Fracture Toughness of Periodic Beam Lattices
Gergely Molnár, Julien Réthoré
The study tackles the challenge of accurately modeling fracture behavior in beam lattices, which is essential for designing robust architected materials. Our research focuses on evaluating how the lattice's microstructure and material properties affect fracture toughness. We employed finite element simulations based on the Euler-Bernoulli beam theory to investigate crack propagation, using a failure criterion that initiates beam fracture when maximum axial stress exceeds critical strength. Building on observations from these simulations, we developed a multi-phase-field fracture model with Cosserat elasticity to integrate consistent toughness characteristics into a comprehensive framework for lattice design. This model was validated through experimental tests, ensuring a close match between theoretical predictions and physical reality. Our findings reveal that the energy release rate remains relatively stable during crack propagation, underscoring its reliability as a measure of the toughness of periodic lattice structures. We discovered that toughness is predominantly influenced by beam height and material properties such as tensile strength and Young's modulus, while slenderness has minimal impact. Additionally, cracks were observed to preferentially propagate along the lattice's structural directions due to stress localization effects, highlighting the importance of the microstructure in fracture behavior. The implications of this research are significant, suggesting that improved modeling of fracture in lattice structures can enhance material design reliability and optimization. This study bridges the gap between theoretical models and real-world applications, providing valuable insights for the development of advanced materials with tailored fracture properties.
Mechanics of engineering. Applied mechanics
Impact of pH and chloride content on the biodegradation of magnesium alloys for medical implants: An in vitro and phase-field study
S. Kovacevic, W. Ali, T. K. Mandal
et al.
The individual contributions of pH and chloride concentration to the corrosion kinetics of bioabsorbable magnesium (Mg) alloys remain unresolved despite their significant roles as driving factors in Mg corrosion. This study demonstrates and quantifies hitherto unknown separate effects of pH and chloride content on the corrosion of Mg alloys pertinent to biomedical implant applications. The experimental setup designed for this purpose enables the quantification of the dependence of corrosion on pH and chloride concentration. The in vitro tests conclusively demonstrate that variations in chloride concentration, relevant to biomedical applications, have a negligible effect on corrosion kinetics. The findings identify pH as a critical factor in the corrosion of bioabsorbable Mg alloys. A variationally consistent phase-field model is developed for assessing the degradation of Mg alloys in biological fluids. The model accurately predicts the corrosion performance of Mg alloys observed during the experiments, including their dependence on pH and chloride concentration. The capability of the framework to account for mechano-chemical effects during corrosion is demonstrated in practical orthopaedic applications considering bioabsorbable Mg alloy implants for bone fracture fixation and porous scaffolds for bone tissue engineering. The strategy has the potential to assess the in vitro and in vivo service life of bioabsorbable Mg-based biomedical devices.
An infection-responsive collagen-based wet-spun textile fibre for wound monitoring
Jonathon Gorman, Charles Brooker, Xinyu Li
et al.
Wound infections are a significant clinical and socioeconomic challenge, contributing to delayed healing and increased wound chronicity. To enable early infection detection and inform therapeutic decisions, this study investigated the design of pH-responsive collagen fibres using a scalable wet spinning process, evaluating product suitability for textile dressings and resorbable sutures. Type I collagen was chemically functionalised with 4-vinylbenzyl chloride, enabling UV-induced crosslinking and yielding mechanically robust fibres. Bromothymol blue, a halochromic dye responsive to pH changes, was incorporated via drop-casting to impart visual infection-responsive colour change. Gravimetric analysis and Fourier Transform Infrared Spectroscopy confirmed high dye loading, whereby a Loading Efficiency of 99+/-3 wt.% was achieved. The fibres exhibited controlled swelling in aqueous environments (Swelling Ratio: 323+/-79 - 492+/-73 wt.%) and remarkable wet-state Ultimate Tensile Strength (UTS: 12+/-3 - 15+/-7 MPa), while up to ca. 30 wt.% of their initial crosslinked mass was retained after 24 hours in a collagenase-rich buffer (pH 7.4, 37°C, 2 CDU) and ethanol series dehydration. Importantly, distinct and reversible colour transitions were observed between acidic (pH 5) and alkaline (pH 8) environments, with up to 88 wt.% dye retention following 72-hour incubation. The fibres were successfully processed into woven dressing prototypes and demonstrated knotting ability suitable for suture applications. Overall, these wet-spun collagen fibres integrate infection-responsive capability, biodegradability, and scalable fabrication, representing a promising platform for smart wound dressings and resorbable sutures.
en
physics.med-ph, physics.app-ph
Diagnosis of Pulmonary Hypertension by Integrating Multimodal Data with a Hybrid Graph Convolutional and Transformer Network
Fubao Zhu, Yang Zhang, Gengmin Liang
et al.
Early and accurate diagnosis of pulmonary hypertension (PH) is essential for optimal patient management. Differentiating between pre-capillary and post-capillary PH is critical for guiding treatment decisions. This study develops and validates a deep learning-based diagnostic model for PH, designed to classify patients as non-PH, pre-capillary PH, or post-capillary PH. This retrospective study analyzed data from 204 patients (112 with pre-capillary PH, 32 with post-capillary PH, and 60 non-PH controls) at the First Affiliated Hospital of Nanjing Medical University. Diagnoses were confirmed through right heart catheterization. We selected 6 samples from each category for the test set (18 samples, 10%), with the remaining 186 samples used for the training set. This process was repeated 35 times for testing. This paper proposes a deep learning model that combines Graph convolutional networks (GCN), Convolutional neural networks (CNN), and Transformers. The model was developed to process multimodal data, including short-axis (SAX) sequences, four-chamber (4CH) sequences, and clinical parameters. Our model achieved a performance of Area under the receiver operating characteristic curve (AUC) = 0.81 +- 0.06(standard deviation) and Accuracy (ACC) = 0.73 +- 0.06 on the test set. The discriminative abilities were as follows: non-PH subjects (AUC = 0.74 +- 0.11), pre-capillary PH (AUC = 0.86 +- 0.06), and post-capillary PH (AUC = 0.83 +- 0.10). It has the potential to support clinical decision-making by effectively integrating multimodal data to assist physicians in making accurate and timely diagnoses.
Expressing general constitutive models in FEniCSx using external operators and algorithmic automatic differentiation
Andrey Latyshev, Jérémy Bleyer, Corrado Maurini
et al.
Many problems in solid mechanics involve general and non-trivial constitutive models that are difficult to express in variational form. Consequently, it can be challenging to define these problems in automated finite element solvers, such as the FEniCS Project, that use domain-specific languages specifically designed for writing variational forms. In this article, we describe a methodology and software framework for FEniCSx / DOLFINx that enables the expression of constitutive models in nearly any general programming language. We demonstrate our approach on two solid mechanics problems; the first is a simple von Mises elastoplastic model with isotropic hardening implemented with Numba, and the second a Mohr-Coulomb elastoplastic model with apex smoothing implemented with JAX. In the latter case we show that by leveraging JAX's algorithmic automatic differentiation transformations we can avoid error-prone manual differentiation of the terms necessary to resolve the constitutive model. We show extensive numerical results, including Taylor remainder testing, that verify the correctness of our implementation. The software framework and fully documented examples are available as supplementary material under the LGPLv3 or later license.
Mechanics of engineering. Applied mechanics
Facile One Pot Synthesis of Hybrid Core-Shell Silica-Based Sensors for Live Imaging of Dissolved Oxygen and Hypoxia Mapping in 3D cell models
Helena Iuele, Stefania Forciniti, Valentina Onesto
et al.
Fluorescence imaging allows for non-invasively visualizing and measuring key physiological parameters like pH and dissolved oxygen. In our work, we created two ratiometric fluorescent microsensors designed for accurately tracking dissolved oxygen levels in 3D cell cultures. We developed a simple and cost-effective method to produce hybrid core-shell silica microparticles that are biocompatible and versatile. These sensors incorporate oxygen-sensitive probes (Ru(dpp) or PtOEP) and reference dyes (RBITC or A647 NHS-Ester). SEM analysis confirmed efficient loading and distribution of the sensing dye on the outer shell. Fluorimetric and CLSM tests demonstrated the sensors' reversibility and high sensitivity to oxygen, even when integrated into 3D scaffolds. Aging and bleaching experiments validated the stability of our hybrid core-shell silica microsensors for 3D monitoring. The Ru(dpp)-RBITC microparticles showed the most promising performance, especially in a pancreatic cancer model using alginate microgels. By employing computational segmentation, we generated 3D oxygen maps during live cell imaging, revealing oxygen gradients in the extracellular matrix and indicating a significant decrease in oxygen levels characteristic of solid tumors. Notably, after 12 hours, the oxygen concentration dropped to a hypoxic level of PO2 2.7 +/- 0.1%.
en
physics.med-ph, physics.chem-ph
Mesh Density and Geodesic Tortuosity in Planar Triangular Tesselations Devoted to Fracture Mechanics
Joffrey Lhonneur, Nawfal Blal, Yann Monerie
In fracture mechanics, the mesh sensitivity is a key issue. It is particularly true concerning cohesive volumetric finite element methods in which the crack path and the overall behavior are respectively influenced by the mesh topology and the mesh density. Poisson-Delaunay tessellations parameters, including the edge length distributions, were widely studied in the literature but very few works concern the mesh density and topology in Delaunay type meshes suitable for finite element simulations, which is of crucial interest for practical use. Starting from previous results concerning Poisson-Delaunay tessellations and studying in detail the Lloyd relaxation algorithm, we propose estimates for the probability density functions of the edge length and triangle top angles sets. These estimates depend both on the intensity of the underlying point process and on an efficiency index associated to the global quality of the mesh. The global and local accuracies of these estimates are checked for various standard mesh generators. Finally the mesh density and geodesic tortuosity are estimated for standard random or structured triangular meshes typically used in finite element simulations. These results provide practical formulas to estimate bias introduced by the mesh density and topology on the results of cohesive-volumetric finite element simulations.
Mechanics of engineering. Applied mechanics
An explicit dynamics framework suited to highly non-smooth interface behaviors
David Dureisseix, Paul Larousse, Anthony Gravouil
et al.
Dynamic systems, and in particular mechanical structures, may be subjected to non-smooth loadings such as impacts or shocks. Moreover, their behavior itself may exhibit more or less non-smooth evolutions, as when fracture occurs. Therefore, robust simulation models are of interest to capture such behaviors. A particular focus is made herein on time-stepping explicit dynamics schemes to allow efficient simulations, and non-smoothness is embedded within the discrete resolution model, so that robust simulations can be obtained, with a minimum number of numerical parameters. The original contributions of this article lie in the way the non-smooth behavior is formulated to be embedded in an explicit dynamics framework. This study focuses on the solver for dynamics with non-smooth interface behavior, rather than on the behavior models themselves. The applications concern non-smooth interface behaviors at macroscopic scale, between displacement jump on the 2D interface surface with no thickness, and interfacial force distributions acting on the bodies apart the interface. The proposed test cases which can serve as benchmarks for simulation codes, concern in a first step contact and perfectly plastic interface behavior (for illustrative purpose, on a 0D example). The last numerical test deals with contact, friction, fracture and adhesion for an extrinsic perfectly brittle interface behavior, to exemplify the feasibility on a full 3D finite element model.
Mechanics of engineering. Applied mechanics
Accounting for the mechanical response of the cell membrane during the uptake of random nanoparticles
Sarah Iaquinta, Shahram Khazaie, Frédéric Jacquemin
et al.
In order to improve the efficiency of the delivery of cancer treatments to cancer cells, the cellular uptake of nanoparticles (NPs), used as drug delivery systems, is numerically investigated through a mechanical approach. The objective is to optimize the NP's mechanical and geometrical properties to enhance their entry into cancer cells while avoiding benign ones. In previous studies, these properties are modeled as constant during the process of cellular uptake. However, recent observations of the displacement of the membrane's constituents towards the region in the cell membrane where the uptake of the NPs takes place show that the mechanical properties of the membrane vary during this process. Reason for writing The important contribution of adhesion to the wrapping process is already well documented in literature. It is therefore crucial to model this parameter properly as the conclusions made with a constant adhesion model may not be accurate compared to reality. Methodology Based on the existing knowledge on the reaction of membrane constituents to interaction with NPs, a 3-parameter sigmoidal function, accounting for the delay, amplitude, and speed of the reaction, has been used to model the evolution of adhesion. A variance-based sensitivity analysis has then been performed in order to quantify the influence of these parameters on the outputs of the model. Results It was found that the introduction of a variable adhesion tends to alter the predictions of endocytosis of NPs. The contribution of the amplitude and delay is respectively 0.32 and 0.43 times as important as that of the NP's aspect ratio, which is the prominent parameter. The influence of the slope of the transition is the least important parameter and does not appear to contribute to endocytosis. Implications Hence, models of the cellular uptake of NPs should use a variable, instead of constant, adhesion in order a representative as possible of the behavior of the cell membrane. The predictions are different from those obtained using a model with constant adhesion.
Mechanics of engineering. Applied mechanics
Noninvasive Estimation of Mean Pulmonary Artery Pressure Using MRI, Computer Models, and Machine Learning
Michal K. Grzeszczyk, Tadeusz Satlawa, Angela Lungu
et al.
Pulmonary Hypertension (PH) is a severe disease characterized by an elevated pulmonary artery pressure. The gold standard for PH diagnosis is measurement of mean Pulmonary Artery Pressure (mPAP) during an invasive Right Heart Catheterization. In this paper, we investigate noninvasive approach to PH detection utilizing Magnetic Resonance Imaging, Computer Models and Machine Learning. We show using the ablation study, that physics-informed feature engineering based on models of blood circulation increases the performance of Gradient Boosting Decision Trees-based algorithms for classification of PH and regression of values of mPAP. We compare results of regression (with thresholding of estimated mPAP) and classification and demonstrate that metrics achieved in both experiments are comparable. The predicted mPAP values are more informative to the physicians than the probability of PH returned by classification models. They provide the intuitive explanation of the outcome of the machine learning model (clinicians are accustomed to the mPAP metric, contrary to the PH probability).
FIM: A fatigued-injured muscle model based on the sliding filament theory
Fatemeh Jalali, Mohammad Ali Nazari, Arash Bahrami
et al.
Skeletal muscle modeling has a vital role in movement studies and the development of therapeutic approaches. In the current study, a Huxley-based model for skeletal muscle is proposed, which demonstrates the impact of impairments in muscle characteristics. This model focuses on three identified ions: H + , inorganic phosphate Pi and Ca 2+. Modifications are made to actin-myosin attachment and detachment rates to study the effects of H + and Pi. Additionally, an activation coefficient is included to represent the role of calcium ions interacting with troponin, highlighting the importance of Ca 2+. It is found that maximum isometric muscle force decreases by 9.5% due to a reduction in pH from 7.4 to 6.5 and by 47.5% in case of the combination of a reduction in pH and an increase of Pi concentration up to 30 mM, respectively. Then the force decline caused by a fall in the active calcium ions is studied. When only 15% of the total calcium in the myofibrillar space is able to interact with troponin, up to 80% force drop is anticipated by the model. The proposed fatigued-injured muscle model is useful to study the effect of various shortening velocities and initial muscletendon lengths on muscle force; in addition, the benefits of the model go beyond predicting the force in different conditions as it can also predict muscle stiffness and power. The power and stiffness decrease by 40% and 6.5%, respectively, due to the pH reduction, and the simultaneous accumulation of H + and Pi leads to a 50% and 18% drop in power and stiffness.
Optimization of a dynamic absorber with nonlinear stiffness and damping for the vibration control of a floating offshore wind turbine toy model
Pierre-Olivier Mattei, Renaud Côte
Passive vibration mitigation of offshore wind turbines using nonlinear absorbers or nonlinear energy sinks has started to receive attention in the literature. In most cases, little attention has been paid to the possibility of detached resonances that occur when the nonlinear energy sink is attached to the linear system describing the wind turbine. Sea motions that alter the initial conditions of the floating offshore wind turbine may cause the nonlinear energy sink to operate at one or more detached resonances, completely negating its ability to control turbine vibration. In this paper, we are interested in optimizing the parameters of a nonlinear energy sink with nonlinear stiffness and nonlinear viscous damping for vibration control of a toy model (e.g., a linear mass-spring-damper system) of a floating offshore wind turbine over its entire operating range. The mechanism of cancellation of the detached resonance is studied analytically under 1:1 resonance. It is shown that the nonlinear energy sink with properly tuned nonlinear viscous damping allows the complete elimination of undesired regimes and completely restores the absorber's ability to strongly limit the vibration of a floating offshore wind turbine over its entire forcing range. The results obtained over a wide range of parameters suggest that both the optimal nonlinear energy sink parameters (linear and nonlinear stiffness and nonlinear damping) and the damping of floating offshore wind turbine vibration depend on simple power laws of nonlinear energy sink mass and linear damping.
Mechanics of engineering. Applied mechanics
Thermal and energy analysis of DMTA tests
André Chrysochoos, Olivier Arnould
This paper investigates the suitability of the isothermal linear viscoelastic framework to describe the behavior of polymers observed during DMTA tests. A good interpretation of these tests is important because, in practice, they are used to construct master curves using the time-temperature superposition principle at small strain. These curves are then considered to predict the material behavior under experimentally unreachable thermal and/or loading frequency conditions. Currently, the DMTA protocol neglects the temperature variations induced by the deformation of polymers. We wonder if these temperature variations can have an influence on the measurement of dynamic moduli. To answer this question, quantitative infrared techniques were developed and used to assess small temperature variations of samples undergoing cyclic loadings during mechanical spectrometry tests. Thermal and mechanical data were used to quantify the viscous dissipated and the thermoelastic coupling energies that can be both associated with the hysteretic stress-strain response of polymers. Energy balances were then performed to quantify the relative importance of dissipative and thermoelastic coupling heat sources. From the energy standpoint, it is found that the thermoelastic energy rate was dozens of times higher than the dissipation. Especially at low frequencies, thermoelastic effects can have a greater influence on the loss modulus value than viscosity.
Mechanics of engineering. Applied mechanics
Revealing systematic errors in hole drilling measurements through a calibration bench: the case of zero-depth data
Marco Beghini, Tommaso Grossi, Ciro Santus
et al.
An accurate estimation of the measurement error in the hole drilling method is needed to choose an appropriate level of regularization and to perform a sensitivity analysis on the stress results. The latest release of ASTM E837 standard for the hole drilling method includes a procedure aimed at estimatingthe standard deviation of the random error component on strain measurements, proposed by Schajer. Nevertheless, strain measurements are also affected to some extent by systematic errors which are not included in the estimation and need to be compensated. For example, an error in the rosette gage factor orin the identification of the zero-depth datum systematically affects all strain measurements in a strongly correlated fashion. This paper describes a calibration bench, designed to superimpose a reference bending stress distribution on a given specimen while simultaneously performing a hole drilling measurement.Since the reference solution is known a priori and shares the measurement instrumentation, the hole geometry and the stepping process with the actual residual stress distribution, the bench provides the user with a direct validation of the obtained accuracy. In addition, strategies aimed at compensating systematicerrors can be tested on the reference solution and then applied on the residual stress evaluation. The imperfect hole geometry and drilling alignment are proven to cause a significant underestimation of stresses near the surface, as they lead to an incorrect identification of the zero-depth datum. It is shown that this effect can be corrected through the proposed calibration bench.
Mechanics of engineering. Applied mechanics
Solving viscoelastic problems with a Laplace transform approach supplanted by ARX models, suggesting a way to upgrade Finite Element or spectral codes
Stéphane André, Camille Noûs
Finite Element codes used for solving the mechanical equilibrium equations in transient problems associated to (time-dependent) viscoelastic media generally relies on time-discretized versions of the selected constitutive law. Recent concerns about the use of non-integer differential equations to describe viscoelasticity or well-founded ideas based upon the use of a behavior's law directly derived from Dynamic Mechanical Analysis (DMA) experiments in frequency domain, could make the Laplace domain approach particularly attractive if embedded in a time discretized scheme. Based upon the inversion of Laplace transforms, this paper shows that this aim is not only possible but also gives rise to a simple algorithm having good performances in terms of computation times and precision. Such an approach, which fully relies on the Laplace-defined Behavioral Transfer Function (LTBF) can be promoted if it uses AutoRegressive with eXogeneous input parametric models perfectly substitutable to the real LTBF. They avoid the hitherto prohibitive pitfall of having to store all past data in the computer's memory while maintaining an equal computation precision.
Mechanics of engineering. Applied mechanics
An energy approach to asymptotic, higher-order, linear homogenization
Basile Audoly, Claire Lestringant
A higher-order homogenization method for linear elastic structures is proposed. While most existing approaches to homogenization start from the equations of equilibrium, the proposed one works at the energy level. We start from an energy functional depending on microscopic degrees of freedom on the one hand and on macroscopic variables on the other hand; the homogenized energy functional is derived by relaxing the microscopic degrees of freedom and applying a formal two-scale expansion. This method delivers the energy functional of the homogenized model directly, including boundary terms that have not been discussed in previous work. Our method is formulated in a generic setting which makes it applicable to a variety of geometries in dimension 1, 2 or 3, and without any particular assumption on material symmetry. An implementation using a symbolic calculation language is proposed and it is distributed as an open-source library. Simple illustrations to elastic trusses having pre-stress or graded elastic properties are presented. The approach is presented in the context of discrete elastic structures and the connection with previous work on the higher-order homogenization of period continua is discussed.
Mechanics of engineering. Applied mechanics
Capture Agent Free Biosensing using Porous Silicon Arrays and Machine Learning
Simon J. Ward, Tengfei Cao, Xiang Zhou
et al.
Biosensors are an essential tool for medical diagnostics, environmental monitoring and food safety. Typically, biosensors are designed to detect specific analytes through functionalization with the appropriate capture agents. However, the use of capture agents limits the number of analytes that can be simultaneously detected and reduces the robustness of the biosensor. In this work, we report a versatile, capture agent free biosensor platform based on an array of porous silicon (PSi) thin films, which has the potential to robustly detect a wide variety of analytes based on their physical and chemical properties in the nanoscale porous media. The ability of this system to reproducibly classify, quantify, and discriminate three proteins is demonstrated to concentrations down to at least 0.02g/L (between 300nM and 450nM) by utilizing PSi array elements with a unique combination of pore size and buffer pH, employing linear discriminant analysis for dimensionality reduction, and using support vector machines as a classifier. This approach represents a significant step towards a low cost, simple and robust biosensor platform that is able to detect a vast range of biomolecules.
en
physics.med-ph, cond-mat.mtrl-sci
A simple extension of FFT-based methods to strain gradient loadings - Application to the homogenization of beams and plates with linear and non-linear behaviors
Lionel Gélébart
Because of their simplicity, efficiency and ability for parallelism, FFT-based methods are very attractive in the context of numerical periodic homogenization, especially when compared to standard FE codes used in the same context. They allow applying to a unit-cell a uniform average strain with a periodic strain fluctuation that is an unknown quantity. Solving the problem allows to evaluate the complete stress-strain fields. The present work proposes to extend the use of the method from uniform loadings (i.e. uniform applied strain) to strain gradient loadings (i.e. strain fields with a uniform strain gradient) while keeping the algorithm as simple as possible. The identification of a subset of strain gradient loadings allows for a minimally invasive modification of the iterative algorithm so that the implementation is straightforward. In spite of a reduced subset of 9 independent loadings among the 18 available, the second part of the paper demonstrates that it is enough for considering the homogenization of beams and plates. A first application validates the approach and compares it to another FFT-based method dedicated to the homogenization of plates. The second application concerns the homogenization of beams, for the first time considered (to author's knowledge) with an FFT-based solver. The method applies to different beam cross-sections and the proposition of using composite voxels drastically improves the numerical solution when the beam cross-section is not conform with the spatial discretization, especially for torsion loading. As a result, the massively parallel AMITEX_FFTP code has been slightly modified and now offers a new functionality, allowing the users to prescribe torsions and flexions to beam or plate heterogeneous unit-cells.
Mechanics of engineering. Applied mechanics
Effects of the microstructural uncertainties on the poroelastic and the diffusive properties of mortar
Adrien Socié, Yann Monerie, Frédéric Péralès
The assessment of the durability of civil engineering structures subjected to several chemical attacks requires the development of chemo-poromechanical models. The mechanical and chemical degradations depend on several factors such as the initial composition of the porous medium. A multi-scale model is used to incorporate the multi-level microstructural properties of the mortar material. The present paper aims to study the effect of morphological and local material properties uncertainties on the poroelastic and diffusive properties of mortar estimated with the help of analytical homogenization. At first, the proposed model is validated for different cement paste and mortar by comparison to experimental results and micromechanical models. Secondly, based on a literature study, sensitivity and uncertainty analysis have been developed to assess the stochastic predictions of the multi-scale model. The main result highlights the predominant impact of the cement matrix phases (C-S-H) and interfacial transition area at the mortar scale. Furthermore, the sensitive analysis underlines that the material properties induce more variability than the volume fraction.
Mechanics of engineering. Applied mechanics
A damage criterion based on energy balance for isotropic cohesive zone model
André Chrysochoos, Loïc Daridon, Mathieu Renouf
The objective of this paper is to present an energy damage criterion for cohesive zone models (CZM) within the framework of the non-linear thermodynamics of irreversible processes (TIP). An isotropic elastic damageable material is considered for isothermal transformations. Damage is then the only irreversible effect accompanying the deformation process and this mechanism is supposed to be fully dissipative. Once a separation law and a damage state variable have been chosen, the paper shows that the damage criterion can be automatically derived from the energy balance. From this observation, a CZM is derived for a given choice of traction-separation law and damage state variable and the quality of its numerical predictions is analyzed using an experimental benchmark bending test extracted from literature. Finally, damage, elastic and dissipated energy fields around the crack path are shown during this rupture test.
Mechanics of engineering. Applied mechanics