature distribution being required in the 500 °C isotherm method and the zone method. Temperature dependent material parameters of concrete and steel were adopted according to Eurocode 2. In the case of lack of information in the standards, the authors’ own assumptions were proposed and described. The calculated fire resistance times were compared with the experimental results. The method A has proved to be accurate enough and safe for the cases fulfilling its limitations. The results obtained with the 500 °C isotherm method vary significantly from the experimental results. The zone method is the most complex of these three methods and provides the results more accurate and safer than those obtained with the 500 °C isotherm method. The zone method is recommended for verification of the load-bearing capacity of reinforced concrete columns under fire conditions.

Every year, structural flaws or breakdowns cause thousands of people to be harmed and cost billions of dollars owing to the limitations of design methods and materials to withstand extreme earthquakes. Since earthquakes have a significant effect on sustainability factors, there is a contradiction between these constraints and the growing need for more sustainable structures. There has been a significant attempt to circumvent these constraints by developing various techniques and materials. One of these viable possibilities is the application of smart structures and materials such as shape memory and piezoelectric materials. Many scholars have examined the use of these materials and their structural characteristics up to this point, but the relationship between sustainability considerations and the deployment of smart materials has received little attention. Therefore, through a review of previous experimental, numerical, and conceptual studies, this paper attempts to draw a more significant relationship between smart materials and structural sustainability. First, the significant impact of seismic events on structural sustainability and its major aspects are described. It is then followed by an overview of the fundamentals of smart material’s behaviour and properties. Finally, after a comprehensive review of the most recent applications of smart materials in structures, the influence of their deployment on sustainability issues is discussed. The findings of this study are intended to assist researchers in properly addressing sustainability considerations in any research and implementation of smart materials by establishing a more explicit relationship between these two concepts.

For decades, one of the most critical considerations of civil engineers has been the construction of structures that can sufficiently resist earthquakes. However, in many parts of the globe, ancient and contemporary buildings were constructed without regard for engineering, thus, there is a rising necessity to adapt existing structures to avoid accidents and preserve historical artefacts. There are various techniques for retrofitting a masonry structure, including foundation isolations, the use of Fibre-Reinforced Plastics (FRPs), shotcrete, etc. One innovative technique is the use of Shape Memory Alloys (SMAs), which improve structures by exhibiting high strength, good re-centring capabilities, self-repair, etc. One recent disastrous earthquake that happened in the city of Bam, Iran, (with a large proportion of masonry buildings) in 2003, with over 45,000 casualties, is analysed to discover the primary causes of the structural failure of buildings and its ancient citadel. It is followed by introducing the basic properties of SMAs and their applications in retrofitting masonry buildings. The outcomes of preceding implementations of SMAs in retrofitting of masonry buildings are then employed to present two comprehensive schemes as well as an implementation algorithm for strengthening masonry structures using SMA-based devices.

The aim of the paper is to present a global analysis of a precast, reinforced building structure. At the design stage, information about structural behaviour of particular elements and the whole structure as well as its response to applied loads are obtained. While solving the problem, the load-bearing elements and the type and deformability of connections have to be defined. The latter is especially significant in the case of precast structure models. Calculations according to the analytical method are going to be verified by the finite element method.

Poludniowa obwodnica Poznania stanowi fragment autostrady A2 od wezlaPoznan Zachod do wezla Poznan Wschod. Autostradą A2 pomiedzy tymi wezlamiw ciągu doby porusza sie ponad 45 tys. pojazdow, a z trasy miedzy Komornikamia Luboniem korzysta przeszlo 60 tys. pojazdow w ciągu doby. Wkrotce, wiosną 2019 r. ma sie rozpocząc rozbudowa cześci poludniowejobwodnicy Poznania. Poltora roku potrwa poszerzenie autostrady A2 o trzeci pas ruchuna najbardziej ruchliwym odcinku. Warto przyjrzec sie przy okazji konstrukcji i stanowitechnicznemu obiektow mostowych nad autostradą, ktorych obecnośc jest powaznymproblemem przy poszerzaniu autostrady. Przedmiotem zainteresowania autorow są wiaduktynad autostradą w weźle Krzesiny. Stan techniczny wiaduktow jest odpowiedni napodstawie wizji lokalnej wykonanej w kwietniu 2018 r. W pracy przywolano parametrytechniczne wiaduktow celem uzasadnienia podanych wskazowek dotyczących projektowaniapodobnych obiektow w przyszlości. W szczegolności chodzi o wiekszą skrajniepod wiaduktami, wiekszą dlugośc i szerokośc samych wiaduktow oraz wlaściwe rozmieszczaniepodpor z myślą o przyszlej, nieuchronnej rozbudowie i remontach.

The work is concerned with the determination of effective material parameters of reactive powder concrete (RPC) in the range of its nonlinear response. We have used a two-scale modelling technique and carried out a series of experimental tests which allow us to validate the proposed numerical model of the considered RPC concrete. The behavior of a RPC concrete on a macro scale is described on the basis of phenomena occurring in the microstructure of material. The material microstructure is taken into account by means of a representative volume element (RVE), the structure of which is generated in a stochastic way with data from the designed recipes of RPC. It is assumed that the microstructure of RPC is composed of isotropic linear elastic—(perfectly) brittle constituents and at the macro scale the material is homogenized. This approach is a good basis for a simple modelling of microcracks that cause the nonlinear behaviour of the material at the macro level. The numerical analysis is carried out here for the plane stress state problem, and at each level of analysis the finite element method is applied.

In this paper, computable global bounds on errors due to the use of various mathematical models of physical phenomena are derived. The procedure involves identifying a so-called fine model among a class of models of certain events and then using that model as a datum with respect to which coarser models can be compared. The error inherent in a coarse model, compared to the fine datum, can be bounded by residual functionals unambiguously defined by solutions of the coarse model. Whenever there exist hierarchical classes of models in which levels of sophistication of various coarse models can be defined, an adaptive modeling strategy can be implemented to control modeling error. In the present work, the class of models is within those embodied in nonlinear continuum mechanics.

The paper deals with the holonomic behavior of slackened-elastic–plastic (SEP) skeletal structures (beams, frames, trusses) using the quadratic programming formulations. The considerations are restricted to ‘frictionless’ quasi-static processes, small strains and piecewise linear approximations of the yield and clearance surfaces. The results of numerical experiments for several illustrative examples are presented, including the unilateral contact problem between an elastic-perfectly plastic beam and an elastic–perfectly plastic foundation. In the analysis the discrete FEM-oriented mathematical model [A. Gaw e cki, Elasto-plasticity of slackened systems, Arch. Mech. 1992;44:363–390 was employed.

The paper deals with the mathematical modelling of a class of unilateral elastic-plastic contact problems. The problem is posed in the framework of the so-called slackened systems. The considerations are confined to small strains and piecewise linear approximations of the yield surface and the clearance surface. An incremental formulation is proposed in the form of a linear complementarity problem (LCP). The formulation allows one to analyse a structural system which can be subjected to nonproportional loading paths. The included numerical results illustrate the application of this formulation to an elastic-plastic beam that comes into contact with a unilateral elastic-plastic foundation.

We consider the quasi-static deformation process of an elasto-plastic body, under the assumption of small strains. The elasto-plastic behaviour of the material ss assumed to be governed by the Huber-von Mises yield function with piecewise linear strain hardening (softening). The yield function is written in the terms of the strains, and we define the problem as the system that consists of (a) a variational equation which is the equilibrium condition for the body and (b) a variational inequality expressing the unilateral character of the plastic strain-rate multiplier. An iterative method for solving this nonlinear system, based on an incremental, implicit time integration scheme and on a finite element approximation is proposed. The variational inequality after being discretized using finite elements is solved as a linear complementarity problem. The results of some numerical experiments for a test problem are provided.

We are concerned with the bending problem of composite beams with embedded shape memory alloy in the form of fibres or strips. As a special case, the proposed formulation covers the case of a monolithic beam made of shape memory alloy. Shape memory alloys (SMAs) are materials that may undergo a temperature- or stress-induced martensitic phase transformation, which results in the shape memory effect and the pseudoelastic (superelastic) behaviour. The unique behaviour of SMAs opens new possibilities in design of adaptive structures. Herein we have formulated the quasi-static bending problem for a SMA beam in the form of a evolution variational inequality. After the finite element approximation, the variational inequality is solved incrementally as a sequence of linear complementarity problems. Finally, the predictions of the proposed model, including hysteresis loops, are illustrated with many results of numerical simulations for SMA beams.

An adaptive algorithm is given for the bending of viscoelastic beams and plates resting on viscoelastic, unilateral, frictionless foundations. An a posteriori error indicator proposed here is obtained by making use of upper and lower bounds generated by the saddle functional being a potential for the system of equations and inequalities which govern the contact problem.

A solution algorithm is presented for the analysis of unilateral, frictionless contact between a beam and a viscoelastic foundation. The foundation is modelled as a Winkler-type viscoelastic medium, to which the time integration method [ Mech. Teoret. i Stos. 22 , 209–233 (1984)] was applied. The problem was formulated in the form of a variational inequality, from which, after space discretization by the finite element method, a linear complementarity problem was derived. The solution method covers the time-discontinuities of loads and both loading (reloading) and unloading processes. The applicability of the algorithm is illustrated by selected numerical solutions to some examples.

In this report, computable global bounds on errors due to the use of various mathematical models of physical phenomena are derived. The procedure involves identifying a so-called fine model among a class of models of certain events and then using that model as a datum with respect to which coarser models can be compared. The error inherent in a coarse model, compared to the fine datum, can be bounded by residual functionals unambiguously defined by solutions of the coarse model. Whenever there exist hierarchical classes of models in which levels of sophistication of various coarse models can be defined, an adaptive modeling strategy can be implemented to control modeling error. In the present work, the class of models is within those embodied in nonlinear continuum mechanics.

This paper deals with one of the most dangerous failure modes in fiber reinforced composites, namely delamination. The laminated structure is modeled by a solid–shell finite element. The mechanical modeling of delamination onset and propagation is based upon a cohesive zone model implemented into a cohesive element located between laminae of a composite structure. The numerical simulations are accomplished within the commercial software package ABAQUS by the implementation of a user–written finite element. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

The paper is concerned with the modelling and numerical simulation of fibre-composite plates in the nonlinear range due to large strains and damage. The layer-wise approach is applied. Each layer is treated as elastic-brittle and assumed to be orthotropic in the local material coordinate system. The appearance of damage is controlled according to the failure criteria [1,2,3,4]. When the failure condition is satisfied, the mechanical properties of the material are modified appropriately, depending on the type of damage (fibre breakage, matrix crack, fibre-matrix shear). We have programmed the model as a user subroutine within the ABAQUS environment and carried out a number of numerical simulations. The obtained numerical results are compared with the experimental data available in the literature [3]. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)