Effective Stress-strain Behavior Research Articles

Undrained Failure Criteria for Isotropic and Anisotropic Soils

A new total stress failure criterion applicable to both isotropic and anisotropic soils under undrained conditions is proposed. The new criterion, which is motivated by elastic anisotropy in the underlying effective stress-strain behavior, is shown to be consistent with reported data for undrained shear strengths obtained in triaxial compression, triaxial extension, and direct simple shear tests.

Plastic temperature-dependent constitutive modeling of pure aluminum diaphragms at large strains by using bulge test

A plastic temperature-dependent constitutive model is developed for 0.05 mm thickness pure aluminum diaphragms at large strains by using bulge test method. Rupture strain of the material is recorded below two percent according to tensile tests. In order to achieve the material behavior at larger strains, an own bulge test apparatus is used to extract equi-biaxial stress–strain curves at different temperatures, i.e. from room to 150 °C. Effective stress–strain behavior is then computed via a transformation scheme using the plastic work definition as well as the room temperature uniaxial stress–strain curve. It is illustrated that the Johnson–Cook constitutive model is not able to capture this stress–strain behavior. Thus, a modified Johnson–Cook model is developed in which the strain hardening is assumed to be temperature-dependent accompanying by a novel thermal softening relation. Using the Least-square method as well as the Ant colony optimization algorithm, the material parameters of the both models are calculated. It is depicted that the new model follows the material behavior more precisely than the Johnson–Cook model. The new model is then numerically implemented into finite element software via a user subroutine. In order to compare the accuracy of both models in capturing the hot bi-axial deformation of pure aluminum, an experiment is performed and numerically simulated.

Intrinsic-to-extrinsic transition in fracture toughness through structural design: A lesson from nature

Catastrophic failure of materials and structures due to unstable crack growth could be prevented if fracture toughness could be enhanced at will through structural design, but how can this be possible if fracture toughness is a material constant related to energy dissipation in the vicinity of a propagating crack tip. Here we draw inspiration from the deformation behavior of biomolecules in load bearing biological materials, which have been evolved with a large extensibility and a high breaking strength beyond their elastic limit, and introduce an effective biomimetic strategy to enhance fracture toughness of a structure through an intrinsic to extrinsic (ITE) transition. In the ITE transition, toughness starts as an intrinsic parameter at the basic material level, but by designing a protein-like effective stress–strain behavior the toughness at the system level becomes an extrinsic parameter that increases with the system size without bound. This phenomenon is demonstrated through a combination of numerical simulations, analytic modeling and experiments, and leads to a biomimetic strategy which can be broadly adopted to enhance fracture toughness in engineering systems.

Prediction of Stress–Strain Curves of Metastable Austenitic Stainless Steel Considering Deformation-Induced Martensitic Transformation

Transformation-induced plasticity (TRIP) effect is the outstanding mechanism of austenitic stainless steel. It plays an important role in increasing formability of the steel due to higher local strain hardening during deformation. In order to better understand forming behavior of this steel grade, the strain-induced martensitic transformation of the 304 stainless steel was investigated. Uniaxial tensile tests were performed at different temperatures for the steel up to varying strain levels. Stress–strain curves and work hardening rates with typical TRIP effect characteristics were obtained. Metallographic observations in combination with X-ray diffraction method were employed for determining microstructure evolution. Higher volume fraction of martensite was found by increasing deformation level and decreasing forming temperature. Subsequently, micromechanics models based on the Mecking–Kocks approach and Gladman-type mixture law were applied to predict amount of transformed martensite and overall flow stress curves. Hereby, individual constituents of the steel and their developments were taken into account. Additionally, finite element (FE) simulations of two representative volume element (RVE) models were conducted, in which effective stress–strain responses and local stress and strain distributions in the microstructures were described under consideration of the TRIP effect. It was found that flow stress curves calculated by the mixture law and RVE simulations fairly agreed with the experimental results. The RVE models with different morphologies of martensite provided similar effective stress–strain behavior, but unlike local stress and strain distributions, which could in turn affect the strain-induced martensitic transformation.

Periodic cellular materials with nonlinear elastic homogenized stress-strain response at small strains

We investigate the effective stress-strain behavior of cellular elastomers, structured with a periodic pattern of elliptic holes by means of full scale simulations under small deformations. First, we show that the elastic response behaves non trivially with the pore geometry. In particular, we show that auxetic and anistropic responses arise for a broad range of parameters, when the microstructure becomes sufficiently porous. Second, we show that, in the limit of large and near-circular holes, the stress-strain nonlinearities become very large. Third, we adopt an effective theoretical description where the filaments between the holes are modeled by slender beams to predict the linear response, and by bars and pivots to capture the leading order nonlinear corrections. This approach fully captures the asymptotic observations and open pathways for an effective-beams based homogenization and the design of nonlinear cellular materials.

Coupling digital image correlation and finite element analysis to determine constitutive parameters in necking tensile specimens

A general framework is described for coupling digital image correlation (DIC) with finite element analysis to determine material parameters from measurements of nonuniform displacement fields in a specimen. The approach is to minimize the difference between measured and computed displacement fields and external forces applied to the specimen by repeatedly correcting the material parameters in a chosen constitutive model. The minimization can be accomplished analytically, and the resulting nonlinear system of equations solved using a Newton–Raphson procedure that integrates naturally with standard nonlinear finite element computations. As a representative application, the method is applied to measure the flow behavior of tensile specimens beyond uniform elongation. The results of a series of tensile tests on tapered HSLA 590FB steel specimens show that the effective stress-strain behavior can reliably be extracted to a strain of 60%, well beyond the limits of 20% commonly achieved using traditional engineering analyses on straight-gauge specimens.

Investigation of the Mechanical Behavior of Open‐Cell Ni Foams by Experimental and FEM Procedures

Cellular materials such as wood, bone and other living tissues are frequently encountered in nature. Metal foams are a relatively new class of recyclable materials and various new methods and manufacturing technologies developed recently for their production. Metal foams are increasingly used in many engineering applications due to their low weight in combination with their increased heat transfer potential and mechanical strength. The mechanical behavior of cellular structures is governed by their internal architecture. Given the wide range of potential applications, in the automotive, building and other industries, the study of the mechanicalbehavior of metal foams is considered imperative. Several analytical and numerical approaches can be found in the literature. Analytical models based on beam theory have been derived by Gibson and Ashby giving the effective mechanical properties as functions of the structure’s relative density. Analytical methods and Finite Element simulations based on beam elements are used for analyzing the effective stiffness of open cell metallic foams with tetrakaidecahedral unit cells. In Gong and Kyriakides, and Gong et al., the linear and nonlinear compressive response of polyester urethane open cell foams is modeled using idealized periodic structures consisting of tetrakaidecahedral cells. Analytical and numerical analyses of the effective stress–strain behavior of a two-dimensional foam model in the nonlinear elastic regime are presented by Hohe and Becker. Various three-dimensional open cell structures are studied in Luxner et al., [13] and Luxner et al., using a periodic microfield approach. X-ray tomography has recently proved to be a very powerful tool allowing the characterization of the microstructure of materials or the architecture of cellular materials. X-ray tomography allows large deformations of cellular solids to be imaged in a non destructive way: thus the important buckling, bending or fracture events appearing during the deformation can be visualized. The majority of theoretical simulations which relate the structure of cellular materials with their properties refer to periodic models, while most cellular solids are random materials. There are cases where the theoretical results for such models are in good agreement with the properties of real materials. However, as most real cellular solids are not periodic, there is a need to develop approaches taking into consideration this aspect. In this paper, the elastoplastic behavior of a Nickel opencell foam is investigated under tension loads. A scanning electron microscope equipped with an apparatus of microtension was used. Ex-situ and in-situ micro-tension tests were conducted. The latter allows determination of the mechanical properties through real-time observations of the local deformations of the struts, while correlating them with the imposed. High resolution X-ray tomographies, carried out to capture the exact 3D geometry of the foams were used in turn to simulate mechanical behavior of the foam with the aid of a computational procedure based on Finite Element Modeling (FEM). The porous microstructure of metallic foams causes microscopic stress localization during loading, which reduces the overall strength and therefore limits the application of such materials. The results of the present study also allow the visualization and determination of the local stresses developed in the metal foam.

Geometrically nonlinear stress–strain behavior of hyperelastic solid foams

The present study is concerned with an effective stress analysis of cellular solids in the finite strain regime. The homogenization of the microstructure is performed by means of a strain energy based RVE-procedure which assumes macroscopic equivalence of a representative volume element for the given microstructure and a similar volume element consisting of the effective medium, if the average strain energy density in both volume elements is equal provided that the deformation gradient with respect to both elements is equal in a volume average sense. Disordered microstructures are considered by means of a randomized periodic model in conjunction with a stochastic approach. The model is applied to an analysis of the effective stress–strain behavior of two-dimensional model foams with periodic and disordered microstructure. Special interest is directed to effects of the geometric nonlinearity.

Effective mechanical behavior of hyperelastic honeycombs and two-dimensional model foams at finite strain

The aim of the present study is the analytical and numerical determination of the effective stress–strain behavior of solid foams made from hyperelastic materials in the finite strain regime. For the homogenization of the microstructure, a strain energy-based concept is proposed which assumes macroscopic mechanical equivalence of a representative volume element for the given microstructure with a similar homogeneous volume element if the strain energy of both volume elements is equivalent, provided that the volume average of the deformation gradient is equal for both volume elements. The concept is applied to an analysis of hyperelastic solid foams using a two-dimensional model. The effective stress–strain behavior is analyzed under uniaxial and biaxial loading conditions in the tensile and in the compressive range as well as under simple shear deformation. It is observed that the effective mechanical behavior of cellular solids at infinitesimal and finite deformation is essentially different on both, the quantitative and the qualitative level.

Effective stress-strain relations for two-dimensional cellular sandwich cores: Homogenization, material models, and properties

The theory of sandwich construction has been an active field of research for more than five decades. Aim of the present article is to review the work dedicated to the theoretical determination of the effective stress-strain material behavior of two-dimensional cellular materials with large-scale cells used as core material of structural sandwich panels. Both, the applied homogenization schemes and the applied material models are considered. Explicit expressions for the linear properties of a variety of basic cell geometries are presented, as well as schemes for the analysis of more general cases. In addition, the incorporation of specific effects such as cell wall imperfections or core face sheet constraints and the analysis of nonlinear elastic and elastic-plastic effective material response are reviewed. This review article includes 148 references.

Elastic and plastic properties of metal-matrix composites: geometrical effects of particles

Three-dimensional finite element simulations on the base of cell models and micromechanics have been made in this investigation to predict effective elastic moduli and elastoplastic stress-strain behavior of particulate-reinforced metal-matrix composites. Numerical results are given for the influence of particle volume fraction, shape and orientation to the overall behavior of the composite.