Investigating Fracture Behavior of Lattice Structures Using the XFEM and Equivalent Solid Material Model Techniques

Numerical Simulation of Crack Propagation in Concrete with Prefabricated Array Fractures Based on the Discrete Element Method

Concrete readily develops cracks under service loads, which poses severe risks to the overall safety of engineering structures. In this work, the discrete element method (DEM) integrated with PFC2D 5.0 numerical software is adopted to construct a mesoscale concrete numerical model containing pre-existing internal fractures, and uniaxial compressive loading simulations are subsequently carried out. Unlike previous studies that predominantly examined isolated fracture parameters, this work systematically investigates the coupled effects of fracture inclination angle, length, and quantity on crack propagation mechanisms at the mesoscale, and for the first time establishes a quantitative relationship between microcrack spatial distribution patterns and macroscopic mechanical degradation. Parametric analyses are performed to quantify the influences of fracture geometric characteristics, including fracture inclination angle (30°, 45°, 60°), fracture length (short, long and extra-long), fracture quantity (4, 8 and 16), as well as the comparison between intact and fractured concrete specimens. The fracture quantities of 4, 8, and 16 are selected to represent low, medium, and high levels of initial defect density within the concrete matrix, corresponding to approximately 1%, 2%, and 4% of the total specimen area, respectively, thereby enabling a systematic investigation into the progressive deterioration of mechanical performance with increasing internal damage severity. The whole evolution process of crack initiation, crack propagation and ultimate failure patterns of concrete is systematically explored. Numerical results reveal that specimens with larger fracture angles exhibit higher compressive strength yet generate abundant newly formed microcracks, whereas low-angle prefabricated fractures are prone to triggering abrupt brittle failure. Specimens embedded with shorter fractures achieve superior mechanical strength and develop denser, more intensive microcrack distributions; in contrast, long pre-existing fractures drastically degrade compressive strength while limiting the generation of secondary cracks. Reducing the number of internal defects simultaneously improves compressive strength and expands the coverage range of the induced fracture network. Specimens with 16 prefabricated fractures deliver the weakest mechanical performance, owing to the excessively high initial defect density inside the matrix. In comparison with fractured samples, intact concrete without pre-set fractures achieves better comprehensive performance in terms of compressive strength, deformation compatibility and uniform microcrack development. A core conclusion drawn from this study is that the total quantity of microcracks cannot serve as a direct indicator to evaluate the damage degradation degree of concrete; instead, the spatial distribution pattern of microcracks dominates the deterioration level. Evenly scattered microcrack populations maintain relatively high residual strength, whereas the concentrated coalescence of microcracks into continuous penetrating macrocracks leads to an abrupt decline in structural load-carrying capacity. The findings of this research can provide theoretical references for stability evaluation and safety diagnosis of defective concrete structures in practical engineering.

Generalised Phase Field Modelling of Fracture in Gyroid Structures: Numerical and Experimental Insights Using Additively Manufactured Polylactic Acid (PLA) Specimens

This study presents a three‐dimensional cohesive phase field framework for simulating quasi‐static fracture in Gyroid lattice structures. To the authors' knowledge, this is one of the first experimentally validated applications of a diffuse cohesive phase field model to describe damage and fracture evolution in additively manufactured polylactic acid (PLA) lattice specimens. Due to the softening‐like mechanical behaviour exhibited by the 3D‐printed PLA specimens, the present work employs a high‐order cohesive generalised phase field model capable of capturing material softening once the maximum load‐carrying capacity is reached and energy dissipation becomes dominant. This modelling choice is essential to reproduce the gradual post‐peak degradation observed experimentally, which would not be adequately described by a purely brittle AT1/AT2‐type formulation. After validation in a two‐dimensional case, the approach is extended to the analysis of 3D‐printed Gyroid specimens subjected to tensile and compressive loading. Different Gyroid configurations, including unit cells and 2×2×2$$ 2\times 2\times 2 $$ clusters, were tested under tensile and compressive loading regimes using an in situ tensile/compression testing stage, with deformations and failure modes directly monitored through in situ imaging. Each experiment was recorded from multiple angles during tensile and compressive loading of the additively manufactured Gyroid specimens and compared frame by frame with simulation outputs, revealing good agreement in the prediction of crack initiation and propagation paths. The comparison between experimental and numerical results confirms the model's ability to capture the main tensile failure mechanisms and the softening‐driven fracture evolution in architected PLA lattices, while the compressive response is interpreted with caution in the late post‐peak regime due to mechanisms such as buckling, contact and densification. This versatile modelling framework lays the foundation for future studies incorporating additional physical phenomena—such as surface coatings, residual stresses, or micron‐scale effects—and for extension to other triply periodic minimal surface (TPMS) topologies beyond the Gyroid.

Modeling damage and fracture in additively manufactured polymeric triply periodic minimal surface lattices

Architected triply periodic minimal surface (TPMS) lattices offer superior specific energy absorption, toughness, fatigue strength, and tunability. While recent advancements have established rate-dependent viscoplastic constitutive models to capture the complex nonlinear deformation response of additively manufactured polymeric TPMS structures, predicting fracture and the resulting structural failure remains a significant challenge. We address this by performing systematic experiments on unit cells and lattices of various sizes under tension, compression, and non-monotonic loading. The experiments inform the development of a new constitutive model that captures the damage and fracture behavior of polymeric TPMS lattices. We first implement a high-fidelity viscoplastic deformation constitutive model from Ma et al. (2026) into finite element software Abaqus/Explicit via a user material subroutine. We then propose a damage initiation criterion for amorphous polymers based on stored elastic energy and equivalent plastic strain. The damage model is implemented in Abaqus using gradient-damage framework following Konale and Srivastava(2025). The damage model and numerical simulation capability are quantitatively and qualitatively validated using experimental results for a unit cell under non-monotonic loading and lattices under tension. The proposed damage model and simulation capability enable in silico design of architected polymer structures.

Effect of porosity parameters on the static buckling behavior of FGP plates using the Ritz method and first-order shear deformation theory

This study investigates the static buckling behavior of functionally graded porous (FGP) plates. A theoretical model is developed based on the first-order shear deformation theory (FSDT), while the Ritz method is utilized to solve the governing equations. In this model, the material properties are considered to vary continuously through according to three distinct porosity schemes, including uniform, symmetric, and asymmetric distributions. The validity and accuracy of the developed model are confirmed by benchmarking the results against available data reported in the literature. A comprehensive numerical study is carried out to explore the effects of key parameters, such as porosity characteristics (distribution patterns and coefficients) and geometric properties, on the critical buckling load. The outcomes of this investigation contribute to a better understanding and serve as a valuable resource for the design and optimization of engineering structures fabricated from advanced functional materials.

Research on the Stability of Arc-Fractured Rock–Concrete Composites: Mechanical Response and Energy Evolution

To mitigate the violent movement of overlying strata in goaf areas, rock–concrete composite support systems are widely utilized. However, the mechanical behavior of such systems under the influence of complex pre-existing defects, such as arc-shaped fractures, remains insufficiently understood. This study aims to clarify the failure mechanisms and the evolution of stability in these composites by evaluating the influence of fracture inclination angles. A synergistic methodology was adopted, combining laboratory uniaxial compression tests with discrete-element method simulations. Based on energy dissipation theory and the strain equivalence hypothesis, a statistical damage constitutive model was established to bridge the gap between microscopic damage and macroscopic mechanical response. The results demonstrate that fracture inclination significantly dictates the energy partitioning and crack propagation patterns within the composite. The established constitutive model, validated by numerical results ( R 2 > 0.999), effectively quantifies how increasing inclination angles enhance energy absorption efficiency and retard structural damage progression. Due to the high toughness of the concrete component, the composite maintains substantial residual bearing capacity, preventing instantaneous failure. These findings provide a robust theoretical framework and practical guidance for optimizing support designs in deep underground excavations with intricate geological defects.

Numerical Simulation of Dominant Fracture Mechanisms in a Nickel-Based Alloy XH73M within the Phase Field Approach