We present a new class of solvers for direct data-driven mechanical problems based on a sparse basis representation of equilibrium stress fields. Our first contribution is an efficient algorithm for computing the required sparse null-space basis on tetrahedral meshes. Only a single QR decomposition is needed to compute a small remaining set of dense basis vectors associated with boundary conditions and topological holes which can be handled efficiently via a partitioned Cholesky factorization. Building on this, we demonstrate how standard iterative solvers-such as the Newton-Raphson method-can be applied to direct data-driven formulations. The proposed approach is particularly valuable for challenging problems with complex data distributions requiring systematic exploration of the space of equilibrium stress fields. To this end, we introduce an algorithm that constructs a hierarchical solution set through an eigenvalue decomposition in the joint space of equilibrium stress and compatible strain fields. We demonstrate the proposed methodology with a numerical example involving brittle fracture with probabilistic tensile strength. The resulting family of failure patterns offers valuable insights for uncertainty quantification and design decision-making.

ABSTRACT Unsaturated soils exhibit complex behaviour under various stress paths, particularly at small strains. Current models often fail to capture nonlinearity. This paper extends a bounding-surface isotropic model to triaxial stress space, accurately predicting soil behaviour across different stress paths while accounting for small-strain shear stiffness. The model relies on a previously proposed mechanical law that utilizes scaled stress as the primary variable. A significant feature of this model is its ability to predict nonlinear shear stiffness by employing an empirical equation for shear modulus reduction. The model also supports both associated and non-associated flow rules, adding flexibility with only two extra parameters for the non-associated case. Validation against existing experimental data – covering isotropic and triaxial stress paths and small strains up to 1% – demonstrates the model’s high accuracy in reproducing stress–strain curves across different loading scenarios. It outperforms traditional elastoplastic models in capturing the strong nonlinearity at small strains.

Perceptions and experiences of family members in the ICU waiting room.

The permanent deformation of unbound granular materials (UGMs) is a key factor affecting the long-term performance of flexible pavements. This study investigates the influence of intermediate principal stress on the deformation behaviour of pavement materials under undrained conditions. The findings indicate that the variations of intermediate principal stress amplitude remarkably influence the strain accumulation patterns. Additionally, the results reveal that both resilient strain and modulus vary with changes in the intermediate principal stress. The distance to the failure line was defined as Δ by normalizing the applied stress ratio. Larger Δ consistently coincided with larger terminal slopes, indicating a shift from shakedown to sustained accumulation as the applied stress ratio approached the failure slope. To capture this stress-dependent behaviour, a mechanistic-empirical prediction model was proposed to capture the stress-dependent behaviour of UGMs. This model incorporates the effects of stress history and the intermediate principal stress, making it more adaptable to the realistic pavement loading conditions. • The study examines how intermediate principal stress affects cyclic deformation of granular materials. • Higher b cyc reduces axial strain accumulation. • Resilient strain and resilient modulus change notably with variations in b cyc . • A larger normalized distance to the failure line (Δ) leads to more sustained permanent strain. • The proposed model incorporates intermediate principal stress to accurately predict permanent deformation.

This paper presents a novel multidimensional, elastoplastic, stochastic damage constitutive model for concrete developed through the phenomenological approach, with the aim of providing a more objective description of the mechanical behavior of concrete under multidimensional stress states. First, an isotropic hardening model of concrete was established within the effective stress space based on Ottosen's criterion. This approach ensures that the yield surface remains smooth and continuous, thus preventing potential nonconvergence issues in numerical calculations that may arise due to strain softening. Subsequently, a novel methodology was established, grounded on the non-associative flow criterion of plastic mechanics, to address the issue of plastic deformation in the elastoplastic stochastic damage constitutive model. Finally, the multidimensional, elastoplastic, stochastic damage constitutive model of concrete was imported into COMSOL Multiphysics for a numerical analysis of reinforced concrete (RC) beams without web reinforcement. The obtained results were analyzed and compared with the simulation results derived from ABAQUS in terms of the plastic deformation, damage evolution, and force–displacement curves. The findings indicated that the proposed multidimensional, elastoplastic, stochastic damage constitutive model for concrete could more accurately capture the progression of plastic deformation and comprehensively represent the evolution process of concrete damage under loading conditions when compared with ABAQUS simulations. The force–displacement curve derived from this model exhibited a closer agreement with the experimental data, with the discrepancies between the calculated and tested values of the concentrated loads across various deflections remaining within 10%. The proposed constitutive model effectively encapsulates the nonlinear and stochastic characteristics inherent in concrete.

The prediction of fatigue life is critical in the design process, and current models offer a viable alternative to costly and time-consuming experimental fatigue testing. The constitutive fatigue model used integrates low-cycle and high-cycle fatigue behavior. This model is grounded on the concept of fatigue damage evolution and incorporates a moving endurance surface within the stress space, eliminating the need for ambiguous cycle-counting methods. An interesting observation is that many polymers exhibit macroscopic fatigue characteristics, specifically, the form of the S-N curve similar to those observed in metals. Consequently, all fatigue model parameters were expressed in terms of the well-established Coffin-Manson-Basquin model parameters. However, the constitutive mathematical modeling itself is computationally time-consuming, particularly when applied to predict high-cycle fatigue across large design spaces. Therefore, the proposed model was utilized exclusively to generate high-quality data for training machine learning models that offer significantly improved computational efficiency. The high-cycle fatigue design of polymers and other ductile materials, traditionally dependent on expensive and time-consuming experimental methods, is now expedited through an advanced modeling framework that combines constitutive mathematical modeling with AI-based approaches.

Simulation and experiment study on rock damage evolution mechanism of cut blasting: coupled effect of three-dimensional in-situ stress and compensation space coefficient

Abstract Over recent years, substantial efforts have been devoted to developing reliable geomechanical models for methane hydrate‐bearing sediments (MHBS). Understanding MHBS behavior is critical for simulating engineering processes related to methane extraction from hydrate‐rich deposits worldwide. Methane hydrate, a solid ice‐like substance forming within soil pores, significantly changes the sediment behavior. Numerous constitutive models have been proposed, mostly adapted from frameworks originally designed for conventional soils. Notably, different models, often based on contrasting assumptions, can reproduce the same experimental data—highlighting the complexity of capturing the true mechanical trends of MHBS. This paper presents a new approach in which essential mechanical features, including yield criterion, flow rule, and strain‐hardening behavior, are derived directly from experimental observations, independent of prior modeling assumptions. By mapping experimental data into a continuous stress space, the essential behavioral trends and their shape functions are directly identified. The results reveal clear key features: deviatoric hardening, an almost flat yield surface, and a non‐associative flow rule. These characteristics are integrated into a new constitutive model tailored for MHBS, offering a more direct and empirical basis for understanding and predicting their mechanical response in engineering applications.

This paper investigates how Toronto's Portuguese-Azorean community has shaped the city's multicultural and psychological landscape, focusing particularly on intergenerational experiences of trauma among immigrant youth. Framed within North America's broader migration dynamics, the study explores the creation and transformation of the ethnic enclave "Little Portugal" as both a space of cultural resilience and chronic urban stress. It introduces the concept of chronic urban trauma to describe the persistent psychosocial impact of displacement, assimilation pressures, and gentrification on young Portuguese-Azorean Canadians. While first-generation immigrants constructed cohesive ethnic infrastructures grounded in work, faith, and language, younger generations face cultural dissonance, linguistic loss, and identity fragmentation that manifest as emotional distress and social alienation. These experiences illustrate how structural urban change can perpetuate transgenerational trauma within immigrant families. By integrating perspectives from urban geography, trauma studies, and migration theory, this theoretical work underscores the need for trauma-informed educational and social policies that promote inclusion, belonging, and mental well-being among immigrant youth. Ultimately, the study positions "Little Portugal" as a microcosm of how multicultural cities negotiate the intersections of ethnicity, urban transformation, and psychological resilience.

This paper offers a new machine learning framework to analyse site suitability of Urban Green Infrastructure (UGI) in the Mumbai area. Mumbai is one of the megacities of India struggling with environmental stress and limited green space. Through incorporation of spatial data which is GIS-based, the proposed framework integrates machine learning methods, compositing layers like NDVI, land use, PM 2.5, slope, and population density in order to identify the best locations for green infrastructure. The stepwise, flexible solution allows making decisions based on the data without dependence on conventional heuristics. Designed for scalability and interpretability, it supports urban planners in prioritising impactful greening interventions, advancing Mumbai’s sustainability and resilience goals while offering a transferable model for other high-density urban regions.

To elucidate the micromechanical origins of the macroscopic anisotropic behavior of granular materials, this study develops a micromechanically based elastoplastic constitutive model for sand. First, anchored in the static equilibrium hypothesis and granular micromechanics theory, a true stress tensor is introduced to characterize the authentic inter-particle contact forces. Serving as a coupled variable of the macroscopic stress and the microscopic fabric tensor, this formulation not only quantifies the directional distribution of the contact network but also enables the mapping of anisotropic yielding and deformation analyses into an equivalent isotropic true stress space. Subsequently, a comprehensive constitutive framework is established by integrating critical state theory, an anisotropic fabric evolution law, and an energy-based stress–dilatancy relationship that explicitly accounts for the evolution mechanism of the microscopic coordination number. The physical interpretation, calibration procedure, and sensitivity analysis of the model parameters are also presented. The predictive capability of the model is rigorously validated against conventional triaxial tests on Ottawa sand, true triaxial numerical simulations, and experimental data for Toyoura sand with inherent anisotropy. The comparisons demonstrate that the model accurately captures not only the stress–strain response and volumetric deformation under conventional loading but also the strength dependency on loading direction and mechanical characteristics under complex stress paths, substantiating the validity and universality of the proposed micromechanical approach.

Abstract Carbon-fiber-reinforced (CFR) composites in aircraft structures are subjected to complex, multiaxial loading conditions that may induce fatigue damage prior to final failure. To ensure structural safety, reliable failure criteria must be established for both undamaged and fatigue-affected materials. This study presents experimental investigations of tubular CFR composite specimens subjected to combined axial force and internal pressure, generating complex stress states in the thin-walled gage section. The specimens were loaded to failure along various stress paths, enabling construction of a failure surface in principal stress space. Three distinct failure modes were observed: resin matrix puncture, longitudinal cracking, and circumferential cracking with specimen separation. A probabilistic approach was introduced to account for the large scatter in experimental data, replacing deterministic failure stresses with stress values corresponding to specified survival probabilities. The results indicate that the maximum principal stress criterion, formulated in three-dimensional principal stress space with axes aligned to fiber directions, provides a suitable framework for the investigated composite. Incorporating probabilistic assessment improves reliability in predicting composite failure under complex loading.

Abstract Mixed methods for linear elasticity with strongly symmetric stresses of lowest order are studied in this paper. On each simplex, the stress space has piecewise linear components with respect to its Alfeld split (which connects the vertices to barycenter), generalizing the Johnson–Mercier two-dimensional element to higher dimensions. Further reductions in the stress space in the three-dimensional case (to 24 degrees of freedom per tetrahedron) are possible when the displacement space is reduced to local rigid displacements. Proofs of optimal error estimates of numerical solutions and improved error estimates via postprocessing and the duality argument are presented.

Purpose This study examines how expatriate hospitality workers navigate emotional labor amid prolonged crises. It explores the dual emotional burden of maintaining professional composure while experiencing personal distress due to conflict in their homeland. The study advances emotional labor theory by incorporating cultural resilience, coping mechanisms and workplace relational dynamics under extreme stress. Design/methodology/approach A grounded theory approach was employed, using in-depth interviews with expatriate hotel workers in a non-conflict host country. Thematic coding and analysis were used to develop a conceptual framework addressing emotional labor in crisis contexts. Findings Four key themes emerged: (1) cultural resilience as a coping resource, (2) work as a paradoxical refuge from distress, (3) the role of empathetic customer interactions in shaping emotional labor and (4) the intensification of emotional labor due to gendered cultural expectations. Additionally, the study identifies four distinct types of guilt that shape expatriates’ emotional experiences. Practical implications Findings suggest that hospitality organizations should implement structured interventions to support expatriate employees during crises. These include developing workplace routines that provide emotional stability, integrating cultural and gender-sensitive training, offering counseling resources and fostering workplace environments where customer empathy reduces emotional strain on staff. Originality/value This study extends emotional labor theory by incorporating cultural, crisis and organizational dimensions. It introduces work as a dual-functioning space of stress and refuge, underlines the transformative role of customer interactions and highlights the underexplored interplay between privilege, guilt and emotional labor in crisis contexts.

Numerical Solution of the Equations of A.A. Ilyushin’s Coplanarity Hypothesis for a Loading Process in the Deviatoric Stress Space

BackgroundChronic obstructive pulmonary disease (COPD) is a leading cause of mortality, and exercise has been shown to reduce both. Health conditions, environmental factors, and logistical challenges are often barriers for participation in pulmonary rehabilitation (PR). Given the barriers many individuals with COPD face when attending health care centers for PR, virtual home-based cycling exercise could be an option.ObjectiveThis study aimed to explore the development of a home-based cycling exercise intervention for individuals with COPD, focusing on aspects such as bicycle selection, app functionality, and pilot testing. Furthermore, it aimed to explore participants' and nonparticipants' attitudes toward the intervention.MethodsUsing a phenomenological-hermeneutic approach, data were gathered from 15 semistructured interviews, including test pilots, participants, and nonparticipants. A thematic analysis was used to analyze the data.ResultsThematic analysis identified 8 key themes: bicycle selection, individual guidance needs, geographical and video quality, online connectivity, comfort and accessibility of home-based cycling, flexibility, energy levels, and practical limitations. Findings highlighted a preference for pedal bicycles with adjustable intensity, the importance of flexibility in scheduling, and the autonomy provided by a home-based setup. While participants appreciated the virtual journey on videos, barriers such as lack of energy, stress, and limited space were reported by nonparticipants.ConclusionsRecommendations include enhancing app features and addressing individual needs to improve adherence. The study underscores the potential of tailored home-based exercise interventions in overcoming traditional PR challenges.International Registered Report Identifier (IRRID)RR2-10.1136/bmjresp-2024-002573

Characterizing the degeneracy of local stress states is a central challenge in obtaining the complete statistical mechanics of disordered media. Here, we introduce a minimal force-balance model for isolated granular clusters to probe the structure of the stress space through principal stress orientation and stress anisotropy. We further show that when complemented by physically motivated pairwise constraints, the model produces predictions for the stress alignment in packings of repulsive hard spheres. We compare these predictions against simulation data for grains in hopper and simple shear flows, finding qualitative agreement. This demonstrates the promise of modeling bulk athermal disordered systems through the combinatorics of few primitive geometric motifs.

Abstract. Rocks break if shear stresses exceed their strength. It is therefore important for typical geoscientific applications to take shear failure mechanism and the subsequent development of mode-II shear bands or faults into account. Many existing codes incorporate non-associated Drucker-Prager or Mohr-Coulomb plasticity models to simulate this behavior. Yet, when effective mean stress becomes extensional, for example when fluid pressure becomes large, the dominant failure mode changes to a mode-I (opening) mode, which initiates plastic volumetric deformation. It is rather difficult to represent both failure modes in numerical models in a self-consistent manner, while also accounting for the nonlinear visco-elastic host rock rheology, which varies from being nearly incompressible in the mantle to being compressible in surface-near regions. Here, we present a simple plasticity model that is designed to overcome these difficulties. We employ a combination of a linearized Drucker-Prager shear failure envelope with a circular tensile cap function in way that ensures continuity and smoothness of both yield surface and flow potential in the entire stress space. A Perzyna-type viscoplastic regularization ensures that the resulting localization zones are mesh-insensitive. To deal with the near incompressibility condition, a mixed two-field finite element formulation is employed. The local nonlinear iterations at the integration-point level are used to determine the stress increments. The global Newton-Raphson iterations are applied to solve the discretized momentum and continuity residual equations. The presented plasticity model is implemented in an open-source 2D unstructured finite element code GeoTech2D. The results of several typical test cases that range from crustal scale deformation to the propagation of fluid-induced tensile failure zones demonstrate rapid convergence. The robustness of the solution scheme is enhanced by the adaptive time stepping algorithm.

Sessile marine organisms form the foundation of many coastal ecosystems, playing crucial roles in functions like water filtration and habitat provision. Understanding their population dynamics—particularly the interplay of growth, reproduction, and detachment under environmental stress—is essential for both ecological research and effective coastal management. This work presents a comprehensive numerical model for simulating the growth, reproduction, mortality and detachment of sessile organisms using a hybrid dynamic energy budget (DEB)–statistical approach. Our model incorporates bioenergetic processes, environmental stress responses, space competition, and layering dynamics. The simulation framework considers the effects of temperature, salinity, dissolved oxygen, and food availability on organism physiology while tracking growth, reproduction, and mortality and detachment. Model validation was performed using field data collected from sessile invertebrate populations around a floating platform in the estuary of the Sumida River in Tokyo, Japan, from September 2002 to September 2003. Our approach successfully reproduced observed patterns with high accuracy. The model revealed that temperature stress and salinity fluctuations interact synergistically, amplifying mortality and detachment rates beyond what would be predicted by each factor independently. Comparative analyses with reduced models lacking either mortality or detachment components demonstrated the importance of including both processes for the accurate prediction of population dynamics. Our case study provides a robust framework for predicting sessile organism responses to environmental variability and highlights key areas for future research in benthic ecosystem modeling.

Abstract To explore the influence of stress space rotation on roadway stability, this study establishes Cartesian and principal stress axes, obtains principal stress characteristic parameters and direction cosine matrix, and determines the conversion process between coordinate axes. By breaking through the traditional plane strain mechanics model, a full plane strain model of rectangular roadway considering the deflection effect of principal stress axis is established. The analytical solution of stress complex variation of any element around the roadway is derived, and the calculation method of plastic zone is given. The influence of stress deflection on the stress of roadway and the shape distribution of plastic zone is discussed and the control system of roadway under the action of principal stress deflection in spatial region is established. The research results show that: (1) the shear stress and normal stress formed in the remote of the roadway during the stress rotation are in the same order of magnitude, and the plastic quantitative calculation of the roadway cannot simply consider the normal stress. (2) Stress deflection causes the distribution of stress and plastic zone around the roadway to show ‘asymmetric’ failure characteristics, and the transient deflection of stress may cause the rapid expansion of the plastic zone of the roadway. (3) The distribution characteristics of plastic zone calculated by this study are compared with the deformation and failure feature and peep results of the return air roadway in Cuncaota Mine, and the comparison results are good. The supporting system and technology of roadway under the action of principal stress deflection in space area are put forward, and the field application effect is good.