• Interaction and multiscale mechanics
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• v.1 no.1
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• pp.83-101
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• 2008

A derivation is given of two-scale models that are able to describe deformation and flow in a fluid-saturated and progressively fracturing porous medium. From the micromechanics of the flow in the cavity, identities are derived that couple the local momentum and the mass balances to the governing equations for a fluid-saturated porous medium, which are assumed to hold on the macroscopic scale. By exploiting the partition-of-unity property of the finite element shape functions, the position and direction of the fractures are independent from the underlying discretization. The finite element equations are derived for this two-scale approach and integrated over time. The resulting discrete equations are nonlinear due to the cohesive crack model and the nonlinearity of the coupling terms. A consistent linearization is given for use within a Newton-Raphson iterative procedure. Finally, examples are given to show the versatility and the efficiency of the approach.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.14 no.1
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• pp.29-38
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• 1994

Linear composite theory as well as a finite element program is developed for axisymmetric elastomeric bearings. This study is limited to axisymmetrically loaded horizontal layered systems with linear, elastic, small' deformation conditions. A multiscale method is used in the development of the composite theory which enables us to model inhomogeneous layered composites as equivalent homogeneous, orthotropic material. Only continuity of the prime variables is required for the finite element analysis, allowing the use of simple $C_o$ elements whereas rather complicated theories presented in the past need more requirements. Four node isoparametric elements are used in the study. The developed theory of this paper is limited to linear conditions, however, the analysis can be extended to nonlinear behavior of flexible material in elastomeric bearing by using multiscale method presented here. Two numerical examples are examined and compared to the results of discrete and previously obtained composite analysis to verify the theory.

• Advances in aircraft and spacecraft science
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• v.9 no.3
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• pp.217-242
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• 2022

This paper proposes a novel time-domain homogenization model combining the viscoelastic constitutive law with Eshelby's inclusion theory-based micromechanics model to predict the mechanical behavior of the particle reinforced composite material. The proposed model is intuitive and straightforward capable of predicting composites' viscoelastic behavior in the time domain. The isotropization technique for non-uniform stress-strain fields and incremental Mori-Tanaka schemes for high volume fraction are adopted in this study. Effects of the imperfectly bonded interphase layer on the viscoelastic behavior on the dynamic mechanical behavior are also investigated. The proposed model is verified by the direct numerical simulation and DMA (dynamic mechanical analysis) experimental results. The proposed model is useful for multiscale analysis of viscoelastic composite materials, and it can also be extended to predict the nonlinear viscoelastic response of composite materials.

• Interaction and multiscale mechanics
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• v.2 no.1
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• pp.69-89
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• 2009

Reinforced and prestressed concrete (RC and PC) thin walls are crucial to the safety and serviceability of structures subjected to shear. The shear strengths of elements in walls depend strongly on the softening of concrete struts in the principal compression direction due to the principal tension in the perpendicular direction. The past three decades have seen a rapid development of knowledge in shear of reinforced concrete structures. Various rational models have been proposed that are based on the smeared-crack concept and can satisfy Navier's three principles of mechanics of materials (i.e., stress equilibrium, strain compatibility and constitutive laws). The Cyclic Softened Membrane Model (CSMM) is one such rational model developed at the University of Houston, which is being efficiently used to predict the behavior of RC/PC structures critical in shear. CSMM for RC has already been implemented into finite element framework of OpenSees (Fenves 2005) to come up with a finite element program called Simulation of Reinforced Concrete Structures (SRCS) (Zhong 2005, Mo et al. 2008). CSMM for PC is being currently implemented into SRCS to make the program applicable to reinforced as well as prestressed concrete. The generalized program is called Simulation of Concrete Structures (SCS). In this paper, the CSMM for RC/PC in material scale is first introduced. Basically, the constitutive relationships of the materials, including uniaxial constitutive relationship of concrete, uniaxial constitutive relationships of reinforcements embedded in concrete and constitutive relationship of concrete in shear, are determined by testing RC/PC full-scale panels in a Universal Panel Tester available at the University of Houston. The formulation in element scale is then derived, including equilibrium and compatibility equations, relationship between biaxial strains and uniaxial strains, material stiffness matrix and RC plane stress element. Finally the formulated results with RC/PC plane stress elements are implemented in structure scale into a finite element program based on the framework of OpenSees to predict the structural behavior of RC/PC thin-walled structures subjected to earthquake-type loading. The accuracy of the multiscale modeling technique is validated by comparing the simulated responses of RC shear walls subjected to reversed cyclic loading and shake table excitations with test data. The response of a post tensioned precast column under reversed cyclic loads has also been simulated to check the accuracy of SCS which is currently under development. This multiscale modeling technique greatly improves the simulation capability of RC thin-walled structures available to researchers and engineers.

• Interaction and multiscale mechanics
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• v.5 no.3
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• pp.211-228
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• 2012

This paper reports the development of a generalized inverse analysis formulation for the parameter estimation of four-parameter Burger model. The analysis is carried out by formulating the problem as a mathematical programming formulation in terms of identification of the design vector, the objective function and the design constraints. Thereafter, the formulated constrained nonlinear multivariable problem is solved with the aid of fmincon: an in-built constrained optimization solver module available in MatLab. In order to gain experience, a synthetic case-study is considered wherein key issues such as the determination and setting up of variable bounds, global optimality of the solution and minimum number of data-points required for prediction of parameters is addressed. The results reveal that the developed technique is quite efficient in predicting the model parameters. The best result is obtained when the design variables are subjected to a lower bound without any upper bound. Global optimality of the solution is achieved using the developed technique. A minimum of 4-5 randomly selected data-points are required to achieve the optimal solution. The above technique has also been adopted for real-time settlement of four oil refineries with encouraging results.

• Interaction and multiscale mechanics
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• v.4 no.4
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• pp.321-336
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• 2011

This paper presents the results of static vertical load tests carried out on a model building frame supported by pile groups embedded in cohesionless soil (sand). The effect of soil interaction on displacements and rotation at the column base and also the shears and bending moments in the columns of the building frame were investigated. The experimental results have been compared with those obtained from the finite element analysis and conventional method of analysis. Soil nonlinearity in the lateral direction is characterized by the p-y curves and in the axial direction by nonlinear vertical springs along the length of the piles (${\tau}-z$ curves) at their tips (Q-z curves). The results reveal that the conventional method gives the shear force in the column by about 40-60%, the bending moment at the column top about 20-30% and at the column base about 75-100% more than those from the experimental results. The response of the frame from the experimental results is in good agreement with that obtained by the nonlinear finite element analysis.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.14 no.1
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• pp.39-48
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• 1994

An equivalent homogeneous 3-D linear composite analysis and accomponying finite element program is presented for elastomeric bearings. This study is limited to the 3-D layered system with linear, elastic, isoparametric small deformation. And we used method of multiscale to model the 3-dimensional configurations and overall response of the layered elastomeric bearings with global and local coordinates. The primary dependent variables for the theory have been selected that require only $C_o$ continuity of the finite element analysis. As a result, it is very simple and computationally economical. The presented theory can also be applied easily to the analysis of nonlinear behavior of layered systems. And those of past are not applicable to nonlinear analysis, because it uses superposition theory. Numerical examples are presented to verify the theory and to illustrate potential applications of the analysis.

• Multiscale and Multiphysics Mechanics
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• v.1 no.2
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• pp.143-156
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• 2016

Reinforced concrete (RC) structures require advanced analysis techniques for better estimation of their seismic responses, especially in the case of exhibiting complex three-dimensional coupling of torsional and flexural behaviors. This study focuses on validating a numerical approach for evaluating the seismic response of a three-dimensional unsymmetrical RC structure through the participation in the SMART 2013 international benchmark program. The benchmark program provides material properties, detailed drawings of the RC structure, and input ground motions for the seismic response evaluation. In this study, nonlinear constitutive models of concrete and rebar were formed and local tests were conducted to verify the constitutive models in finite element analysis. Elastic calibration of the finite element model of the SMART 2013 RC structure was performed by comparing numerical and experimental results in modal and linear time history analyses. Using the calibrated model, nonlinear earthquake analysis and seismic fragility analysis were performed to estimate the behavior and vulnerability of the RC structure with various ground motions.

• Interaction and multiscale mechanics
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• v.6 no.4
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• pp.395-409
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• 2013

Molecular dynamics (MD) systems are highly nonlinear and nonlocal, and the conventional model order reduction methods are ineffective for MD systems. The RBF-POD method (Lee and Chen, 2013) employed a radial basis function (RBF) approximated potential energies and inter-atomic forces of MD systems under the framework of the proper orthogonal decomposition (POD) method for the reduced-order modeling of MD systems. In this work, we focus on the numerical procedures of the RBF-POD method and demonstrate how to apply this approach to the modeling of ds-DNA molecules under stretching and bending conditions.

• Interaction and multiscale mechanics
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• v.3 no.2
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• pp.192-211
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• 2010

In most framed structures the nonlinearities and the damages are localized, extending over a limited length of the structural member. In order to capture the details of the local damage, the segments of a member that have entered the nonlinear range may need to be analyzed using the three-dimensional element (3D) model whereas the rest of the member can be analyzed using the simpler one-dimensional (1D) element model with fewer degrees of freedom. An Element-Coupling model was proposed to couple the small scale solid 3D elements with the large scale 1D beam elements. The mixed dimensional coupling is performed imposing the kinematic coupling hypothesis of the 1D model on the interfaces of the 3D model. The analysis results are compared with test results of a reinforced concrete pipe column and a structure consisting of reinforced concrete columns and a steel space truss subjected to static and dynamic loading. This structure is a reduced scale model of a direct air-cooled condenser support platform built in a thermal power plant. The reduction scale for the column as well as for the structure was 1:8. The same structures are also analyzed using 3D solid elements for the entire structure to demonstrate the validity of the Element-Coupling model. A comparison of the accuracy and the computational effort indicates that by the proposed Element-Coupling method the accuracy is almost the same but the computational effort is significantly reduced.