Stress Recovery Procedure Research Articles

How is music listening purpose related to stress recovery? - two preliminary studies in men and women.

Studies have suggested that listening to music can reduce psychological and biological responses to a stressor. However, it is unclear whether music has the same effect on stress recovery. According to field studies, people commonly use music in daily life for the specific purpose of relaxation. We explored whether individuals who generally use music for relaxation purposes show improved recovery from an acute stressor. In two independent studies, twenty-seven healthy female participants (Mage = 24.07) (Study 1) and twenty-one healthy male participants (Mage = 23.52) (Study 2) were separated into two groups based on their frequency of using music for relaxation purposes (low vs. high). All participants underwent a lab-based psychosocial stress test. Subjective stress levels were measured using visual analogue scales. Salivary cortisol and salivary alpha-amylase were measured to assess endocrine and autonomic stress responses, respectively. Subjective stress levels and saliva samples were measured nine times throughout the stress induction and recovery procedure. Chronic stress levels were assessed using the Perceived Stress Scale and the Screening Scale of Chronic Stress. No significant differences were observed in subjective stress levels, salivary alpha-amylase activity, or cortisol concentration between the two groups in either of the two studies. Further analyses revealed that among male participants, increased use of music for relaxation purposes was related to more chronic stress levels (t (10.46) = 2.45, p = 0.03, r = 0.60), whereas female participants exhibited a trend in the opposite direction (t (13.94) = -1.92, p = 0.07, r = 0.46). Contrary to our expectations, the results indicate that habitual music listening for relaxation purposes is not associated with improved recovery from a stressor. However, due to the small sample size, future exploration is necessary to enhance the statistical power of the results of the study.

Recovery strategies, a posteriori error estimation, and local error indication for second‐order G/XFEM and FEM

AbstractThis article presents a computationally efficient and straightforward to implement a posteriori error estimator for second‐order G/XFEM and FEM approximations. The formulation is based on the recently proposed block‐diagonal Zienkiewicz–Zhu (ZZ‐BD) a posteriori error estimator. The focus is on linear elastic fracture mechanics (LEFM) problems but the proposed error estimator formulation is general and can be adapted to other types of problems such as those involving material interfaces. The proposed ZZ‐BD error estimator is based on a new strategy to recover stress fields from second‐order G/XFEM and FEM approximations. This recovery procedure involves locally weighted projections of raw stresses on an approximation space for discontinuous and singular stress fields. The basis functions for these stress approximations are defined using a low‐order partition of unity together with polynomial, discontinuous, and singular recovery enrichment functions. These singular enrichments are provided by the gradient of G/XFEM enrichments for LEFM problems and are, thus, available in most G/XFEM implementations. They also lead to a more computationally efficient stress recovery procedure than the one in the original ZZ‐BD error estimator. The adopted G/XFEM are optimally convergent with the error in the energy norm of . Numerical experiments show that the error of the recovered stress field converges at the same rate as the discretization error. They also show that the effectivity index of the error estimator is close to the unity and that it provides good local error indicators for mesh adaptivity algorithms. Second‐order FEM for elasticity problems is a special case of the G/XFEM adopted here. This is exploited to define a block‐diagonal ZZ error estimator for the FEM as a special case of the proposed estimator for the G/XFEM. This brings the computational efficiency, simplicity, and accuracy of the ZZ‐BD error estimator, originally developed for the G/XFEM, to second‐order standard FEM.

Fracture analysis of cracked magneto-electro-elastic functionally graded materials using scaled boundary finite element method

This paper develops the scaled boundary finite element method to analyse fracture of functionally graded magneto-electro-elastic materials. Polygon meshes are employed to discretize the domain. No asymptotic solution, local mesh refinement or other special treatments around a crack tip are required to calculate the intensity factors. When the material gradients of the coefficients in the constitutive matrix are expressed as a series of power functions of the scaled boundary coordinates, the stiffness matrices can be integrated analytically. The formulation enables the generalized intensity factors of stress, electric displacement and magnetic induction fields along the radial direction to be represented analytically. This permits the calculation of the generalized intensity factors directly from the scaled boundary finite element solution of the singular stress, electric displacement and magnetic induction fields by following the standard stress recovery procedures in the finite element method. Several numerical benchmarks are presented to validate the proposed technique with the results reported in the literature.

An improved stress recovery technique for the unfitted finite element analysis of discontinuous gradient fields

AbstractStress analysis is an all‐pervasive practice in engineering design. With displacement‐based finite element analysis, directly‐calculated stress fields are obtained in a post‐processing step by computing the gradient of the displacement field—therefore less accurate. In enriched finite element analysis (EFEA), which provides unprecedented versatility by decoupling the finite element mesh from material interfaces, cracks, and structural boundaries, stress recovery is further aggravated when such discontinuities get arbitrarily close to nodes of the mesh; the presence of small area integration elements often yields overestimated stresses, which could have a detrimental impact on nonlinear analyses (e.g., damage or plasticity) since stress concentrations are just a nonphysical numerical artifact. In this article, we propose a stress recovery procedure for enhancing the stress field in problems where the field gradient is discontinuous. The formulation is based on a stress improvement procedure (SIP) initially proposed for low‐order standard finite elements. Although generally applicable to all EFEA, we investigate the technique with the Interface‐enriched Generalized Finite Element Method and compare the procedure to other post‐processing smoothing techniques. We demonstrate that SIP for EFEA provides an enhanced stress field that is more accurate than directly‐calculated stresses—even when compared with standard FEM with fitted meshes.

Dog-bone Samples may not Provide Direct Access to the Longitudinal Tensile Strength of Clear-wood

Background: Testing standards prescribe dog-bone samples for the determination of clear-wood longitudinal tensile strength. However, the literature reports a high number of invalid tests due to the unexpected failure of the sample outside the gauge length. Motivation: The paper aims at understanding the reason for the premature failure of dog-bone samples and suggesting possible strategies for improving testing protocols. Methods: The paper starts with a comparative review of standards for different orthotropic materials. Thereafter, it analyzes the stress distribution in a clear-wood dog-bone sample using a recently proposed stress-recovery procedure and Finite Elements. Finally, the sample failure is considered applying Tsai-Wu and SIA criteria. Results: Comparative review highlights the controversy on the choice of the sample geometry. Both analytical and numerical results confirm the presence of shear and transversal stresses in necking regions, overlapping with axial stress greater (up to 2%) than the one in the gauge region. As a consequence, clear-wood dog-bone samples fail not due to a pure axial stress state in the gauge region (as expected), but due to complex stress state in necking region, where failure index is 4 ~ 5% greater than the one in gauge region. Conclusion: Assuming that dog-bone samples fail in the gauge region due to pure axial stress is simplistic, as demonstrated by analytical and numerical evidence. As a consequence, interpretations of experimental results based on this belief are misleading and testing protocols should be refined. Indeed, the presence of spurious stresses interfering with expected pure axial stress seems unavoidable. Therefore, clear-wood testing standards should allow to use prismatic samples or, alternatively, to consider as valid also tests on samples breaking outside the gauge region. Both the proposed solutions apparently reduce the accuracy of the experiments, while in contrast, they provide the best achievable results, speeding up the testing procedure and reducing the testing costs.

Stress Recovery Procedure for the Bonded Particle Model

In the simulation of discontinuous block systems, the discrete element method (DEM) has better computational efficiency and convergence than the finite element method (FEM). When several DEM particles are bonded together with parallel bonds (the bonded particle model, BPM), various shapes and block fractures can be simulated. The main aim of the BPM is to simulate a continuous material in which the stress distribution is continuous. Since the existing stress result for a single particle is an average value over the particle’s area, stress results do not exist in the area between particles. In this paper, the stress value for a single two-dimensional DEM particle is deduced. A stress recovery procedure with a linear stress function for a triangular element generated by the centroids of three bonded particles is proposed. In this way, the recovered stress field for the whole mesh composed of all triangular elements is continuous. A stress gradient exists in the whole mesh. This can also provide more accurate stress values for judging a fracture inside a block. Symmetrical and asymmetrical models are simulated by the BPM and FEM. Similar to the FEM results, the recovered stress results for the BPM can describe the stress distribution in the simulated continuous blocks. For the model with the theoretical stress solution, the recovered result and the theoretical solution coincide well.

A stress recovery procedure for laminated composite plates based on strong-form equilibrium enforced via the RBF Kansa method

Often the employment of the full potentialities of laminated composite materials is restrained by the scarceness of cost-effective simulation strategies in the design stage. Albeit cheap modelling techniques exist, they typically prove ineffective in retrieving interlaminar stresses, the first responsible for the damage of laminates. In this paper, we propose a strategy to reconstruct the out-of-plane stress components in composite laminates, post-processing FEM data obtained with coarse models simplified according to the classical theory of laminates. The described approach relies on radial basis function interpolation and Kansa method to enforce equilibrium in strong form, within a meshless approach. The obtained results successfully compare with those from complete layup modeling for test cases where an analytical solution is available.

Three-dimensional stress analyses of complex laminated shells with a variable-kinematics continuum shell element

This paper presents a new variable-kinematics continuum shell (VKCS) element that can be used to model laminated shell structures with arbitrary geometry in a finite element (FE) setting. The novelty is in the implementation of variable-kinematics capability in a continuum shell formulation, using Carrera’s Unified Formulation (CUF). The resultant model has completely general geometric and kinematic descriptions. In the formulation, the geometrical representation is based on a numerical isoparametric map with no simplifying assumptions on the shell geometry; whereas the element displacement fields are written in terms of the Fundamental Nuclei according to CUF. In the variable-kinematics framework, the levels of hp– and p–refinements in the through-thickness and in-plane domains are free parameters that can be varied independently. By parametrically varying in-plane mesh densities and model kinematics, model settings with good trade-offs in computational cost and desired level of accuracy can be identified. In addition to the existing literature benchmarks, we include new 3D stress benchmarks for laminated shells with complex geometrical features, such as spatially varying curvatures, non-orthogonal coordinate lines and variable thicknesses. The higher-order models yield asymptotically correct three-dimensional stresses, even in regions near singularities, without requiring numerical artefacts nor stress recovery procedures. In terms of computational efficiency, the model variants utilising high p-level require fewer total degrees of freedom (dofs) compared with linear 3D finite element method (FEM) for convergence of the 3D stress field. In terms of wider applications, the compact formulation can allow for the same computer code and model mesh to be used across a wide range of analyses for complex shell structures that requires different model fidelity, with minimal inputs from the user.

Efficient and accurate stress recovery procedure and a posteriori error estimator for the stable generalized/extended finite element method

SummaryThis paper presents a new stress recovery technique for the generalized/extended finite element method (G/XFEM) and for the stable generalized FEM (SGFEM). The recovery procedure is based on a locally weighted L2 projection of raw stresses over element patches; the set of elements sharing a node. Such projection leads to a block‐diagonal system of equations for the recovered stresses. The recovery procedure can be used with GFEM and SGFEM approximations based on any choice of elements and enrichment functions. Here, the focus is on low‐order 2D approximations for linear elastic fracture problems. A procedure for computing recovered stresses at re‐entrant corners of any internal angle is also presented. The proposed stress recovery technique is used to define a Zienkiewicz‐Zhu (ZZ) a posteriori error estimator for the G/XFEM and the SGFEM. The accuracy, computational cost, and convergence rate of recovered stresses together with the quality of the ZZ estimator, including its effectivity index, are demonstrated in problems with smooth and singular solutions.

An equilibrium‐based stress recovery procedure for the VEM

SummaryWithin the framework of the displacement‐based virtual element method (VEM), namely, for plane elasticity, an important topic is the development of optimal techniques for the evaluation of the stress field. In fact, in the classical VEM formulation, the same projection operator used to approximate the strain field (and then evaluate the stiffness matrix) is employed to recover, via constitutive law, the stress field. Considering a first‐order formulation, strains are locally mapped onto constant functions, and stresses are piecewise constant. However, the virtual displacements might engender more complex strain fields for polygons, which are not triangles. This leads to an undesirable loss of information with respect to the underlying virtual stress field. The recovery by compatibility in patches, originally proposed for finite element schemes, is here extended to VEM, aiming at mitigating such an effect. Stresses are recovered by minimizing the complementary energy of patches of elements over an assumed set of equilibrated stress modes. The procedure is simple, efficient, and can be readily implemented in existing codes. Numerical tests confirm the good performance of the proposed technique in terms of accuracy and indicate an increase of convergence rate with respect to the classical approach in many cases.

An improved stress recovery technique for low‐order 3D finite elements

SummaryIn this paper, we propose a stress recovery procedure for low‐order finite elements in 3D. For each finite element, the recovered stress field is obtained by satisfying equilibrium in an average sense and by projecting the directly calculated stress field onto a conveniently chosen space. Compared with existing recovery techniques, the current procedure gives more accurate stress fields, is simpler to implement, and can be applied to different types of elements without further modification. We demonstrate, through a set of examples in linear elasticity, that the recovered stresses converge at a higher rate than that of directly calculated stresses and that, in some cases, the rate of convergence is the same as that of the displacement field.

A cost-effective isogeometric approach for composite plates based on a stress recovery procedure

Abstract This paper introduces a cost-effective strategy to simulate the behavior of laminated plates by means of isogeometric 3D solid elements. Exploiting the high continuity of spline functions and their properties, a proper out-of-plane stress state is recovered from a coarse displacement solution using a post-processing step based on the enforcement of equilibrium in strong form. Appealing results are obtained and the method is shown to be particularly effective on slender composite stacks with a large number of layers. These are indeed the cases where traditional (e.g., “layerwise”) approaches are more computationally heavy and where researchers are more inclined to look for alternatives, making the proposed method a very attractive solution.

Stress recovery from one dimensional models for tapered bi-symmetric thin-walled I beams: Deficiencies in modern engineering tools and procedures

This paper highlights several issues of the procedures nowadays adopted for the recovery of cross-sections stress distribution within tapered thin-walled I beams. In particular, deficiencies are evident even considering bi-symmetric structural elements behaving under the assumption of plane stress. In fact, analytical results available in the literature since the first half of the past century highlight that the continuous variation of the height of a infinite long wedge induces shear stress distributions substantially different from the ones occurring in prismatic beams. Unfortunately, this peculiarity of non-prismatic beams is neglected or treated with coarse approaches by most of the modern engineering tools and procedures, leading to inaccurate descriptions (and also severe underestimations) of the real stress magnitude. After a comprehensive literature review on this specific topic, the paper compares most common stress-recovery procedures with a new, simple, and effective tool derived from a recently proposed non-prismatic planar beam model. The numerical examples reported in the paper highlight that the approaches available in the literature and widely used in practice estimate the parameters of interest for practitioners with errors bigger than 50% leading therefore to unreliable results. Conversely, the herein proposed tool leads to errors smaller than 5% in all the considered cases, paving the way to a new generation of effective tools that practitioners can use for the design of such structural elements.

Equivalent Single Layer, Zig-Zag, and Layer Wise theories for variable angle tow composites based on the Generalized Unified Formulation

Variable Angle Tow (VAT) composites remove the constraint of having straight fibers, typical of traditional composite structures. This dramatically increases the design space and allows a more effective tailoring of the material properties to minimize the weight and increase structural performance. To provide an accurate prediction of the displacement and stress fields in an efficient computational framework, a multi-theory architecture based on the Generalized Unified Formulation (GUF) is proposed. In particular, Equivalent Single Layer, Zig-Zag, and Layer Wise theories with different orders of expansions for the different variables are generated with a theory-invariant mathematical model. This feature allows the user to tailor the computational accuracy and cost to the needs of the case under investigation and is inherently well suited for optimization and reliability problems. For the in-plane discretization, a fourth-order triangular shell element presenting 15 nodes is adopted. The interlaminar displacement continuity is imposed in the finite element assembling in the thickness direction of the layer stiffness matrices, whereas the inter-element displacement compatibility is enforced with the penalty method. This approach allows one to use independent GUF discretization for any desired direction within each element, providing significant versatility (accuracy vs computational time) in the structural modeling. A transverse stress recovery procedure taking into account the variability of the structural properties due to the fibers’ curvilinear paths is also presented. Results are compared with the literature and a commercial software (NX NASTRAN) featuring 3D finite elements.

A posteriori stress and strain recovery procedure for the static analysis of laminated shells resting on nonlinear elastic foundation

Abstract The numerical analysis of laminated composite plates and shells resting on nonlinear elastic foundation is the main topic of the paper. The generalized differential quadrature (GDQ) technique and the Newton-Raphson iteration are employed to obtain the solution of the static problems under consideration. The nonlinear elastic foundation is modeled using the Winkler-Pasternak model embedded with quadratic and cubic nonlinearities in order to a have a more complete description of the interaction. The structural behavior is modeled by means of higher-order displacement fields developed in the framework of a unified formulation. Several lamination schemes are studied. The class of sandwich structures with an inner soft-core is also taken into account with the help of the Murakami’s function, which correctly captures the so-called zig-zag effect. The presented approach can deal with doubly-curved surfaces characterized by two radii of curvature that can vary in each point of the reference domain, whereas most of the examples available in the literature considers only shells with constant curvature, such as spherical and cylindrical shells. Solutions are presented in terms of through-the-thickness variations of strains, stresses, and displacements. For these purposes, a posteriori recovery procedure based on the GDQ method is introduced. The accuracy and effectiveness of the proposed approach are proven by means of the comparison with the numerical results obtained by a three-dimensional finite element model.

Linear static response of nanocomposite plates and shells reinforced by agglomerated carbon nanotubes

Abstract The static response of composite plates and shells reinforced by agglomerated nanoparticles made of Carbon Nanotubes (CNTs) is investigated in the present paper. A two-parameter agglomeration model is taken into account to describe the micromechanics of such particles, which show the tendency to agglomerate into spherical regions when scattered in a polymer matrix. From the macro mechanical point of view, the structures under consideration are characterized by a gradual variation of their mechanical properties along the thickness direction, since various distributions are employed to describe the volume fraction of the reinforcing phase. Several Higher-order Shear Deformation Theories (HSDTs) are taken into account and compared. The fundamental equations which govern the static problem in hand are solved numerically by means of the Generalized Differential Quadrature (GDQ) method. The variation of the agglomeration parameters, as well as the through-the-thickness profiles which describe the CNT volume fraction, are investigated to show the effect of the reinforcing phase on the static response of these nanocomposite plates and shells. In particular, a posteriori stress and strain recovery procedure is developed for these purposes. The current approach is validated through the comparison with the results available in the literature or obtained by a three-dimensional finite element model.

Stress Recovery in Composite Laminates Including Geometrically Nonlinear and Dynamic Effects

Stress recovery based on results from a two-dimensional plate-theory solution is a common method to estimate the transverse stresses in a plate. The development of a stress-recovery procedure is presented that is based directly on plate-theory finite element solutions applicable to situations in which geometrically nonlinear and inertial effects are important. The key reason for employing the stress-recovery procedure is its computational efficiency compared to three-dimensional finite element analyses. The developed procedure is applied to an example flat plate under the influence of dynamic loading. Results from the developed procedure are discussed; they compare well to those from a benchmark three-dimensional finite element solution. The range of applicability of the procedure, considering plate span-to-thickness ratio and degree of nonlinearity, is illustrated. Finally, a discussion is included in which the computational effort to obtain an accurate transverse-stress distribution by the stress-recovery method is compared to that of the benchmark three-dimensional solution.

Inter-laminar stress recovery procedure for doubly-curved, singly-curved, revolution shells with variable radii of curvature and plates using generalized higher-order theories and the local GDQ method

ABSTRACTThe stress and strain recovery procedure already applied for solving doubly-curved structures with variable radii of curvature has been considered in this article using an equivalent single layer approach based on a general higher-order formulation, in which the thickness functions of the in-plane displacement parameters are defined independently from the ones through the shell thickness. The theoretical model considers composite structures in such a way that employs the differential geometry for the description of doubly-curved, singly-curved, revolution with variable radii of curvature and degenerate shells. Furthermore, the structures at hand can be laminated composites made of a general stacking sequence of orthotropic generically oriented plies. The governing static equilibrium equations are solved in their strong form using the local generalized differential quadrature (GDQ) method. Moreover the generalized integral quadrature (GIQ) is exploited for the evaluation of the stress resultants of the model under study. Several numerical applications are presented and the local GDQ results are compared with finite element method (FEM) commercial codes.

Generalized stress–strain recovery formulation applied to functionally graded spherical shells and panels under static loading

The present investigation concludes the triad of papers by the first three authors concerning the 2D-unconstrained third order shear deformation theory for shell-like structures. Here, the static behavior of functionally graded spherical shells and panels subjected to uniform loadings at the extreme surfaces is studied. The material properties are graded in the thickness direction according to a four parameter power law. The structural model involves the a posteriori stress and strain recovery procedure. The obtained governing equations are solved by means of the GDQ numerical technique. An extensive numerical investigation is carried out to characterize the effect of material parameters on the stress, strain and displacement profiles along the thickness direction. The second order equilibrium operators, of the fundamental system of equations for functionally graded spherical shells and panels, are reported in the extended form.

The simulation of crack opening-closing and aggregate interlock behaviour in finite element concrete models

The ability to model crack closure behaviour and aggregate interlock in finite element concrete models is extremely important. Both of these phenomena arise from the same contact mechanisms and the advantages of modelling them in a unified manner are highlighted. An example illustrating the numerical difficulties that arise when abrupt crack closure is modelled is presented and the benefits of smoothing this behaviour are discussed. We present a new crack-plane model that uses an effective contact surface derived directly from experimental data and which is described by a signed-distance function in relative-displacement space. The introduction of a crack-closure transition function into the formulation improves its accuracy and enhances its robustness. The characteristic behaviour of the new smoothed crack-plane model is illustrated for a series of relative-displacement paths. We describe a method for incorporating the model into continuum elements using a crack band approach and address a previously overlooked issue associated with scaling the inelastic shear response of a crack-band. A consistent algorithmic tangent and associated stress recovery procedure are derived. Finally, a series of examples are presented demonstrating that the new model is able to represent a range of cracked concrete behaviour with good accuracy and robustness. This article is protected by copyright.