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Most solid bodies are porous and in such bodies we expect the material properties to vary with porosity and hence with the density. Such bodies whose properties depend on the density cannot be described by the classical linearized elastic constitutive relation when they are undergoing small deformations, as the material moduli cannot depend on density. A constitutive relation which is valid in the small displacement gradient range wherein the material moduli are dependent on the density can be developed by linearizing implicit constitutive relations for describing elastic bodies introduced recently by Rajagopal [1]. In this paper, we determine the stress concentration due to a hole in a slab that is subject to biaxial loading in a body described by such a constitutive relation. We find that the stress concentration can be much as 147% higher than that for classical linearized elasticity for the range of loadings considered in the study. [ABSTRACT FROM AUTHOR]

The paper presents a strain measurement technique to be applied on repetitive knitted nets. The application of the procedure is focused on large deployable reflectors used in space applications. Manufacturing of these structures involves knitting of thin metallic wires. Besides space antennas, the method herein developed is advantageous for many other types of knitted tissues such as elastic coatings, elastic bandages for medical applications, or any other woven fabric requiring a defined elastic behaviour. All of them display an almost regular repetitive pattern whose variations due to imposed loads are the core of the method. Deformation of such kind of structural elements must be analysed in two dimensions, because the knitting causes an accentuated orthotropic behaviour. Strain measurement is tricky and requires special computational techniques. Indeed, the application of standard experimental methods and indirect strain determination, through well-established image analysis algorithm, can be totally unsuccessful or unsuitable because of the lack of continuity of these structures. The paper presents a method based on two-dimensional Fourier analysis. Numerical examples, supported by some experimental evidences, confirm the feasibility of the technique. Furthermore, a newly proposed frequency zooming algorithm, based on fast Fourier transform, makes the computational costs of the indirect strain measurement affordable. [ABSTRACT FROM AUTHOR]

Predicting the deformations of deep reservoirs due to fluid withdrawal/injection is a challenging task that could have important environmental, social, and economical impacts. Finite element models, if endowed with an appropriate constitutive law, represent a useful tool for computing the displacements, the deformations, and the stress distributions in reservoir applications. Several studies show that hypoelastic laws, based on a stress-dependent vertical compressibility, are able to provide accurate results, confirmed by in situ and satellite measurements. On the other hand, such laws present some weaknesses related to the numerical implementation, in particular due to the nonsymmetry of the tangent operator. This paper presents a new constitutive model based on 2 invariants (the mean normal and deviatoric stresses), characterized by a variable pressure-dependent bulk modulus K. This constitutive law allows for overcoming most shortcomings of the hypoelastic law, although preserving the same accuracy, reliability, and ease of use and calibration. This paper presents a procedure to identify the parameters of the new model, starting from the typically available data on the vertical compressibility. Numerical results show a good agreement between the 2 laws, suggesting the proposed approach as a valid alternative in reservoir applications. [ABSTRACT FROM AUTHOR]

This paper reports a new type of auxetic yarn made with circular braiding technology to overcome the yarn slippage problem in the conventional helical auxetic yarn structure. Various auxetic yarn structures are firstly produced on a vertical circular braiding machine with 16 yarn carries by changing the number and arrangement of stiff yarn as well as diameter of elastic yarn and core yarn, and then tested under single and repeating tensile conditions. The results show that not only yarn slippage problem could be overcome in the newly developed auxetic yarn structure, but also an early activation and a higher magnitude of negative Poisson's ratio could be achieved. The results also show that all structural parameters including stiff yarn number and arrangement, core yarn, and elastic yarn diameter have an influence on the auxetic effect of the novel yarn structure. Since the new auxetic yarn is produced by using standard braiding manufacturing technique and conventional non-auxetic yarns, there are few technological barriers for its largescale manufacture for practical application. [ABSTRACT FROM AUTHOR]

Standard diffraction‐based measurements of elastic strains in polycrystalline materials rely on shifts of Bragg peaks. Measurement results are usually given in the form of a single tensor assumed to represent the average stress in the material, but the question about the true relationship between the tensor and the average stress generally goes without notice. This paper describes a novel procedure for analysis of data obtained from such measurements. It is applicable in cases when spatial correlations in the material are ignored and statistical information about the polycrystalline specimen is limited to texture‐related intensity pole figures and strain pole figures. A tensor closest to auxiliary strain tensors linked to the results of measurements in particular specimen directions is considered to represent the strain state. This tensor is shown to be a good approximation of the average strain tensor. A closed‐form expression allowing for its direct computation from experimental pole figures is given. The performance of the procedure is illustrated using simulated data. [ABSTRACT FROM AUTHOR]

We propose in this paper analytical and numerical models that describe the in-plane uniaxial elastic properties (Young's moduli and Poisson's ratios) of a honeycomb structure with curved walls. We perform a parametric analysis of the mechanical performance of this honeycomb also by taking into account the different types of deformations acting inside the cell walls. The curved wall honeycomb possesses higher magnitudes of the Poisson's ratio ν12 in the auxetic configuration compared to classical center symmetric configuration with straight cell wall. The presence of the curvature also allows creating configurations with positive Poisson's ratio even for negative internal cell angles, and makes this honeycomb design attractive for mechanical tailoring. [ABSTRACT FROM AUTHOR]

The paper presents the fundamental solutions established for the equilibrium equations written in terms of displacements in the gradient model describing the deformation of two-component elastic composites with stochastic structure. In the paper 2D and 3D problems are constructed on the basis of the theory of generalized functions. [ABSTRACT FROM AUTHOR]

SUMMARY With the concept of generalized plasticity, a constitutive model for describing the deformation behavior of sandstone is proposed in this paper. This proposed model is characterized by the following features: (i) nonlinear elasticity under hydrostatic and shear loading; (ii) associated flow rule for pre-peak simulation; (iii) substantial plastic deformation during shear loading; and (iv) significant shear dilation and distortion prior to the failure state. This model requires 10 material parameters, including three for elasticity and seven for plasticity. All of the parameters can be determined, in a straightforward manner, by the suggested procedures. The proposed model has been validated by comparing the triaxial test results of the Mushan sandstone under different hydrostatic stress, different stress paths, and cyclic loading condition. It is also versatile in simulating the deformation behaviors of two other sandstones. Upon slight modification of the model, the post-peak behavior of sandstone can be reasonably predicted using proposed model. Copyright © 2012 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Plastic deformation of crystals is mostly mediated by the motion of dislocations. During the last two decades a lot of effort was directed towards including more knowledge about dislocations in continuum descriptions of plasticity. Promising approaches towards building continuum plasticity theories on averages of the behavior of many single dislocations have been formulated under the assumption of small deformations. In the current paper we derive the kinematics of single dislocations moving inside a dislocated crystal simultaneously deforming by the motion of other dislocations in the language of large deformation plasticity. The evolution equation of a single dislocation is connected to the formation of kinks and jogs due to cutting by other dislocations and is shown to parallel the evolution equation of the dislocation density tensor in finite deformation formulation. Implications for dislocation based modeling of plasticity are discussed. [ABSTRACT FROM AUTHOR]

This paper proposes a Trefftz method for evaluating the T-stress for cracks emanating from a hole in a rectangular plate. In this method, the displacement and the stress field are an elasticity solution, which is derived from complex potentials. The complex potentials are assumed in a series form with undetermined coefficients. After using the minimum potential energy principle, an algebraic equation for the undetermined coefficients can be formulated. The coefficients can be obtained from the equation, and the whole stress field is determined. Stress intensity factor and T-stress can be evaluated immediately from the known solution. Merit of the suggested method is addressed. For three particular cases, R=0, R/w=0.25 and R/w=0.5, the computed results are tabulated. Copyright © 2007 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

There are many approaches in continuum mechanics involving incompatible deformations, one well-known example being the polar decomposition of the deformation gradient tensor. Such deformations have in the past been regarded rather in the context of local configurations. In the present paper, we discuss incompatible deformations among others, also from the point of view of material lines. Related covariant derivatives and spatial differential operators are introduced and investigated. In particular, it is shown that components of curvature tensors, present in many gradient constitutive theories, may be expressed in terms of the difference between different connections for the same manifold. These issues are illustrated with reference to multiplicative decompositions of deformation gradient tensors into elastic and plastic parts. Two classes of model materials are addressed, non-polar and micropolar ones. [ABSTRACT FROM AUTHOR]

The importance of a two-parameter approach in the fracture mechanics analysis of many cracked components is increasingly being recognized in engineering industry. In addition to the stress intensity factor, the T stress is the second parameter considered in fracture assessments. In this paper, the path-independent mutual M- integral method to evaluate the T stress is extended to treat plane, generally anisotropic cracked bodies. It is implemented into the boundary element method for two-dimensional elasticity. Examples are presented to demonstrate the veracity of the formulations developed and its applicability. The numerical solutions obtained show that material anisotropy can have a significant effect on the T stress for a given cracked geometry. [ABSTRACT FROM AUTHOR]

The computational significance of the case of two or three equal principal stretches in large deformation analysis is investigated in this paper. A detailed analytical study shows that the previously suggested solutions, based on numerical perturbations, are not adequate and might lead to erroneous results. A number of examples are presented to illustrate the approach. Copyright © 2005 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The paper reports some numerical experiments on the effectivity of the Zienkiewicz-Zhu error estimate (1987) and comparisons of two adaptive mesh generators: ADMESH, developed by Jin and Wiberg (1990) and MAD2D by Peraire et al. (1987) and Zhu et al. (1990-91). From the experiments we observe that: (1) without any empirical correction, the effectivity of the error estimate for linear triangular elements is good if post-processed continuous stresses are obtained by adequately using an iterative stress recovery procedure (Zienkiewicz et al., 1985), and is also acceptable by using a simple `averaging' procedure; (2) these two mesh generators are basically comparable. [ABSTRACT FROM AUTHOR]