Stress Space Research Articles

An interfacial damage-plastic model for the simulation of masonry structures under monotonic and cyclic loadings

A damage plasticity based interface constitutive model for simulating complex mixed behaviour of masonry joints is proposed in this paper. To improve the computational efficiency and robustness of the interface model, a novel modelling strategy is adopted to algorithmically decouple the damage and plastic deformations, which are treated separately in two stages. This approach helps to simulate elastic-perfectly-plastic behaviour in effective stress space and provides a non-evolving yield surface in the first stage which significantly improves the convergence of stress return mapping. In the second stage, a separate function is employed to model the evolution of damage used to quantify stress softening. The interface model is implemented within a finite element code used to analyse masonry structures of different scales/sizes under monotonic and cyclic loads. The experimental validation of the simulated results demonstrates good performance of the model in terms of accuracy and robustness. Moreover, the effects of different parameters on the model performance are investigated. One of the key parameters is the degradation of dilation angle incorporated through an energy based evolution function, which is observed to have importance in improving physical response and numerical performance.

Glacially Induced Stress Across the Arctic From the Eemian Interglacial to the Present—Implications for Faulting and Methane Seepage

AbstractStrong compressive and shear stresses generated by glacial loading and unloading have a direct impact on near‐surface geological processes. Glacial stresses are constantly evolving, creating stress perturbations in the lithosphere that extend significant distances away from the ice. In the Arctic, periodic methane seepage and faulting have been recurrently associated with glacial cycles. However, the evolution of the Arctic glacial stress field and its impact on the upper lithosphere have not been investigated. Here, we compute the evolution in space and time of the glacial stresses induced in the Arctic lithosphere by the North American, Eurasian and Greenland ice sheets during the latest glaciation. We use glacial isostatic adjustment (GIA) methodology to investigate the response of spherical, viscoelastic Earth models with varying lithospheric thickness to the ice loads. We find that the GIA‐induced maximum horizontal stress (σH) is compressive in regions characterized by thick ice cover, with magnitudes of 20–25 MPa in Fennoscandia and 35–40 MPa in Greenland at the last glacial maximum. Simultaneously, a tensile regime with σH magnitude down to −16 MPa dominates across the forebulges with a mean of −4 MPa in the Fram Strait. At present time, σH in the Fram Strait remains tensile with an East‐West orientation. The evolution of GIA‐induced stresses from the last glaciation to present could destabilize faults along tensile forebulges, for example, the west‐coast of Svalbard. A more tensile stress regime as during the Last Glacial Maximum would have more impact on pre‐existing faults that favor gas seepage from gas reservoirs.

A Strain Rate‐Dependent Constitutive Model for Asymmetric Hardening Behavior of TB9 Titanium Alloy

The TB9 titanium alloy is one of the most promising materials for engineering application due to high strength, high toughness, and corrosion resistance. Constitutive modeling is an important issue for investigating the materials properties and mechanical behaviors of TB9 titanium alloys using the numerical simulation method. This article presents a pressure‐dependent elastoplastic asymmetric constitutive model that has a high capability of describing the deformation behavior of TB9 titanium alloy. The strain rate sensitivity model of strength differential coefficient evolution is proposed for an accurate simulation of the asymmetric yielding effect. Furthermore, an idea of yield surface plotted in the deviatoric stress space is presented for the decoupling of coupling effect of hydrostatic pressure and lode angle. The validity of this constitutive model is confirmed by comparing the compression stress–strain responses calculated using the proposed model with the experimental observations on TB9 titanium alloy.

STUDY OF THE INFLUENCE OF THE KINETICS OF HYDROGEN SATURATION ON THE STRESS-DEFORMED STATE OF A SPHERICAL SHELL MADE FROM TITANIUM ALLOY

In this paper, a mathematical model is considered that allows one to determine the stress-strain state of a spherical shell made of titanium alloy VT1-0, the external load is assumed to be transverse uniformly distributed, acting on the outer surface, the medium is assumed to act on the inner surface of the shell. For this, a nonlinear model was used, presented in normalized stress spaces. Fastening along the contour of the shell is rigid. Nonlinear resolving equations for calculating a spherical shell are obtained. An algorithm for solving the problem of hydrogenation of titanium alloy shells has been developed. A practical solution was made by a two-step method of sequential perturbations of parameters using the MatLab and Maple software packages. To solve the system of the obtained differential equations, the method of finite differences is applied. The calculation of the stress-strain state of the shell is obtained taking into account the diffusion process of an aggressive hydrogen-containing medium, and the obtained solution is compared with the results of the classical nonlinear theory without taking into account the aggressive medium. The results of comparing these solutions demonstrate quantitative differences in the parameters of the shell deformation process, which are explained by a more accurate account of the influence of the type of stress state. This approach has a rather flexible mechanism for considering the initial and induced differential resistance, demonstrates a high accuracy of matching the obtained theoretical results with empirical data on loading a wide range of materials under complex types of stress state.

Allotropy in ultra high strength materials

Allotropic phase transformations may be driven by the application of stresses in many materials; this has been especially well-documented for pressure driven transformations. Recent advances in strengthening materials allow for the application of very large shear stresses as well – opening up vast new regions of stress space. This means that the stress space is six-dimensional (rather than one for pressure) and that phase transformations depend upon crystal/grain orientation. We propose a novel approach for predicting the role of the entire stress tensor on phase transformations in grains of all orientations in any material. This multiscale approach is density functional theory based and guided by nonlinear elasticity. We focus on stress tensor dependent allotropic phase transformations in iron at high pressure and ultra-fine grained nickel and titanium. The results are quantitatively consistent with a range of experimental observations in these disparate systems. This approach enables the balanced design of high strength-high ductility materials.

An Anisotropic Continuum Damage Mechanics Model for the Simulation of Yield Surface Evolution and Ratcheting

A new anisotropic continuum damage model was presented on the basis of irreversible thermodynamics. Second rank symmetric damage tensor, kinematic hardening tensor, and damage potential surface were introduced. The yield surface in this study has been modeled to distort in the stress space by the evolution of the damage tensor. The new model was applied in yield surface characterization and led to a well description of the subsequent yield surfaces. This model is then applied to predict experimental results of the cyclic nonproportional loading paths obtained by Kang et al. [2004], Hassan et al. [2002] and Taleb and Cailletaud [2011]. It is demonstrated that the new model can predict the yield surface distortion and the ratcheting strains of multiaxial nonproportional cyclic loading with acceptable accuracy and by using less material constants with respect to the previous models.

An undrained expansion solution of cylindrical cavity in SANICLAY for K0-consolidated clays

This paper proposes a rigorous undrained solution for cylindrical cavity expansion problems in K0-consolidated clays, adopting a simple non-associated and anisotropic model, SANICLAY. The cavity expansion theory is well extended to consider non-associativity, K0-consolidation and stress-induced anisotropy with combined rotational and distortional hardening of yield surface and plastic potential in the multiaxial stress space. The developed solution can be recovered for validation against the modified Cam-clay (MCC) solution by simply setting model constants, avoiding non-associativity and anisotropy. The source code is provided to facilitate the use for extensions. After investigating the effects of overconsolidation ratio on the cavity pressure curves, stress distributions, evolutions of anisotropic parameters and stress paths, the variations with three-dimensional (3D) evolutions of yield surface and plastic potential during undrained cavity expansion are shown for various K0-consolidated clays. A parametric study on the model constants is presented to depict the influences on the stress distributions and paths, critical state surfaces and Lode's angles at failure. The proposed solution also provides a general framework for formulating equations for undrained expansion of cylindrical cavities under an initial cross anisotropic condition using sophisticated anisotropic soil models. It serves as a precise benchmark for extensions of analytical solutions, numerical simulations of cavity expansion, and back-calculations of geotechnical problems.

A numerical prediction of failure probability under combined compression-shear loading for unidirectional fiber reinforced composites

Microbuckling (MB) is the dominant failure mode in unidirectional fiber reinforced polymers (FRPs) under predominantly compression loads. MB is highly sensitive to material imperfections and nonlinear material behavior. Material imperfections are spread in the form of fiber misalignment in the volume of the material. Because of high sensitivity of MB failure to the fiber misalignment, the MB strength shows uncertainty. It has been shown in the literature that the nature of the misalignment in FRPs is correlated random, where the misalignment of a fiber depends on the other fibers in its surroundings. To represent the misalignment in numerical models for the prediction of MB strength while preserving the spatial correlation information, the spectral representation method is employed in this investigation. For this purpose spectral densities were calculated for measured distributions of the fiber misalignment using computed tomography scans on specimens. This information was subsequently used to generate realistic distributions of the fiber misalignment in numerical modeling of FRPs for prediction of MB strength. Quantification of uncertainty in MB failure is essential for reliable design practices. Therefore, the current investigation aims for a probabilistic prediction of MB failure under axial compression and combined compression-shear loads. Different model series, each containing a large number of realizations, were developed based on spectral densities calculated from the measurements of the fiber misalignment from different specimens. The resulting distributions of strengths under the axial compression load case from these model series are compared and a suitable model series was chosen for further analysis. The stress–strain response under different combinations of combined compression-shear loads is discussed. A comparison of numerically predicted strengths against experimentally obtained results under the axial compression loads is included. Since the sizes of the model and the experimental specimen were different, this comparison was performed on the basis of a scaling law for the compression strength. Finally, the numerically determined probabilistic failure envelopes in stress and strain spaces are presented with lower percentiles of distributions of failure. The failure enveloped are also compared against classical failure criteria from the literature to highlight the limitations of the classical criteria.

The mechanical response of commercially pure copper under multiaxial loading at low and high strain rates

In this paper, we present the dynamic response of commercially pure copper subjected to combined tension-torsion loads representative of real case impact scenarios. Experiments were conducted both quasi statically, at a strain rate equal to 10−3 s−1, and dynamically at strain rates in the region between 500 s−1 and 1000 s−1. All high rate experiments were conducted using a novel Split Hopkinson Tension-Torsion Bar instrumented with high-speed photographic equipment. The dynamic combined loading experiments demonstrate the capability of the apparatus to generate longitudinal and torsional stress waves which are synchronised upon loading of the specimen. The presented data show that dynamic equilibrium conditions and nearly steady strain rates were achieved during the experiments. Additionally, the analyses of the loading paths show that nearly proportional strain loading was attained during testing.The measured experimental results illustrate, for the first time, the failure stress locus of the material over a wide range of stress states including pure torsion, shear-dominated combined tension-shear, tension-dominated combined tension-shear and plain tension. The quasi-static and dynamic failure envelopes are herein presented in the normal stress vs shear stress space to motivate the development of accurate and effective constitutive models. To conclude, the Drucker-Prager criterion was employed to approximate the failure loci and to assess the rate sensitivity of the material. A moderate asymmetry of the uniaxial ultimate stresses in tension and compression is predicted both at quasi-static and dynamic strain rates.

Non-Quadratic Pseudo Dual Potentials for Plastic Flow Modeling

The existence of dual flow potentials is well established in mathematical theory of plasticity since the seminal work by Hill in 1987. For a metal undergoing plastic flow, a flow stress potential is used to compute its plastic strain increments when the applied yield stress is known. On the other hand, the corresponding dual flow strain-rate potential is used to compute the stress on the flow surface when the plastic strain increments are given. This work examines some issues associated with plasticity modeling using non-quadratic dual flow potentials. Unlike the quadratic case where flow stress and strain-rate potentials are the exact dual to each other, it is often difficult if not impossible to obtain analytically the dual of a non-quadratic flow stress or strain-rate potential. The study instead focuses on formulating and assessing various non-quadratic pseudo dual flow potentials that approximate the actual flow surfaces in either stress or strain-rate space. The difference and connection between the yield surface and flow surface in non-associated plasticity are also investigated. Although only one of the dual flow potentials is actually needed for their applications in associated and non-associated plasticity modeling, the unique advantage of having both dual flow potentials on hand even in their pseudo forms is pointed out for new computational analyses.

Isotropic and anisotropic elasto-plastic coupling in clays: a thermodynamic approach

In many solids, like soils and rocks, the elastic behaviour exhibited for very small stress/strain perturbations often depends on the previously experienced plastic dissipative processes: this is commonly referred to as elasto-plastic coupling. In this paper, this phenomenon is examined in a thermodynamic-based constitutive modelling perspective.Within the framework of hyperplasticity theory, a new formulation considering isotropic and rotational hardening is proposed to illustrate two forms of isotropic and anisotropic elasto-plastic coupling for clays. The thermodynamic approach allows some specific features of the phenomenon to be highlighted in more detail as compared to what conventionally derived from the elasto-plasticity theory, with particular reference to the effects of coupling on the yield domain in the Cauchy stress space and the resulting non-associated flow rules.The predictive capability of the model is illustrated with reference to a series of numerical simulations of real and ideal laboratory tests on reconstituted clays.

Optimal Data-Generation Strategy for Machine Learning Yield Functions in Anisotropic Plasticity

Trained machine learning (ML) algorithms can serve as numerically efficient surrogate models of sophisticated but numerically expensive constitutive models of material behavior. In the field of plasticity, ML yield functions have been proposed that serve as the basis of a constitutive model for plastic material behavior. If the training data for such ML flow rules is gained by micromechanical models, the training procedure can be considered as a homogenization method that captures essential information of microstructure-property relationships of a given material. However, generating training data with micromechanical methods, as for example, the crystal plasticity finite element method, is a numerically challenging task. Hence, in this work, it is investigated how an optimal data-generation strategy for the training of a ML model can be established that produces reliable and accurate ML yield functions with the least possible effort. It is shown that even for materials with a significant plastic anisotropy, as polycrystals with a pronounced Goss texture, 300 data points representing the yield locus of the material in stress space, are sufficient to train the ML yield function successfully. Furthermore, it is demonstrated how data-oriented flow rules can be used in standard finite element analysis.

Calibration of the PA6 Short-Fiber Reinforced Material Model for 10% to 30% Carbon Mass Fraction Mechanical Characteristic Prediction.

Short-fiber reinforced composites are widely used for the mass production of high-resistance products with complex shapes. Efficient structural design requires consideration of plasticity and anisotropy. This paper presents a method for the calibration of a general material model for stress–strain curve prediction for short-fiber reinforced composites with different fiber mass fractions. A Mori–Tanaka homogenization scheme and the J2 plasticity model with layered defined fiber orientation were used. The hardening laws: power, exponential, and exponential and linear were compared. The models were calibrated using experimental results for melt front, orientation tensor analysis, fiber length, and diameter and tension according to ISO 527-2, for samples of PA6 which were either non-reinforced, or reinforced with 10%, 15%, 20%, and 30% carbon fiber mass fractions. The novelty of this study lies in the transition from the strain–stress space to the strain–stress–fiber fraction space in the approximation of the material model parameters. We found it necessary to significantly reduce the fiber aspect ratio for the correct prediction of the mechanical characteristics of a composite using the Mori–Tanaka scheme. This deviation was caused by the ideal solution of ellipsoidal inclusion in this homogenization scheme. The calculated strength limits using Tsai–Hill failure criteria, based on strain, could be used as a first approximation for failure prediction.

Hydroponic Technique: A New approach for Crop Production at Trans Himalayan High-altitude Cold Desert Regions of India

Aims: The trans-Himalayan high-altitude cold desert regions of India is characterized by a rugged topography at an altitude ranging from 2550 to 7742 meters above sea level. It has a vast geographical area of 72976 km2 with very little cultivated area of about 13726 hectare. Hydroponic is a soilless cultivation technique which may produce fresh vegetable in areas where environmental stress (cold, heat, dessert etc.) and limited space or on non-arable land is a major constrains for agriculture production.
 Methodology: The experiment was conducted under open natural ventilated double layer polycarbonate green house in cold desert high altitude conditions of Leh, India. The hydroponic structures were designed for crop production (viz. leafy greens, vegetables, fruits etc) in deep water culture (DWC) and nutrient film technique (NFT) hydroponic techniques and compared them with conventional soil grown system. Nutrient solution for growing vegetables was prepared and standardized.
 Results: The result obtained has shown that crop yield was significantly higher in hydroponic system as compared to traditional system for all crops. The recorded increase in yield for various crops in hydroponic system compared to soil grown system were: arugula 221%, atriplex 248%, coriander 288%, fenugreek 208%, lettuce 293%, mint 237%, mustard 227%, spinach 294%, cucumber 533%, strawberry 280%, summer squash 229% and tomato 345% which were significantly higher. Hydroponics can be explored to grow vegetables round the year especially for leafy greens. The hydroponic systems may come out as a valuable asset to forward and remote area of trans-Himalayan region for growing fresh vegetables where cultivated land and availability of the water are the limiting factors for crop production.

Experimental determination of a probabilistic failure envelope for carbon fiber reinforced polymers under combined compression–shear loads

The compressive strength of fiber reinforced composites is sensitive to material imperfections. Material imperfections are spread in the volume in an apparently random manner in the form of fiber misalignment, resulting in non-deterministic strength in compression dominated load cases. The main factors dictating failure under compression dominated loads are the fiber misalignment and the nonlinear material behavior. To enable reliable failure prediction, a quantification of the strength uncertainty is required. Therefore, the current investigation considers different experimental aspects of the problem such as measurements of the fiber misalignment and the material characterization. To implement combined compression–shear loading, a newly in-house developed combined loading fixture was used. A statistically significant number of specimens was tested under aforementioned load cases. Macroscopic images of the failed specimens and a micrograph of the fracture surface are shown to provide evidence of microbuckling failure mode under combined compression–shear loads. Using the experimental strain measurements, a probabilistic failure envelope in strain space is presented. Results of the axial compression load case are interpreted in the context of the notion of the effective misalignment angle using an analytical model. A failure envelope in stress space is derived using an analytical solution for the combined compression–shear load cases and the effective global misalignment angle calculated from the measurements. Applied far field stresses of different load cases are compared, and a visual depiction of the strain localization phenomenon leading to microbuckling failure using digital image correlation is presented.

Critical dynamic stress for the frozen subgrade soil

Triaxial dynamic tests at the temperature −6 °C were performed on frozen subgrade soil to study accumulative deformation and resilient deformation properties. Based on the shakedown theory, a reliable evaluation for the long-term serviceability of the frozen subgrade was further presented. The influences of confining pressure, dynamic stress amplitude, initial stress path and initial stress ratio on dynamic properties of frozen subgrade soil were analysed. The evolution features of accumulative permanent strain under cyclic loading were experimentally determinated. The boundary functions for plastic shakedown area and plastic creep area were further established. Critical dynamic stresses for the different deformation areas can be calculated by the experimental data and the proposal formula. The influences of consolidation pressure and initial stress ratio on critical dynamic stress were discussed in detail. The distribution characteristics (envelope line loci) of the critical dynamic stress were investigated in the mean stress-the shear stress space.

Shear Behaviour of Aeolian Sand with Different Density and Confining Pressure

Different from the other roadbed material, the unique mechanical properties of aeolian sand bring great difficulties to the construction and maintenance of desert highways. However, the main attention was usually paid to the engineering properties of aeolian sand, such as collapsibility, strong permeability, and poor gradation. To investigate the shear behaviour of aeolian sand under different engineering conditions, the drained and undrained tests were performed on aeolian sand with relatively large range of density and confining pressure. Under this condition, both the drained and undrained tests tend to the same critical state line, and the shear behaviour of aeolian sand is directly dependent on its density. Under the undrained condition, the q-ε1 curves and the effective stress paths in triaxial stress space exhibit four types of undrained shear behaviour, such as flow, limited flow, strain hardening, and strain softening. Meanwhile all the specimens exhibit three types of failure, such as flow slip, bulging failure, and shear bands. In the q-p’ plane, the analogous drained and undrained stress paths can be followed by aeolian sand with same initial relative density but different confining pressures, and there are two critical state lines due to the generation of shear bands for dense sand. In addition, the critical state lines in e-lnp’ plane decrease with increasing initial relative density Dr, that is, the material constant eᴦ decreases with increasing Dr, and the λ is also not constant but decreases with the increase in Dr. The results suggest that the strength behaviours of aeolian sand can be fitted by a straight line considering relative density and confining pressure and that two empirical formulas are established to describe this feature.

Multiyield-Surface Implementation of a Simplified Three-Dimensional Hoek–Brown Strength Criterion

This work presents the implementation of a simplified three-dimensional Hoek–Brown strength criterion using a multiyield-surface plasticity approach. The adopted three-dimensional simplification of the strength criterion accounts for the intermediate principal stress influence, maintaining the simplicity in the numerical implementation. This criterion corresponds to a paraboloid surface of circular cross section in the principal stress space. The introduction of multiple yield surfaces allows for a smooth definition of the nonlinear stress–strain behavior of the material. In addition, a kinematic hardening rule is adopted, allowing yield surfaces to translate with loading, enabling a hysteretic and path-dependent stress–strain response.

Split stress rate plasticity formulation

A novel general constitutive formulation framework of rate independent plasticity is presented where the stress rate tensor is split in two components, and plastic loading is affected separately by each one of these two components in relation to a common loading direction normal to a single smooth yield surface in stress space. This split-stress rate separate effect provides greater flexibility for simulating the material response under combined stress rate components loading. The difficulty arises when loading and unloading events may occur interchangeably between the two stress rate components and special attention is required to avoid irrational results and guarantee continuity of response upon rotation of the total stress rate direction at a loading stress point. The formulation can acquire two different analytical schemes, one more complicated but incrementally linear, while the other is simpler but incrementally nonlinear. The key constitutive ingredient of split stress rate definition is a multifaceted choice, and three options are presented. One option which is of particular interest to granular mechanics, splits the stress rate into a component that changes the stress principal values at fixed principal axes, while the other component does exactly the opposite, i.e., rotates the stress principal axes at fixed principal values. For this option various constitutive ingredients and new concepts are introduced and extensively elaborated, with emphasis on dilatancy, understanding that these elaborations are of an exploratory nature intending to prompt further research along the proposed guidelines.

A computational multiscale model for anisotropic failure of sheet molding compound composites

We present a holistic multiscale approach for constructing anisotropic criteria describing the macroscopic failure of sheet molding compound composites based on full-field simulations of microscale damage evolution. We use an anisotropic damage model on the microscale that directly operates on the compliance tensor, captures matrix and bundle damage via dedicated stress-based damage criteria and allows for a comparison of simulation and experimental results. To identify the damage material-parameters used in the non-linear and time-consuming full-field simulations, we utilize Bayesian optimization with Gaussian processes. We validate the full-field predictions on the microscale and subsequently identify macroscopic failure criteria based on distributions taken from experimental findings. We propose failure surfaces in stress space and stiffness-reduction triggered failure surfaces to cover both a structural analysis and a design process perspective.