Monotonic Paths Research Articles

A plastic-damage cohesive zone model for shear rupture band in geomaterials under mixed-mode and cyclic loading

The characterization of the mechanical behavior of the shear rupture band is essential to the analysis of the strain localization failure of geotechnical structures, with a key focus on describing the plastic-damage behavior and dilatancy of the geomaterial. A novel plastic-damage cohesive zone model is presented based on the unified plastic-damage modeling framework, in which an enhanced dilatancy angle evolution law is put forward to capture the dilatancy, and the yield function and the dissipation potential function are proposed to account for the tension/compression-shear coupling effect. The capability of the proposed model is demonstrated by its constitutive responses under several typical monotonic and cyclic loading paths, and further validated by simulating three laboratory tests of rock joint and silt-steel interface. The notable agreement between the simulation results and their experimental counterparts illustrates the effectiveness of the proposed model in characterizing the mechanical behavior of the shear rupture band under mixed-mode and cyclic loading conditions, including post-peak hardening/softening, plastic-damage behavior, and hysteresis.

Shear response of iron ore tailings under monotonic loadings

Dry stacking is a disposition method that is quickly becoming a trend for the mining industry in Brazil. With several cases in which compacted mine tailings are positioned on the top of hydraulically disposed tailings which were placed into pits. The present research assessed the mechanical response of hydraulically disposed iron ore tailings collected from a pit that was formerly a mining site. To better understand the mechanical behaviour of mine tailings under such conditions, the investigation of their monotonic response is of great importance. The studied material was classified as a silty sand with traces of clay size. A very loose condition with distinct confining stresses was tested monotonically on a simple shear equipment. Simple shear tests were performed in an apparatus that can directly measure pore pressure, guaranteeing an effective stresses analysis. A plane strain condition was applied on fully saturated samples under undrained loading conditions. Results showed the agreement of the strength envelopes of monotonic stress paths, the effective friction angle of the material was 33.2° and no cohesive intercept.

The high-cyclic model for sand tested beyond the usual ranges of application

The high-cycle accumulation (HCA) model proposed by Niemunis et al. (Comput Geotech 32(4):245–263, 2005) predicts permanent deformations due cyclic loading with many small cycles (i.e. N≥104\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$N \\ge 10^4$$\\end{document} cycles of strain amplitudes εampl≤10-3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\varepsilon }^{{\\rm ampl}}\\le 10^{-3}$$\\end{document}). In the presented tests, the pressure range pav\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$p^{{\\rm av}}$$\\end{document} is extended from 3 to 9 bar; the influence of the void ratio e∈(0.72,0.95)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$e \\in (0.72, 0.95)$$\\end{document} and amplitudes of strains εampl∈(0.1%,1%)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varepsilon ^{{\\rm ampl}} \\in (0.1{\\%}, 1{\\%})$$\\end{document} is tested in the extended range. Some empirical HCA functions could be confirmed and some require modifications. An interesting qualitative controversy pertains to the direction of circulation in the P–Q-plane for a validation of the polarization function fπ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f_\\pi $$\\end{document}, which does influence the rate of accumulation contrarily to the HCA assumption. The previous assumption that ε˙acc\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\dot{\\varepsilon }^{{{\\rm acc}}}$$\\end{document} remains constant above a certain pressure level, i.e. is independent of pav\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$p^{{{\\rm av}}}$$\\end{document}, was experimentally refuted. Investigations on the cyclic preloading (f˙N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\dot{f}_N$$\\end{document}) using 21 cyclic triaxial tests with varried monotonic strain paths between the cycle packages found a relationship of the direction of the monotonic strain path and the capacity to reduce cyclic preloading. This study’s findings deepen the understanding of how cyclic preloading is reduced, but the tests also highlight the need for future research in the area.

A standard thermodynamic-based extension of the Modified Cam-Clay soil model and its applications

For mechanical behaviours of granular soils considered here (sands, silts and stiff clays), we propose a thermodynamic-based formulation which relies on the Modified Cam-Clay constitutive model. To this end, and in the framework of Generalized Standard Materials (GSM) framework, we introduce a free energy and a yield criterion (or equivalently a dissipation potential) which account for an isotropic nonlinear elastic behaviour and a volumetric hardening law. Based on available works with coupled hardening laws for von Mises plasticity, we propose for pressure-sensitive materials a new nonlinear deviatoric hardening preserving the well-known critical state existence.Taking advantage of the GSM framework, we establish an incremental variational formulation of the model whose solution obeys to a minimization principle. This has required an approximation of the incremental dissipation. The resulting equations are detailed for the use of an implicit resolution scheme with a standard Newton–Raphson algorithm. The constitutive model parameters are calibrated on a pool of experimental data on isotropic, shearing and triaxial tests on loose sand specimen. The investigations of the model responses allow to better predict the nonlinear regimes of soils specimen on monotonic and cyclic loading paths. Numerical finite element simulations finally underline the predictive capabilities of the model on structures.

SANISAND-H: A sand bounding surface model for high pressures

This paper presents a new bounding surface constitutive model for sand, named SANISAND-H, capable of predicting the shear and volumetric behavior of the material under extra-high range of pressures, in addition to normal pressures. The model is an extension of the SANISAND08 model (Taiebat and Dafalias, 2008) with a closed cone-type yield surface that obeys rotational and isotropic hardening. The critical state line and the limiting isotropic compression curve of the SANISAND08 model are modified to accommodate a wide range of pressures. A new constitutive ingredient is the definition of a reference compression curve that serves as bounding surface for establishing the isotropic hardening rule of the yield surface. The kinematic hardening rule and stress-dilatancy relationship of the SANISAND08 model are significantly modified, to better capture the response of sands under high pressure. The value of the back stress ratio at the initiation of a new loading process is re-introduced, ensuring a smooth elastic-plastic transition necessary for accurate simulation of the response under loading reversals. The SANISAND-H model simulations are in very good agreement with test data for Toyoura and Cambria sands under various drained and undrained monotonic stress loading paths in a wide range of densities and pressures.

Continuum damage mechanics-based finite-volume homogenization of unidirectional elastoplastic fiber-reinforced composites

The Finite-Volume Direct Averaging Micromechanics (FVDAM) method has been further extended to predict nonlinear behaviors of unidirectional boron/aluminum (B/Al) composites, induced by plastic deformation and ductile damage for the first time. The latter is considered by gradual stiffness degradation via the continuum damage mechanics (CDM) model. The convergence of homogenized and local response generated by the new FVDAM damage framework has been demonstrated by considering the hexagonal and square repeating unit cells (RUC) with different mesh discretizations under transverse tensile, transverse shear and axial shear loading paths. Then, the reliability of the developed approach to predict the nonlinear response of B/Al composites has been verified extensively vis-à-vis the experimental response available in the literature, under monotonic loading path with various off-axis angles. To accurately capture the experimental response, an RUC with actual microstructure characterized by a random fiber distribution is constructed and utilized in the numerical simulations. In addition, the developed model is also applied to predict the cyclic response of B/Al composites with different off-axis angles in further support of the theory’s potential to capture the macroscopic behaviors of B/Al composites under complex loading conditions.

Instrumented indentation for determining stress and strain levels of pre-strained DC01 sheets

In classical mechanical testing, determining the stress and strain states of complex shape specimens turns out to be very challenging, especially in the most deformed regions. In the latter case, when not enough material is present, non-destructive testing is needed for determining the corresponding mechanical state. In this study, a novel approach, based on the local quasi-non-destructive instrumented indentation technique (IIT) coupled with the inverse analysis technique (IAT), is used to determine the stress and strain levels of pre-strained DC01 specimens using monotonic and non-monotonic loading paths. Monotonic and cyclic shear tests as well as Marciniak tests, in both plane and equi-biaxial strain states, are used to apply different pre-strain levels. For monotonic loading paths, i.e. monotonic shearing and Marcianiak tests, the applied methodology showed very satisfying results in determining the stress and strain states of the pre-strained specimens, especially for pre-strain values close to the representative indentation strain values. A maximum stress error of less than 15% was obtained in the case of the highest applied pre-strain value (29.04%). The purely isotropic Voce hardening law was adopted for determining the hardening behavior of the studied specimens in both cases: as-received and pre-strained. In the case of cyclic shear, a mixed isotropic-kinematic hardening law is to be used to determine the stress and strain states of the pre-strained specimens. Adopting a mixed isotropic-kinematic Chaboche hardening law led to satisfying results where the estimation errors of the applied pre-strain value and corresponding yield stress didn't exceed 6% and 1.3%, respectively. The obtained results show that the proposed indentation-based method can be very useful in estimating the work-hardening level and corresponding plastic deformation of pre-strained parts under various loading paths

Evolving asymmetric and anisotropic hardening of CP-Ti sheets under monotonic and reverse loading: Characterization and modeling

Commercially pure titanium (CP-Ti) sheets are promising to manufacture high-performance and lightweight components in many fields such as aerospace, marine, energy, electrics and healthcare. However, due to its low symmetric hexagonal close-packed (HCP) structure and complex thermal-mechanical processing history, CP-Ti sheets may exhibit significant asymmetry and anisotropy under monotonic and reverse loading. Therefore, the coupling effect of loading-path dependent asymmetric and anisotropic hardening behaviors of CP-Ti sheets need to be systemically characterized and accurately described under monotonic and reverse loading paths. In this study, firstly, the rheological tests were performed to systemically explore the evolving asymmetric and anisotropic hardening behavior of CP-Ti sheet under monotonic and reverse loading modes. With the help of anti-buckling support fixture and DIC system in tension and compression tests, the coupling effect of asymmetric and anisotropic hardening under monotonic and reverse loading of CP-Ti sheet was identified. Secondly, a loading-path dependent constitutive modeling framework was constructed in which the stress invariants-based model (SIM) integrated with distorted hardening (DH) under reverse loading (RL) conditions (SIM+DH+RL) were considered. Within the proposed modeling framework, a judging criterion of stress reversal for explicit solution method and an activation criterion of different reverse loading modes were introduced. Finally, the proposed SIM+DH+RL model was implemented, calibrated and further applied to simulate typical V-/U-bending of CP-Ti sheets. The results show that the proposed SIM+DH+RL model can significantly improve the prediction accuracy of V-/U-bending springback with the relative errors less than 7.8% and 2.1%, compared with 15.2% and 12% relative errors of Mises+IH, 19.5% and 7.3% relative errors of SIM+DH, 15.1% and 8.4% relative errors of Yoon2014+IH, 14.5% and 5.2% relative errors of CPB06+IH, and 17.3% and 11.5% relative errors of Hill48+IH. It is noted that for the thickness distributions after V-/U-bending springback, the above used models have similar prediction accuracies with the relative errors less than 1.8%.

The Hardest Hamiltonian Cycle Problem Instances: The Plateau of Yes and the Cliff of No

We use two evolutionary algorithms to make hard instances of the Hamiltonian cycle problem. Hardness (or ‘fitness’), is defined as the number of recursions required by Vandegriend–Culberson, the best known exact backtracking algorithm for the problem. The hardest instances, all non-Hamiltonian, display a high degree of regularity and scalability across graph sizes. These graphs are found multiple times through independent runs, and by both evolutionary algorithms, suggesting the search space might contain monotonic paths towards the global maximum. For Hamiltonian-bound evolution, some hard graphs were found, but convergence is much less consistent. In this extended paper, we survey the neighbourhoods of both the hardest yes- and no-instances produced by the evolutionary algorithms. Results show that the hardest no-instance resides on top of a steep cliff, while the hardest yes-instance turns out to be part of a plateau of 27 equally hard instances. While definitive answers are far away, the results provide a lot of insight in the Hamiltonian cycle problem’s state space.

Collaborative multicenter reverse logistics network design with dynamic customer demands

The vehicle routing problem for waste recycling has been created to improve resource utilization and reduce environmental pollution as a result of the rapid consumption of natural resources and the negative impact of waste on the environment. This study investigates a collaborative multicenter vehicle routing problem with time windows and dynamic customer demands. The collaboration among logistics facilities is an effective mechanism to reduce the number of vehicles and improve resource utilization in a multicenter reverse logistics network. A multi-objective mathematical programming model is proposed to coordinate static and dynamic customer demands while minimizing the total operating cost, the number of vehicles, and the total waiting time. A hybrid heuristic algorithm comprising an improved k-medoids clustering algorithm and an extended reference point-based non-dominated genetic algorithm- III, is designed to solve the multi-objective optimization model. The clustering algorithm is implemented to reduce the network complexity. The extended reference point-based non-dominated genetic algorithm- III with a dynamic insertion strategy is proposed to adjust service routes for dynamic customer demands and find the Pareto optimal solution for the multi-objective optimization model. The performance of the proposed algorithm is evaluated, and results suggest that the extended reference point-based non-dominated genetic algorithm- III has superior solutions in solving the collaborative multicenter vehicle routing problem with time windows and dynamic customer demands compared with other algorithms. The cost savings resulting from optimization are fairly distributed among participants in a collaborative alliance via the minimum cost remaining savings and principle of strictly monotonic path selection. The proposed methods are applied in a case study of a realistic reverse logistics network in Chongqing City, China. Different service periods and optimization strategies are discussed and compared to verify the effectiveness of the proposed solution methods. The optimization results indicate that the collaborative mechanism and dynamic insertion strategy can improve resource utilization and transportation efficiency and contribute to a sustainable urban logistics transportation system.

Consequences of large strain anisotropic work-hardening in cold forging

The influence of anisotropic work-hardening on the component properties and process forces in cold forging is investigated. The focus is on the material behaviour exhibited after strain path reversals. The work-hardening of three steels is characterized for large monotonic strains (equivalent strains up to 1.7) and subsequent strain path reversals (accumulated strains up to 2.5). Tensile tests on specimens extracted from rods forward extruded at room temperature reveal an almost linear work-hardening for all investigated steels. The application of compressive tests on extruded material gives insights into the non-monotonic work-hardening behaviour. All previously reported anisotropic work-hardening phenomena such as the Bauschinger effect, work-hardening stagnation and permanent softening are present for all investigated steels and intensify with the pre-strain. Experimental results of 16MnCrS5 were utilized to select constitutive models of increasing complexity regarding their capability to capture anisotropic work-hardening. The best fit between experimental and numerical data was obtained by implementation of a modified Yoshida-Uemori model, which is able to capture all observed anisotropic work-hardening phenomena. The constitutive models were applied in simulations of single- and multi-stage cold forming processes, revealing the significant effect of anisotropic hardening on the predicted component properties and process forces, originating in the process-intrinsic strain path reversals as well as in strain path reversals between subsequent forming stages. Selected results were validated experimentally.

Two-Echelon Multidepot Logistics Network Design with Resource Sharing

Resource sharing within a logistics network offers an effective way to solve problems resulting from inefficient and costly operations of individual logistics facilities. However, the existing analysis of resource sharing and profit allocation is still limited. Therefore, this study aims to model resource sharing in two-echelon delivery and pickup logistics networks to improve the overall efficiency and decrease the total network operating cost. A bi-objective integer programming model is first proposed for two-echelon collaborative multidepot pickup and delivery problems with time windows (2E-CMDPDTW) to seek the minimization of operating costs and number of vehicles. Integrating a customer clustering algorithm, a greedy algorithm, and an improved nondominated sorting genetic algorithm-II (Im-NSGA-II), a hybrid method is then designed to handle the 2E-CMDPDTW model. The customer clustering and the greedy algorithms are employed to generate locally optimized initial solutions to accelerate the calculating velocity and guarantee the diversity of feasible solutions. The Im-NSGA-II combines the order crossover operation and the polynomial mutation process to find the optimal solution of the 2E-CMDPDTW. The comparative results show that the proposed hybrid method outperforms the NSGA-II and the multiobjective genetic algorithm. Furthermore, a Shapley value method is used for allocating total profits of established alliances and finding an optimal coalition sequence of the logistics facilities joining alliances based on the strictly monotonic path strategy. Finally, a case study of 2E-CMDPDTW in Chongqing China is conducted to validate the feasibility. Results indicate that this study contributes to long-term partnerships between logistics facilities within multi-echelon logistics networks in practice and contributes to the long-term sustainability of urban logistics pickup and delivery networks’ development.

A combined intelligent and game theoretical methodology for collaborative multicenter pickup and delivery problems with time window assignment

Collaborative multicenter pickup and delivery problems with time window assignment (CMPDPTWA) are introduced in this paper and formulated and solved as a two-stage optimization problem. First, the collaborative mechanism achieves optimal transportation resource configuration in a multicenter logistics network. Second, open-closed mixed pickup and delivery routes satisfying the demands and time windows of customers are proposed to enhance transportation efficiency and reduce the total logistics operating cost. A set of candidate-time windows is assigned to the corresponding customers through time window assignment (TWA) strategy to increase the operational efficiency of logistics network. A bi-objective programming model for CMPDPTWA is formulated to minimize the number of vehicles and total operating cost. An improved k-means clustering algorithm is used to cluster customers according to their proximities to pickup and delivery centers for reducing the computational complexity to solve the abovementioned problem. A self-learning non-dominated sorting genetic algorithm-II (SNSGA-II) is proposed to optimize the open-closed mixed pickup and delivery routes in CMPDPTWA. An update mechanism for the probabilities of crossover and mutation is devised to improve the efficiency of searching the solution space, and thus to accelerate the convergence of SNSGA-II. The performance of the proposed algorithm is compared with that of other algorithms, and the results indicate that it can generate near-optimal solutions for CMPDPTWA. A game theoretical method involving a cost gap allocation model and the strictly monotonic path strategy is proposed to find the best profit allocation scheme and the optimal coalition sequence for stabilizing the collaborative coalition. Finally, the proposed method is applied to a case study using the real-world logistics network in Chongqing City, China. Six scenarios with and without the collaborative mechanism and TWA strategy are simulated and compared with one another to verify the efficacy of the proposed method. The results show that the collaborative mechanism and TWA strategy can improve the utilization of transportation resources and operational efficiency. Thus, they can facilitate an efficient and sustainable urban logistics network.

Enumeration of coalescent histories for caterpillar species trees and p-pseudocaterpillar gene trees

For a fixed set X containing n taxon labels, an ordered pair consisting of a gene tree topology G and a species tree topology S bijectively labeled with the labels of X possesses a set of coalescent histories—mappings from the set of internal nodes of G to the set of edges of S describing possible lists of edges in S on which the coalescences in G take place. Enumerations of coalescent histories for gene trees and species trees have produced suggestive results regarding the pairs (G,S) that, for a fixed n, have the largest number of coalescent histories. We define a class of 2-cherry binary tree topologies that we term p-pseudocaterpillars, examining coalescent histories for non-matching pairs (G,S) in the case in which S has a caterpillar shape and G has a p-pseudocaterpillar shape. Using a construction that associates coalescent histories for (G,S) with a class of “roadblocked” monotonic paths, we identify the p-pseudocaterpillar labeled gene tree topology that, for a fixed caterpillar labeled species tree topology, gives rise to the largest number of coalescent histories. The shape that maximizes the number of coalescent histories places the “second” cherry of the p-pseudocaterpillar equidistantly from the root of the “first” cherry and from the tree root. A symmetry in the numbers of coalescent histories for p-pseudocaterpillar gene trees and caterpillar species trees is seen to exist around the maximizing value of the parameter p. The results provide insight into the factors that influence the number of coalescent histories possible for a given gene tree and species tree.

Reliability modeling of the bivariate deteriorating product with both monotonic and non-monotonic degradation paths

Fiber optical gyroscope (FOG) is a highly reliable navigation element, and the degradation trajectories of its two accuracy indexes are monotonic and non-monotonic respectively. In this paper, a flexible accelerated degradation testing (ADT) model is used for analyzing the bivariate dependent degradation process of FOG. The time-varying copulas are employed to consider the dynamic dependency structure between two marginal degradation processes as the Wiener process and the inverse Gaussian process. The statistical inference is implemented by utilizing an inference function for the margins (IFM) approach. It is demonstrated that the proposed method is powerful in modeling the joint distribution with various margins.

Exploring Multiple Analog Placements With Partial-Monotonic Current Paths and Symmetry Constraints Using PCP-SP

Modern analog placement techniques require consideration of current path and symmetry constraints. The symmetry pairs can be efficiently packed using the symmetry island configurations, but not all these configurations result in minimum gate interconnection, which can impact the overall circuit routing and performance. This article proposes the first work that reformulates this problem considering all of them together in the form of parallel current path (PCP) constraints. PCP constraints, in addition to monotonic current paths, also consider partial-monotonic current paths to generate a more compact placement. We use a novel two-step approach to detect symmetry-feasible sequence-pairs (SFSPs) without doing placement construction by using representative sequence-pair (RSP). Then a placement algorithm satisfying these constraints is formulated to reduce a vast search space via efficient sequence pair manipulation. The experimental results show that this formulation and algorithm can generate multiple placement solutions that satisfy all the constraints in a more tightly packed configuration, resulting in smaller wirelength, reduced parasitics, and thus better post-layout performance.

Two-echelon collaborative multi-depot multi-period vehicle routing problem

Collaboration among logistics operators offers an effective way to improve customer service and freight transportation efficiency. One form of collaboration is the sharing of logistics resources (e.g., delivery vehicles). Existing studies on collaboration and resource sharing have not sufficiently accounted for the time frame within which collaboration happens, and they mostly assume that collaboration among logistics operators occurs in a single time period. This study addresses the issue of collaboration across multiple time periods, in which logistics resources can be shared between different service time periods, by formulating and solving a two-echelon collaborative multi-depot multi-period vehicle routing problem (2E-CMDPVRP). The 2E-CMDPVRP is formulated as a multi-objective integer programming model that minimizes logistics operational costs, service waiting times, and number of vehicles in multiple service periods. A hybrid heuristic algorithm with three-dimensional k-means clustering and improved reference point-based non-dominated sorting genetic algorithm-III (IR-NSGA-III) is proposed to solve the multi-objective optimization model. Comparative analysis results show that the proposed IR-NSGA-III outperforms existing algorithms in terms of the minimization of logistics operational costs, service waiting times, and number of vehicles. The minimum costs remaining saving method and strictly monotonic path selection principle are combined to determine the best profit allocation schemes and the optimal coalition sequences. An empirical case study of a multi-depot multi-period logistics network in Chongqing, China, is used to validate the proposed model and solution algorithm. Results suggest that the proposed collaborative mechanism with multi-depot and multi-period resource sharing can improve the degree of synchronization within a collaborative logistics network, and thus contribute to sustainable development of urban logistics distribution networks.

Strain-path dependent hardening models with rigorously identical predictions under monotonic loading

Accurate sheet metal simulation often requires advanced strain-path dependent material models, in order to predict the material response under complex loading conditions, including monotonic, reverse and orthogonal paths. More and more flexible models imply higher and higher costs in terms of parameter identification, computer implementation and simulation time, and robust comparison is often compromised by the inconsistent predictions of advanced models under monotonic loading. In this paper, a simple and general approach is proposed for the alteration of advanced hardening models in order to make them rigorously identical to each other under monotonic loading. This objective was reached without any drawback other than the addition of the corresponding equations. On the contrary, the flexibility and accuracy of the selected models was improved, and the parameter identification procedure became simpler, more accurate and more robust. Three material models of increasing complexity were selected to demonstrate the interest of this approach with respect to a complete set of characterisation experiments for a DP600 sheet steel.

Cyclic and creep combination effects on the long-term undrained behavior of overconsolidated clay

Soft soil subjected to cyclic loading typically exhibits an increase in excess pore pressure under undrained condition which brings the soil to an overconsolidated state. Then, under a subsequent large number of cycles (e.g. more than one million) which also takes time, the creep at overconsolidated state influences the cyclic effect and thus results in a complicated long-term undrained behavior. This paper aims to clarify this long-term undrained behavior of overconsolidated clay. The reconstituted samples are prepared from natural samples retrieved in the north of France. First, the shear strength characteristics along monotonic triaxial stress paths are identified. Then load control cyclic tests on overconsolidated specimens are conducted in fully saturated and undrained conditions. Small cyclic deviatoric stresses are applied in order to investigate more particularly the behavior under a very large number of cycles, during which an unusual pore pressure evolution is observed. To explain this, undrained triaxial creep tests are performed on reconstituted specimens with different values of OCRs under some specified stress states. The evolutions of axial strain, excess pore pressure, stress ratio, stress path, plastic strain rates and stress dilatancy during undrained creep are discussed. The additional undrained creep tests also show that two processes are simultaneously acting in a competitive manner: increase in the pore pressure due to the cyclic loading and decrease in the pore pressure because of creep.

DEM analysis of monotonic and cyclic behaviors of sand based on critical state soil mechanics framework

A series of monotonic and cyclic triaxial shearing tests on Toyoura sand are simulated by discrete element method (DEM) incorporating rolling resistance. The input parameters are calibrated against laboratory triaxial test data considering different initial states and monotonic loading paths. The calibrated DEM model successfully captures the density and stress dependency of sand behavior under both monotonic and cyclic conditions. It is shown that when approaching liquefaction, contact yielding alters from sliding-dominant to rolling-dominant. The expression of mechanical redundancy index (IR) is derived considering both effects of contact sliding and rolling. The IR = 1.0 condition is shown to be a unified criterion distinguishing between solid state and liquid state upon both monotonic and cyclic liquefactions. A unique micro critical state line (CSL) is obtained in MCN-p′ plane. The cyclic resistance ratio is exponentially correlated with both the macro state parameter (ψe0) derived from the e-p′ CSL and the micro state parameter (ψMCN0) determined from the MCN-p′ CSL. The specimens with the same ψe0 may have distinct cyclic behaviors, while cyclic behaviors of specimens with the same ψMCN0 are close to each other, indicating that ψMCN0 is a more plausible state variable for characterizing the behavior of sand than ψe0.