Effective Tangent Modulus Research Articles

A two-scale homogenization analysis of porous magneto-electric two-phase composites

A computational homogenization analysis for the simulation of porous magneto-electric composite materials is presented. These materials combine two or more ferroic states with each other enabling a coupling between magnetization and electric polarization. This magneto-electric coupling finds application in sensor technology or data storage devices. Since most single-phase multiferroics show coupling at very low temperatures beyond technically relevant applications, two-phase composites, consisting of a ferroelectric and a ferromagnetic phases, are manufactured. They generate a strain-induced magneto-electric coupling at room temperature. The performance and reliability of these materials is influenced by defects or pores, which can arise during the manufacturing process. We analyze the impact of pores on the magnitude of the magneto-electric coupling coefficient. In order to determine the effective properties of the composite, a two-scale finite element ( $$\hbox {FE}^2$$ ) homogenization approach is performed. It combines the macroscopic and microscopic scale by direct incorporation of the microscopic morphology. We derive the basic equations for the localization and the homogenization of the individual field variables and give an algorithmic expression for the effective tangent moduli. We discuss the influence of pores on the magneto-electric coupling in two-phase composites by analyzing numerical examples.

Algorithmic two-scale transition for magneto-electro-mechanically coupled problems: FE2-scheme: Localization and homogenization

In this paper we present a computational homogenization procedure for the simulation of magneto-electro-mechanically coupled boundary value problems (bvp)s on two scales. We derive the basic equations for the localization and the homogenization of the individual field variables and give an algorithmic expression for the effective tangent moduli. The resulting algorithmic two-scale transition procedure is implemented into an FE2-method, which allows us to compute macroscopic boundary value problems in consideration of attached microscopic representative volume elements. The challenge in the simulation of magneto-electro-mechanically coupled materials is the modeling of the complicated interactions between magnetical, electrical and mechanical quantities on both scales. A primer example for such interactions is given by magneto-electric composites. Thus, we apply the presented method to the two-scale simulation of a variety of versions of magneto-electric composites. In detail, we consider two-phase composites composed of (i) piezomagnetic and piezoelectric, (ii) piezomagnetic and non-linear electrostrictive, as well as (iii) piezomagnetic and non-linear dissipative ferroelectric phase. Based on numerical examples, we discuss aspects of the applicability, the numerical stability as well as the predictive capability of the proposed method.

Tangent moduli of hot-rolled I-shaped axial members considering various residual stress distributions

This paper presents an equation for the effective tangent moduli for steel axial members of hot-rolled I-shaped section subjected to various residual stress distributions. Because of the existence of residual stresses, the cross section yields gradually even when the member is subjected to uniform axial stresses. In the elasto-plastic stage, the structural response can be easily traced using rational tangent modulus of the member. In this study, the equations for rational tangent moduli for hot-rolled I-shaped steel members in the elasto-plastic stage were derived based on the general principle of force-equilibrium. For practical purpose, the equations for the tangent modulus were presented for conventional patterns of the residual stress distribution of hot-rolled I-shaped steel members. Through a series of material nonlinear analyses for steel axial members modeled by shell elements, the derived equations were numerically verified, and the presented equations were compared with the CRC tangent modulus equation, the most frequently used equation so far. The comparative study shows that the presented equations are extremely effective for accurately analyzing elasto-plastic behavior of the axially loaded members in a simple manner without using complex shell element models.

Computational homogenization in magneto-mechanics

This work presents a geometrically nonlinear homogenization framework for composites with magneto-mechanical behavior whereby the composite can be subject to large deformation processes. The magneto-mechanical governing equations in the material description for both the overall body and its microstructure are presented, and the connections between micro- and macro-scale field variables are identified. Considering periodic boundary conditions for the microscopic unit cell, a finite element framework for computing the macroscopic field variables and the effective tangent moduli is developed. The proposed methodology is utilized to study a variety of two- and three-dimensional numerical examples. In particular, the behavior of fiber and particle reinforced composites with magneto-mechanical constitutive laws are illustrated. Finally, a specific physically motivated problem of a magnetorheological elastomer, consisting of a polymer matrix and iron particles, under finite deformation and applied magnetic field is analyzed and the results are given for several combinations of deformation modes and applied magnetic fields.

Homogenization of elastoplastic composites with generalized periodicity in the microstructure

In this paper, a consistent theory of homogenization for complex heterogeneous elastoplastic structures with generalized periodicity is proposed. The structures under consideration are not necessarily periodic, but their properties (geometry and material) exhibit periodicity with respect to non-linear periodicity functions. The proposed theory is based on an adequate definition of the admissible deformation fields and the corresponding functional setting, and results from the generalization of the two-scale convergence theory. Moreover, the discrete variational formulation is presented, for both the global and local problems. Additionally, the implicit formulation of the homogenization problem is proposed for elastic-J2-plastic constituents with linear hardening in the context of infinitesimal elastoplasticity, including the numerical scheme for homogenization and the derivation of the consistent elastoplastic tangent modulus. Finally, the computational algorithm for the proposed theory is deployed, consisting of four interacting problems, the macroscale, the microscale, the iterative plastic scheme and the effective tangent modulus problem. The theory and the numerical and computational scheme are supplemented by two examples, one of a wavy multilayered structure and one of a multilayered tube.

고강도 강재보의 비탄성 횡-비틀림좌굴 제어를 위한 횡지지 거리

In this study, lateral-torsional buckling (LTB) strength of high-strength H-beams built up from 800MPa tensile-strength steel was experimentally and analytically evaluated according to current lateral stability provisions (KBC 2009, AISC-LRFD 2010). The motivation was to evaluate whether or not current LTB provisions, which were originally developed for ordinary steel with different stress-strain characteristics, are still applicable to high-strength steel. Two sets of compact-section specimens with relatively low (Set A) or high (Set B) warping stiffness were prepared and tested under uniform moment loading. Laterally unbraced lengths of the test specimens were controlled such that inelastic LTB could be induced. All specimens exhibited LTB strength exceeding the minimum limit required by current provisions by a sufficient margin. Moreover, some specimen in Set A reached a rotation capacity required for plastic design, although its laterally unbraced length belonged to the inelastic LTB range. All the test results indicated that extrapolation of current provisions to high-strength steel is conservative. In order to further analyze the test results, the relationship between inelastic moment and laterally unbraced length was also derived in explicit form for both ordinary- and high-strength steel based on the effective tangent modulus of inelastic section. The analytical relationship derived again showed that extrapolation of current laterally unbraced length limit leads to a conservative design in the case of high-strength steel and that the laterally unbraced length to control the inelastic LTB behavior of high-strength steel beam should be specified by including its unique post-yield strain-hardening characteristics.

A multi-scale model for the analysis of the inhomogeneity of elastic properties of DNA biofilm on microcantilevers

In nanoscale diagnostic systems, inhomogeneity in near-surface systems and flexibility in biostructures greatly influence the mechanical/electrical/thermal properties of biosensors and resultant detection signals. This study focuses on inhomogeneity and flexibility of DNA biofilm and characterizes its local interactions and mechanical properties. First, a flexible cylinder model of DNA chain is employed to capture the local geometric deformation characteristics of DNA molecules on microcantilever. In order to describe the inhomogeneous properties of DNA biofilm at thickness direction, the Strey's empirical formula for mesoscopic DNA liquid crystal theory is improved with the assumption of a net charge distribution in film. The model parameters are obtained by curve fitting with experimental data. Second, the biaxial iso-strain compression of thought experiment and the energy conservation law are used to predict macroscopic effective tangent modulus of DNA biofilm in terms of nanoscopic properties of dsDNA, buffer salt concentration.

Plastic-hinge approach for inelastic analysis of steel–concrete framed structures

This paper presents an application of a computational tool, denoted as SAAFE Program, developed to provide a nonlinear inelastic analysis of steel and composite (steel–concrete) 2D framed structures. This procedure allows an accurate description of the structural nonlinear response, with less computational effort when compared to the general FEM formulation. The method, although similar in concept to earlier plastic-hinge approaches, differs with regard to numerical implementation methodology and precision. The proposed plastic-hinge model is formulated in a succinct format based on the following characteristics: (i) stiffness parameter η , evaluated as a function of the yielding progress at each plastic-hinge location; (ii) effective tangent modulus E t concept which reduces the modulus of elasticity in the element stiffness calculation, considering both the residual stress and out-of-straightness effects; (iii) second-order formulation, based on an incremental stiffness approach in which conventional stability functions are used to reflect the effect (on member stiffness) of axial loads on displacements, allowing accurate identification of member instability. Verification examples are analysed by the proposed approach, in which results are compared with those of FEM numerical and available experimental data, showing good agreement. Based on the obtained results, it is possible to infer about the efficiency and robustness of the proposed model to perform inelastic analysis for isolated and full frame members, incorporating geometric and material nonlinearity.

A Damage-coupled Criterion of Localized Necking Based on Acoustic Tensor

The development of a localized necking criterion for strain-softening materials is presented. The criterion is applicable to materials with anisotropic damage and anisotropic plasticity. The critical condition of damage evolution leading to localized necking is of primary interest in this investigation. As a consequence of plastic instability, the singularity of acoustic tensor is taken as the critical condition for localized necking in strain-softening materials, which often occurs prior to fracture. Effective tangent modulus tensor for materials with anisotropic damage is established. The damage-coupled localized necking criterion, along with the inclination angle of localization band, for strain-softening materials is derived. The closed-form expression of the localized necking criterion has potential applications in the failure analysis of strain-softening materials such as hot metals, rocks, soil, solder, etc. Tensile testing at elevated temperature (450°C) has been performed for aluminum alloy Al6061 with multiple unloading paths to determine material damage. The test results displaying the strain-softening and material damage behaviors are employed to formulate the constitutive equations of the material. Forming limit strains for a particular loading path are computed and compared with the test result.

On the Applicability of the Effective Tangent Modulus Method for Evaluating the Ultimate Strength of Super Long-Span Cable-Stayed Bridges

On the Applicability of the Effective Tangent Modulus Method for Evaluating the Ultimate Strength of Super Long-Span Cable-Stayed Bridges

High-Order Mixture Homogenization of Fiber-Reinforced Composites

An asymptotic mixture theory of fiber-reinforced composites with periodic microstructure is presented for rate-independent inelastic responses, such as elastoplastic deformation. Key elements are the modeling capability of simulating critical interaction across material interfaces and the inclusion of the kinetic energy of micro-displacements. The construction of the proposed mixture model, which is deterministic, instead of phenomenological, is accomplished by resorting to a variational approach. The principle of virtual work is used for total quantities to derive mixture equations of motion and boundary conditions, while Reissner’s mixed variational principle (1984, 1986), applied to the incremental boundary value problem yields consistent mixture constitutive relations. In order to assess the model accuracy, numerical experiments were conducted for static and dynamic loads. The prediction of the model in the time domain was obtained by an explicit finite element code. DYNA2D is used to furnish numerically exact data for the problems by discretizing the details of the microstructure. On the other hand, the model capability of predicting effective tangent moduli was tested by comparing results with NIKE2D. In all cases, good agreement was observed between the predicted and exact data for plastic, as well as elastic responses.

A stochastic model for biological tissue elasticity in simple elongation

A mathematical model is described which predicts the effective tangent moduli of biological tissues at each deformed state, which accounts for the contributions of two major load-bearing components — collagen and elastin. The problem is studied from a stochastic point of view based upon the theory of composite materials. It is shown that a simple stochastic model is possible and it can be expressed simply in terms of the volume fractions of collagen and elastin fibers and of the ‘collagen arrival density’. The model is then used in the discussion of stress-strain relationships of the alveolar wall in simple elongation.