Sprain energy consequences for damage localization and fracture mechanics.

The 2023 smooth Lagrangian Crack-Band Model (slCBM), inspired by the 2020 invention of the gap test, prevented spurious damage localization during fracture growth by introducing the second gradient of the displacement field vector, named the "sprain," as the localization limiter. The key idea was that, in the finite element implementation, the displacement vector and its gradient should be treated as independent fields with the lowest ([Formula: see text]) continuity, constrained by a second-order Lagrange multiplier tensor. Coupled with a realistic constitutive law for triaxial softening damage, such as microplane model M7, the known limitations of the classical Crack Band Model were eliminated. Here, we show that the slCBM closely reproduces the size effect revealed by the gap test at various crack-parallel stresses. To describe it, we present an approximate corrective formula, although a strong loading-path dependence limits its applicability. Except for the rare case of zero crack-parallel stresses, the fracture predictions of the line crack models (linear elastic fracture mechanics, phase-field, extended finite element method (XFEM), cohesive crack models) can be as much as 100% in error. We argue that the localization limiter concept must be extended by including the resistance to material rotation gradients. We also show that, without this resistance, the existing strain-gradient damage theories may predict a wrong fracture pattern and have, for Mode II and III fractures, a load capacity error as much as 55%. Finally, we argue that the crack-parallel stress effect must occur in all materials, ranging from concrete to atomistically sharp cracks in crystals.

Atomistic measurement and modeling of intrinsic fracture toughness of two-dimensional materials.

Quantifying the intrinsic mechanical properties of two-dimensional (2D) materials is essential to predict the long-term reliability of materials and systems in emerging applications ranging from energy to health to next-generation sensors and electronics. Currently, measurements of fracture toughness and identification of associated atomistic mechanisms remain challenging. Herein, we report an integrated experimental-computational framework in which in-situ high-resolution transmission electron microscopy (HRTEM) measurements of the intrinsic fracture energy of monolayer MoS2 and MoSe2 are in good agreement with atomistic model predictions based on an accurately parameterized interatomic potential. Changes in crystalline structures at the crack tip and crack edges, as observed in in-situ HRTEM crack extension tests, are properly predicted. Such a good agreement is the result of including large deformation pathways and phase transitions in the parameterization of the inter-atomic potential. The established framework emerges as a robust approach to determine the predictive capabilities of molecular dynamics models employed in the screening of 2D materials, in the spirit of the materials genome initiative. Moreover, it enables device-level predictions with superior accuracy (e.g., fatigue lifetime predictions of electro- and opto-electronic nanodevices).

Strengthened Interficial Adhesive Fracture Energy by Young's Modulus Matching Degree Strategy in Carbon-Based HTM Free MAPbI3 Perovskite Solar Cell with Enhanced Mechanical Compatibility.

Carbon-based hole transport layer-free perovskite solar cells (PSCs) based on methylammonium lead triiodide (MAPbI3 ) have become one of the research focus due to low cost, easy preparation, and good optoelectronic properties. However, instability of perovskite under vacancy defects and stress-strain makes it difficult to achieve high-efficiency and stable power output. Here, a soft-structured long-chain 2D pentanamine iodide (abbreviated as "PI") is used to improve perovskite quality and interfacial mechanical compatibility. PI containing CH3 (CH2 )4 NH3 + and I- ions not only passivate defects at grain boundaries, but also effectively alleviate residual stress during high temperature annealing via decreasing Young's modulus of perovskite film. Most importantly, PI effectively increases matching degree of Young's modulus between MAPbI3 (47.1 GPa) and carbon (6.7 GPa), and strengthens adhesive fracture energy (Gc ) between perovskite and carbon, which is helpful for outward release of nascent interfacial stress generated under service conditions. Consequently, photoelectric conversion efficiency (PCE) of optimal device is enhanced from 10.85% to 13.76% and operational stability is also significantly improved. 83.1% output is maintained after aging for 720 h at room temperature and 25-60% relative humidity (RH). This strategy of regulation from chemistry and physics provides a strategy for efficient and stable carbon-based PSCs.

Ultra-Tough Waterborne Polyurethane-Based Graft-Copolymerized Piezoresistive Composite Designed for Rehabilitation Training Monitoring Pressure Sensors.

Effective training is crucial for patients who need rehabilitation for achieving optimal recovery and reducing complications. Herein, a wireless rehabilitation training monitoring band with a highly sensitive pressure sensor is proposed and designed. It utilizes polyaniline@waterborne polyurethane (PANI@WPU) as a piezoresistive composite material, which is prepared via the in situ grafting polymerization of PANI on the WPU surface. WPU is designed and synthesized with tunable glass transition temperatures ranging from -60 to 0 °C. Dipentaerythritol (Di-PE) and ureidopyrimidinone (UPy) groups are introduced, endowing the material with good tensile strength (14.2 MPa), toughness (62 MJ-1 m-3 ), and great elasticity (low permanent deformation: 2%). Di-PE and UPy enhance the mechanical properties of WPU by increasing the cross-linking density and crystallinity. Combining the toughness of WPU and the high-density microstructure derived by hot embossing technology, the pressure sensor exhibits high sensitivity (168.1 kPa-1 ), fast response time (32 ms), and excellent stability (10 000 cycles with 3.5% decay). In addition, the rehabilitation training monitoring band is equipped with a wireless Bluetooth module, which can be easily applied to monitor the rehabilitation training effect of patients using an applet. Therefore, this work has the potential to significantly broaden the application of WPU-based pressure sensors for rehabilitation monitoring.

New perspective of fracture mechanics inspired by gap test with crack-parallel compression.

The line crack models, including linear elastic fracture mechanics (LEFM), cohesive crack model (CCM), and extended finite element method (XFEM), rest on the century-old hypothesis of constancy of materials' fracture energy. However, the type of fracture test presented here, named the gap test, reveals that, in concrete and probably all quasibrittle materials, including coarse-grained ceramics, rocks, stiff foams, fiber composites, wood, and sea ice, the effective mode I fracture energy depends strongly on the crack-parallel normal stress, in-plane or out-of-plane. This stress can double the fracture energy or reduce it to zero. Why hasn't this been detected earlier? Because the crack-parallel stress in all standard fracture specimens is negligible, and is, anyway, unaccountable by line crack models. To simulate this phenomenon by finite elements (FE), the fracture process zone must have a finite width, and must be characterized by a realistic tensorial softening damage model whose vectorial constitutive law captures oriented mesoscale frictional slip, microcrack opening, and splitting with microbuckling. This is best accomplished by the FE crack band model which, when coupled with microplane model M7, fits the test results satisfactorily. The lattice discrete particle model also works. However, the scalar stress-displacement softening law of CCM and tensorial models with a single-parameter damage law are inadequate. The experiment is proposed as a standard. It represents a simple modification of the three-point-bend test in which both the bending and crack-parallel compression are statically determinate. Finally, a perspective of various far-reaching consequences and limitations of CCM, LEFM, and XFEM is discussed.

Concrete damage analysis based on higher-order beam theories using fracture energy regularization.

This paper presents the numerical damage analysis of concrete structures using higher-order beam theories based on Carrera Unified Formulation (CUF). The concrete constitutive relation is modeled using continuum damage mechanics based on a modified Mazars concrete damage model, in which both the tensile and compressive softening behaviors are regularized with classical fracture energy methodology. An expression is proposed to estimate the characteristic length in higher-order beam theories, to prevent mesh dependency. Both softening constitutive laws and fracture energy calculations are obtained according to Model Code 2010. To assess the efficiency of the proposed model, three classical benchmark quasi-static experiments are taken for validation. From the comparison between numerical and experimental results, the proposed CUF model using continuum damage mechanics can present 3D accuracy with low computational costs and reduce the mesh dependency.

Fracture dynamics of solid materials: from particles to the globe.

Solid materials have been used extensively for various kinds of structural components in our surroundings. Stability of such solid structures, including not only machinery, architectural and civil structures but also our solid earth, is largely governed by fracture development in the solids. Especially, dynamic fracture, once occurring-quite often unexpectedly-evolves very rapidly and can lead to catastrophic structural failures and disasters like earthquakes. However, contrary to slowly enlarging fractures that can be recognized spatio-temporally in detail, it is extremely difficult to trace dynamically growing fractures even in controlled laboratory experimental conditions, and its physics still remains unexplored. This theme issue introduces and summarizes recent advancements in our understanding of the widespread topics of dynamic fracture of solids from well-assorted perspectives, involving laboratory experiments, simulations and analytical methods as well as field observations, with the common background of mechanics of fracture. Multi-scale subjects range from fracture of metals at atom or particle levels to disastrous rock bursts in deep gold mines and detection of unique signals before devastating fracture such as large, global-scale earthquakes. This article is part of the theme issue 'Fracture dynamics of solid materials: from particles to the globe'.

Effect of Acetyl Group on Mechanical Properties of Chitin/Chitosan Nanocrystal: A Molecular Dynamics Study.

Chitin fiber is the load-bearing component in natural chitin-based materials. In these materials, chitin is always partially deacetylated to different levels, leading to diverse material properties. In order to understand how the acetyl group enhances the fracture resistance capability of chitin fiber, we constructed atomistic models of chitin with varied acetylation degree and analyzed the hydrogen bonding pattern, fracture, and stress-strain behavior of these models. We notice that the acetyl group can contribute to the formation of hydrogen bonds that can stabilize the crystalline structure. In addition, it is found that the specimen with a higher acetylation degree presents a greater resistance against fracture. This study describes the role of the functional group, acetyl groups, in crystalline chitin. Such information could provide preliminary understanding of nanomaterials when similar functional groups are encountered.

Tissue histology on the correlation between fracture energy and elasticity.

PURPOSE: Preemptively estimating tissue damage is crucial for a safe surgical procedure. We previously investigated the possibility of estimating the fracture energies of biological tissues based on their elasticities. However, the reason behind the presence of these correlations is poorly understood. In this study, we investigate the effect of a tissue's histology on the correlation between the fracture energy and elasticity. We hypothesize that two tissues with similar fibrous structure will show a similar correlation between the fracture energy and elasticity. METHODS: Porcine duodenum were used for this study. Two tensile tests were performed for each porcine duodenum specimen to determine its elasticity and tearing energy. The correlation between fracture energy and elasticity was then investigated using the results from the mechanical tests. Furthermore, duodenum specimens were fixed in 10% formalin while under tension. Microscopic images were then taken to visualize the fibrous structure within the duodenum tissues under tension. RESULTS: The results from the tensile test showed that the fracture energy had an isotropic positive and linear correlation with the elasticity to the negative 0.5th power (R2 = 0.89), which was also previously reported in small intestinal (jejunum) specimens. Furthermore, the tearing patterns of the duodenum were identical to the ones reported in the jejunum. Hematoxylin and eosin staining on tissues fixed under tension showed that the endomysium fibers are involved in providing resistance toward traction. CONCLUSION: Through mechanical tests, we showed that porcine duodenum tissues also have a correlation between its fracture energy and elasticity. We also discussed that the histological structure of a tissue is an important factor that dictates how the tearing energy of a tissue will correlate to the elasticity. We understood that since the tearing mechanism between the duodenum and jejunum was similar, the correlations between their fracture energies and elasticities were also similar.

Effect of Basalt/Steel Individual and Hybrid Fiber on Mechanical Properties and Microstructure of UHPC.

Ultra High-Performance Concrete (UHPC) is a cement-based composite material with great strength and durability. Fibers can effectively increase the ductility, strength, and fracture energy of UHPC. This work describes the impacts of individual or hybrid doping of basalt fiber (BF) and steel fiber (SF) on the mechanical properties and microstructure of UHPC. We found that under individual doping, the effect of BF on fluidity was stronger than that of SF. Moreover, the compressive, flexural, and splitting tensile strength of UHPC first increased and then decreased with increasing BF dosage. The optimal dosage of BF was 1%. At a low content of fiber, UHPC reinforced by BF demonstrated greater flexural strength than that reinforced by SF. SF significantly improved the toughness of UHPC. However, a high SF dosage did not increase the strength of UHPC and reduced the splitting tensile strength. Secondly, under hybrid doping, BF was partially substituted for SF to improve the mechanical properties of hybrid fiber UHPC. Consequently, when the BF replacement rate increased, the compressive strength of UHPC gradually decreased; on the other hand, there was an initial increase in the fracture energy, splitting tensile strength, and flexural strength. The ideal mixture was 0.5% BF + 1.5% SF. The fluidity of UHPC with 1.5% BF + 0.5% SF became the lowest with a constant total volume of 2%. The microstructure of hydration products in the hybrid fiber UHPC became denser, whereas the interface of the fiber matrix improved.

Cohesive Properties of Bimaterial Interfaces in Semiconductors: Experimental Study and Numerical Simulation Using an Inverse Cohesive Contact Approach.

Examining crack propagation at the interface of bimaterial components under various conditions is essential for improving the reliability of semiconductor designs. However, the fracture behavior of bimaterial interfaces has been relatively underexplored in the literature, particularly in terms of numerical predictions. Numerical simulations offer vital insights into the evolution of interfacial damage and stress distribution in wafers, showcasing their dependence on material properties. The lack of knowledge about specific interfaces poses a significant obstacle to the development of new products and necessitates active remediation for further progress. The objective of this paper is twofold: firstly, to experimentally investigate the behavior of bimaterial interfaces commonly found in semiconductors under quasi-static loading conditions, and secondly, to determine their respective interfacial cohesive properties using an inverse cohesive zone modeling approach. For this purpose, double cantilever beam specimens were manufactured that allow Mode I static fracture analysis of the interfaces. A compliance-based method was used to obtain the crack size during the tests and the Mode I energy release rate (GIc). Experimental results were utilized to simulate the behavior of different interfaces under specific test conditions in Abaqus. The simulation aimed to extract the interfacial cohesive contact properties of the studied bimaterial interfaces. These properties enable designers to predict the strength of the interfaces, particularly under Mode I loading conditions. To this extent, the cohesive zone modeling (CZM) assisted in defining the behavior of the damage propagation through the bimaterial interfaces. As a result, for the silicon-epoxy molding compound (EMC) interface, the results for maximum strength and GIc are, respectively, 26 MPa and 0.05 N/mm. The second interface tested consisted of polyimide and silicon oxide between the silicon and EMC layers, and the results obtained are 21.5 MPa for the maximum tensile strength and 0.02 N/mm for GIc. This study's findings aid in predicting and mitigating failure modes in the studied chip packaging. The insights offer directions for future research, focusing on enhancing material properties and exploring the impact of manufacturing parameters and temperature conditions on delamination in multilayer semiconductors.

Regulation of Hard Segment Cluster Structures for High-performance Poly(urethane-urea) Elastomers.

Elastomers are widely used in daily life; however, the preparation of degradable and recyclable elastomers with high strength, high toughness, and excellent crack resistance remains a challenging task. In this report, a polycaprolactone-based poly(urethane-urea) elastomer is presented with excellent mechanical properties by optimizing the arrangement of hard segment clusters. It is found that long alkyl chains of the chain extenders lead to small and evenly distributed hard segment clusters, which is beneficial for improving mechanical properties. Together with the multiple hydrogen bond structure and stress-induced crystallization, the obtained elastomer exhibits a high strength of 63.3 MPa, an excellent toughness of 431 MJ m-3 and an outstanding fracture energy of 489 kJ m-2, while maintaining good recyclability and degradability. It is believed that the obtained elastomer holds great promise in various application fields and it contributes to the development of a sustainable society.

Assessment of Shear Fracture Energy in Hybrid Composites with Natural and Synthetic Fibers.

Composite materials made with synthetic fibers are extensively employed across a diverse array of engineering structures. However, from an environmental point of view, synthetic fibers do not represent the best choice, since they are not renewable and are not biodegradable as natural fibers. This study investigates the application of adhesive joints with hybrid composites, which combine natural and synthetic fibers, as potential replacements for traditional composites made solely from synthetic fibers. The main focus is on assessing the mechanical performance of these hybrid composites through end-notched flexure (ENF) tests on adhesive joints. Four different configurations of substrates were used, two with only one type of fiber (natural or synthetic) and two hybrids. Digital image correlation (DIC) analysis was conducted to provide detailed insights into the changes in displacement fields for the different configurations tested. The results indicate that adhesive joints with hybrid composites exhibit superior shear fracture energy (GIIC) compared with the joints with purely synthetic fibers. This enhancement in fracture toughness, attributed to the synergistic effects of the natural and synthetic fibers, suggests that hybrid composites could be a viable alternative, offering potential benefits in terms of sustainability and cost without compromising mechanical performance.

Soft, Tough, Antifatigue Fracture Elastomer Composites with Low Thermal Resistance through Synergistic Crack Pinning and Interfacial Slippage.

Soft elastomer composites are promising functional materials for engineer interfaces, where the miniaturized electronic devices have triggered increasing demand for effective heat dissipation, high fracture energy, and antifatigue fracture. However, such a combination of these properties can be rarely met in the same elastomer composites simultaneously. Here a strategy is presented to fabricate a soft, extreme fracture tough (3316 J m-2) and antifatigue fracture (1052.56 J m⁻2) polydimethylsiloxane/aluminum elastomer composite. These outstanding properties are achieved by optimizing the dangling chains and spherical aluminum fillers, resulting in the combined effects of crack pinning and interfacial slippage. The dangling chains that lengthen the polymer chains between cross-linked points pin the cracks and the rigid fillers obstruct the cracks, enhancing the energy per unit area needed for fatigue failure. The dangling chains also promote polymer/filler interfacial slippage, enabling effective deflection and blunting of an advancing crack tip, thus enhancing mechanical energy dissipation. Moreover, the elastomer composite exhibits low thermal resistance (≈0.12 K cm2 W-1), due to the formation of a thermally conductive network. These remarkable characteristics render this elastomer composite promising for application as a thermal interface material in electronic devices.

Tough Hydrogels for Load-Bearing Applications.

Tough hydrogels have emerged as a promising class of materials to target load-bearing applications, where the material has to resist multiple cycles of extreme mechanical impact. A variety of chemical interactions and network architectures are used to enhance the mechanical properties and fracture mechanics of hydrogels making them stiffer and tougher. In recent years, the mechanical properties of tough, high-performance hydrogels have been benchmarked, however, this is often incomplete as important variables like water content are largely ignored. In this review, the aim is to clarify the reported mechanical properties of state-of-the-art tough hydrogels by providing a comprehensive library of fracture and mechanical property data. First, common methods for mechanical characterization of such high-performance hydrogels are introduced. Then, various modes of energy dissipation to obtain tough hydrogels are discussed and used to categorize the individual datasets helping to asses the material's (fracture) mechanical properties. Finally, current applications are considered, tough high-performance hydrogels are compared with existing materials, and promising future opportunities are discussed.

Fracture-Resistant Stretchable Materials: An Overview from Methodology to Applications.

Stretchable materials, such as gels and elastomers, are attractive materials in diverse applications. Their versatile fabrication platforms enable the creation of materials with various physiochemical properties and geometries. However, the mechanical performance of traditional stretchable materials is often hindered by the deficiencies in their energy dissipation system, leading to lower fracture resistance and impeding their broader range of applications. Therefore, the synthesis of fracture-resistant stretchable materials has attracted great interest. This review comprehensively summarizes key design considerations for constructing fracture-resistant stretchable materials, examines their synthesis strategies to achieve elevated fracture energy, and highlights recent advancements in their potential applications.

Experimental Investigation of Water Vapor Concentration on Fracture Properties of Asphalt Concrete.

The effect of moisture on the fracture resistance of asphalt concrete is a significant concern in pavement engineering. To investigate the effect of the water vapor concentration on the fracture properties of asphalt concrete, this study first designed a humidity conditioning program at the relative humidity (RH) levels of 2%, 50%, 80%, and 100% for the three types of asphalt concrete mixtures (AC-13C, AC-20C, and AC-25C).The finite element model was developed to simulate the water vapor diffusion and determine the duration of the conditioning period. The semi-circular bending (SCB) test was then performed at varying temperatures of 5 °C, 15 °C, and 25 °C to evaluate the fracture energy and tensile strength of the humidity-conditioned specimens. The test results showed that the increasing temperature and the RH levels resulted in a lower peak load but greater displacement of the mixtures. Both the fracture energy and tensile strength tended to diminish with the rising temperature. It was also found that moisture had a significant effect on the tensile strength and fracture energy of asphalt concrete. Specifically, as the RH level increased from 2% to 100% (i.e., the water vapor concentration rose from 0.35 g/m3 to 17.27 g/m3), the tensile strength of the three types of mixtures was reduced by 34.84% on average, which revealed that the water vapor led to the loss of adhesion and cohesion within the mixture. The genetic expression programming (GEP) model was developed to quantify the effect of water vapor concentrations and temperature on the fracture indices.

Tensile Strength and Mode I Fracture Toughness of Polymer Concretes Enhanced with Glass Fibers and Metal Chips.

This study experimentally investigates the influence of metal chips and glass fibers on the mode I fracture toughness, energy absorption, and tensile strength of polymer concretes (PCs) manufactured by waste aggregates. A substantial portion of the materials employed in manufacturing and enhancing the tested polymer concrete are sourced from waste material. To achieve this, semi-circular bend (SCB) samples were fabricated, both with and without a central crack, to analyze the strength and fracture behavior of the composite specimens. The specimens incorporated varying weight percentages comprising 50 wt% coarse mineral aggregate, 25 wt% fine mineral aggregate, and 25 wt% epoxy resin. Metal chips and glass fibers were introduced at 2, 4, and 8 wt% of the PC material to enhance its mechanical response. Subsequently, the specimens underwent 3-point bending tests to obtain tensile strength, mode I fracture toughness, and energy absorption up to failure. The findings revealed that adding 4% brass chips along with 4% glass fibers significantly enhanced energy absorption (by a factor of 3.8). However, using 4% glass fibers alone improved it even more (by a factor of 10.5). According to the results, glass fibers have a greater impact than brass chips. Introducing 8% glass fibers enhanced the fracture energy by 92%. However, in unfilled samples, aggregate fracture and separation hindered crack propagation, and filled samples presented added barriers, resulting in multiple-site cracking.

Effect of Fiber Content on Mechanical Properties of Fiber-Reinforced CGF All-Solid-Waste Binder-Solidified Soil.

In order to realize the resource utilization of solid waste and improve the tensile strength and toughness of soil, CCR-GGBS-FA all-solid-waste binder (CGF) composed of general industrial solid waste calcium carbide residue (CCR), ground granulated blast furnace slag (GGBS) and fly ash (FA) was used instead of cement and combined with polypropylene fiber to strengthen the silty soil taken from Dongying City, China. An unconfined compressive strength test (UCS test) and a uniaxial tensile test (UT test) were carried out on 10 groups of samples with five different fiber contents to uncover the effect of fiber content on tensile and compressive properties, and the reinforcement mechanism was studied using a scanning electron microscopy (SEM) test. The test results show that the unconfined compressive strength, the uniaxial tensile strength, the deformation modulus, the tensile modulus, the fracture energy and the residual strength of fiber-reinforced CGF-solidified soil are significantly improved compared with nonfiber-solidified soil. The compressive strength and the tensile strength of polypropylene-fiber-reinforced CGF-solidified soil reach the maximum value when the fiber content is 0.25%, as the unconfined compressive strength and the tensile strength are 3985.7 kPa and 905.9 kPa, respectively, which are 116.60% and 186.16% higher than those of nonfiber-solidified soil, respectively. The macro-micro tests identify that the hydration products generated by CGF improve the compactness through gelling and filling in solidified soil, and the fiber enhances the resistance to deformation by bridging and forming a three-dimensional network structure. The addition of fiber effectively improves the toughness and stiffness of solidified soil and makes the failure mode of CGF-solidified soil transition from typical brittle failure to plastic failure. The research results can provide a theoretical basis for the application of fiber-reinforced CGF-solidified soil in practical engineering.

Smoothed particle hydrodynamics implementation to enhance vertebral fracture finite element model in a cervical spine segment under compression.

Spinal cord injuries (SCIs) can arise from compression loading when a vertebra fractures and bone fragments are pushed into the spinal canal. Experimental studies have demonstrated the importance of both fracture initiation and post-fracture response in the investigation of vertebral fractures and spinal canal occlusion resulting from compression. Finite element models, such as the Global Human Body Models Consortium (GHBMC) model, focused on predicting the initiation location of fractures using element erosion to model hard tissue fracture. However, the element erosion method resulted in a loss of material and structural support during compression, which limited the ability of the model to predict the post-fracture response. The current study aimed to improve the post-fracture response by combining strain-based element erosion with smoothed particle hydrodynamics (SPH) to preserve the volume of the trabecular bone during compression fracture. The proposed implementation was evaluated using a model comprising two functional spinal units (FSUs) (C5-C6-C7) extracted from the GHBMC 50th percentile male model, and loaded under central compression. The original and enhanced models were compared to experimental force-displacement data and measured occlusion of the spinal canal. The enhanced model with SPH improved the shape and magnitude of the force-displacement response to be in good agreement with the experimental data. In contrast to the original model, the enhanced SPH model demonstrated occlusion on the same order of magnitude as reported in the experiments. The SPH implementation improved the post-fracture response by representing the damaged material post-fracture, providing structural support throughout compression loading and material flow leading to occlusion.