Damage-based Approach Research Articles

The ocean carbon sink enhances countries’ inclusive wealth and reduces the cost of national climate policies

Improving our understanding of future ocean carbon uptake requires a nuanced understanding of the value of the annual ocean sink. Here, we combine an abatement cost-based approach and a climate damage-based approach to assess the value of the annual ocean sink. The former shows that the aggregate cost of national climate policies could increase by up to USD 80 billion if the ocean carbon sink weakens by 10 percent. As a complementary perspective, the damage-based approach shows that the annual ocean carbon sink contributes between USD 300 billion and USD 2,332 billion to countries’ inclusive wealth. Despite the conceptual appeal of the damage-based approach for its potential insights into regional wealth redistribution, uncertainties in national social cost of carbon estimates make it less reliable than the abatement cost-based approach, which in turn provides more reliable estimates for a fiscal cost assessment of improved monitoring services of the ocean carbon sink.

Toughening of intrinsically brittle materials by inserting arrays of voids

The aim of the current paper is to find optimum arrangements of voids that are able to catch and trap all possible cracks that might originate from a free surface. The idea is to investigate whether it is possible to apply this crack trapping mechanism to enhance the fracture toughness of intrinsically brittle materials. In doing so, the void volume shall be as small as possible. The investigation applies the crack trajectory interpolation (CTI) method, which is a new, computationally efficient approach to approximate crack trajectories near a single void or stiff particle. Under the assumption of linear superposition, the CTI-method is extended to predict the crack trajectories near arrangements of voids. This is done for uniaxial and biaxial loading conditions. The investigation shows that a symmetrical arrangement of voids should be avoided, since cracks near the symmetry line can bypass the array. Staggered void arrangements provide better conditions for crack trapping. By using elliptical voids with an aspect ratio of 2 instead of circular voids, it is possible to achieve a higher crack trapping efficiency and a lower void volume. A damage-based approach is used to determine the improvements in fracture toughness due to crack trapping for various void arrangements. The Python code of the CTI method is presented in the Appendix of this work.

Fracture toughness improvement due to crack deflection and crack trapping by elliptical voids or particles

The paper investigates how voids and particles can be used to deflect and arrest cracks in order to enhance the failure stress and the fracture toughness of intrinsically brittle materials. This is done by investigating crack propagation near single elliptical voids and particles that are located in an elastic matrix material. The shapes of the inhomogeneities are varied, but their cross section is held constant. Uniaxial and biaxial loading conditions are considered and also the Young’s modulus ratio between particle and matrix material is varied. The crack trajectories near the material inhomogeneities are evaluated by applying a computationally very efficient approach, the crack trajectory interpolation (CTI) method, which has been introduced in an earlier work of the authors. With this method, critical distances are determined where an approaching crack runs into an elliptical void and gets trapped. Similarily, zones for crack arrest and crack deflection near stiff particles are found. Combinations of particles and voids are studied, too. A damage-based approach is used to investigate the improvements in failure stress and fracture toughness when a crack runs into a void. The results show that voids and particles that are elongated perpendicular to the crack plane are most useful for crack arrest. The trapping distances increase with increasing ellipticity of the inhomogeneities. However, the improvement in failure stress is highest for voids with moderate ellipticity. The results of this paper will be used to find optimum arrangements of voids or particle-void combinations for the design of structural components with increased fracture toughness.

A hybrid algorithm to solve a nonlinear inverse problem of boundary conditions and damage identification

In this communication we present a method exploiting displacement data measured at accessible parts of solid’s boundary, for the solution of boundary conditions and damage identification problems encountered in mechanics. Targeted applications are made of materials presenting a nonlinear mechanical behavior with damage-based approaches. A hybrid algorithm has been developed in order to identify the missing data by minimizing a gap-functional. It takes into account the incremental mechanical behavior of the material and the damage evolution inside the solid via the concept of piloting. An application on a solid made of mortar with synthetic measurements is presented to illustrate the efficiency and robustness of the algorithm.

A computational insight on damage-based constitutive modelling in femur mechanics

The present paper addresses femur failure mechanics, by numerically investigating the influence of brittle/ quasi-brittle bone constitutive description when combined with several failure criteria and different descriptions of bone ultimate parameters. Starting from computed tomography images of an experimentally-tested cadaveric femur, the bone geometry has been reconstructed through a semi-automatic segmentation procedure, and patient-specific material properties have been derived. Loading-induced loss of structural integrity has been simulated through a progressive thermodynamically-based damage model, by introducing different strain- and stress-based damage evolution laws. An in-house displacement-driven incremental approach has been implemented in a finite element framework to mimic the in-vitro experimental procedure. An energy-based regularization technique allowed to obtain results which are mesh independent and therefore physically meaningful. Depending on the adopted modelling strategy, significant differences in terms of yield and failure load, as well as in fracture patterns, have been numerically experienced. Comparisons between the proposed numerical results and the available experimental outcomes have been carried out. For the femur model herein analysed, an elastic quasi-brittle bone description combined with strain-based failure criteria seems to be more effective in predicting the mechanical behaviour up to the fracture. Presented mesh-independent results therefore contribute to justify the need of damage-based approaches for predicting in an effective way failure mechanisms of femurs.

A Damage-Based Approach to Determine the Dynamic Increase Factor for Concrete

The failure strength of cementitious materials is often observed to increase significantly under dynamic loading conditions. A physical mechanism believed to be a significant driver of this rate sensitivity is the cracking and fragmentation process in these brittle or quasi-brittle materials. While high-speed photography can be used to make in-situ observations of specimens under dynamic loading, this optical technique is incapable of identifying the onset of strain localization and major unstable crack growth within opaque materials. In this study, the non-destructive high-resolution 3D imaging capabilities of X-Ray micro-computed tomography are implemented to analyze the state of damage within concrete specimens subjected to controlled high strain-rate loading. A modified Kolsky compression bar coupled with a momentum trapping technique was used to achieve dynamic constant strain-rate deformation before rapid unloading at a predetermined stress level allowing recovery of specimens for internal damage analysis. Results from this novel experimental technique reveal that, for the two materials studied here, a total of 38% to 68% of the dynamic strength increase occurs after the onset of major crack propagation. This result indicates that the dynamic increase factor calculated using the dynamic peak failure strength in these materials may include significant contributions from the fragmentation process, which is not representative of the intrinsic material properties. In light of these experimental results, a new logistic regression-based method is proposed to obtain the dynamic damage initiation stress for high-strength concrete and a more accurate definition of the dynamic increase factor is proposed.

A Nonlinear Statistical Damage Constitutive Model for Porous Rocks

In the current paper, the deformation behaviours of rocks during compression are studied by testing 10 groups of sandstone samples with different porosity characteristics. According to the energy theory, the rock material was divided into two parts: solid skeleton and voids. A statistical damage‐based approach was adopted to establish a nonlinear statistical damage constitutive model. The validity of the statistical damage constitutive model is verified by the test data. The statistical damage constitutive model performs well in each stage of rock compression before failure. For different types of rocks, different confining pressures, and different water contents, the statistical damage constitutive model fits well. This model can be applied to most types of rocks and in most engineering environments.

Damage-Based Approach for bimodular and anisotropic materials

espanolEste trabajo pretende presentar el desarrollo de una formulacion basada en Mecanica de Danos para tratar con medios elasticos que presentan comportamientos mecanicos diferentes en regimenes de tension y compresion, asi como algun grado de anisotropia cuando se producen procesos de dano. En primer lugar, se revisa una formulacion para medios elasticos bimodulares y anisotropicos. Con el fin de tener en cuenta los procesos de dano en el material, se proponen algunas mejoras asi como la definicion de un hiperplano para dividir el espacio de deformacion para tratar con materiales bimodulares. Ademas, los tensores anisotropicos de cuarto orden son solicitados por la formulacion dependiendo de la clase de anisotropia. Poco despues, se describen dos modelos constitutivos de danos escritos en concordancia con la formulacion propuesta en este trabajo. Finalmente, se muestra que la formulacion propuesta es una forma facil de escribir y comprender los complejos modelos de dano. EnglishThis work intends to present the development of a formulation based on Continuum Damage Mechanics to deal with elastic media introducing different mechanical behaviors in tension and compression regimes as well as some anisotropy degree when damage processes take place. First of all, a formulation for bimodular and anisotropic elastic media is reviewed. To take into account the damage processes in the material, some improvements are proposed as well as the definition of a hyperplane in order to divide the strain space to deal with bimodular materials. Besides, fourth-order anisotropic tensors are requested by the formulation depending on the class of anisotropy. Soon after, two models of constitutive damage written accordingly with the formulation proposed in this work are described. Finally, it is shown that the proposed formulation is an easy way to write and to understand complex constitutive damage models.

Simultaneous extraction of tensile and shear interactions at interfaces

A simple beam analysis is developed that accounts for the tensile and shear interactions between the surfaces of two beams that have been brought into contact. The generally coupled differential equations for the relative normal and tangential displacements between the interacting surfaces and the normal and shear components of the traction between the two surfaces are decoupled when a balance condition involving the bending stiffness and height of each beam is satisfied. This condition also allows the normal and shear components of the J-integral and the crack tip displacement to be obtained from measurements of the applied loads along with load point displacement and rotation of each beam. As a result, the derivative of each component of the J-integral with respect to its associated crack tip displacement simultaneously provides both the normal and shear traction–separation relations at any value of the mode-mix without invoking any assumption on the particular form. As an application of this method, the normal and shear traction–separation relations for a silicon/epoxy interface were determined over nominal mode-mixes ranging from −53° to 87.5° using non-symmetric end-loaded split (ELS) and end-notched flexure (ENF) specimens. It is found that many of the assumptions made previously in developing traction–separation relations based on potential or damage-based approaches do not apply to this particular interface, which should motivate future theoretical developments.

Modelling bond of GFRP rebar and concrete

The structural performance of concrete structures reinforced using glass-fiber-reinforced-polymer (GFRP) rebars is sometime compromised by debonding failure. For better analyzing the GFRP bar-concrete bond behavior, this study presents two damage-based approaches for assessing the bond damage evolution. One is the secant modulus-based model and other is exponential damage model. Using the exponential damage approach, a simplified analytical model based on only one curve fitting parameter was developed to predict the bond stress-slip relationship. Then, a 3D finite element (FE) model was developed and both proposed damage-based approaches were implemented, to simulate the GFRP bond behavior. The FE model considers the nonlinear behavior of the concrete and the GFRP bar-concrete interface. The analytical and numerical predictions of the GFRP bar-concrete bond behavior are validated by comparing with the relevant results of an experimental program focused on quasi-static pullout tests. At the end, a parametric study was carried out to numerically assess the influence of some critical parameters on the bond behavior.

A damage-based approach for the fatigue design of composite structures

The paper illustrates a fatigue design strategy, based on the physics of the damage evolution, under development by the Composite Group at DTG-University of Padova. After a brief introduction, where the motivations of the work are analysed, examples of damage mechanisms at the microscopic scale are discussed. Then the procedures for the quantitative description of these mechanisms are illustrated.

Maritime shipping and emissions: A three-layered, damage-based approach

Policy emphasis in ship design must be shifted away from global and idealized towards regional based and realistic vessel operating conditions. The present approach to reducing shipping emissions through technical standards tends to neglect how damages and abatement opportunities vary according to location and operational conditions. Since environmental policy originates in damages relating to ecosystems and jurisdictions, a three-layered approach to vessel emissions is intuitive and practical. Here, we suggest associating damages and policies with ports, coastal areas possibly defined as Emission Control Areas (ECA) as in the North Sea and the Baltic, and open seas globally. This approach offers important practical opportunities: in ports, clean fuels or even electrification is possible; in ECAs, cleaner fuels and penalties for damaging fuels are important, but so is vessel handling, such as speeds and utilization. Globally we argue that it may be desirable to allow burning very dirty fuels at high seas, due to the cost advantages, the climate cooling benefits, and the limited ecosystem impacts. We quantify the benefits and cost savings from reforming current IMO and other approaches towards environmental management with a three-layered approach, and argue it is feasible and worth considering.

Fatigue Damage for Sweep-Sine and Random Accelerated Vibration Testing

The vibration testing of components in the automotive industry requires long testing times and the use of expensive facilities. To shorten these testing times an accelerated vibration-testing approach is usually applied. This research tries to shorten these testing times by considering the parameters that define vibration-testing techniques. With special attention to the excitation types sweep-sine and random, a damage-based approach is applied. The phenomenon of fatigue damage is closely observed from the frequency-domain point of view but also by considering the relationship between the time and the frequency domains. The Palmgren-Miner cumulative rule is applied to calculate the fatigue life. Two case studies of measured responses are used to compare the times to failure. The results show that proposed predictions can be used to compare different testing techniques, but they are not so accurate when predicting the actual times to failure.

A Unified Theoretical Model for the Monotonic and Cyclic Response of FRP Strips Glued to Concrete

The mechanical behavior of the adhesive interface between the fiber-reinforced polymer (FRP) strip and the concrete substrate often controls the response of FRP-strengthened reinforced concrete (RC) members. Plenty of studies devoted to understanding the mechanical behavior of FRP strips glued to concrete are currently available in the scientific literature. However, they are mainly focused on the response under monotonic actions, which is certainly relevant in a wide class of practical applications. Conversely, few contributions are currently available to better understand the response of FRP-to-concrete interfaces under cyclic actions, such as those deriving from either seismic excitations or traffic loads. This paper presents a unified numerical approach to simulate both monotonic and cyclic behavior of FRP plates glued on quasi-brittle substrates like those made of concrete. Particularly, a damage-based approach is proposed to simulate the fracture behavior of FRP-to-concrete joints under loading/unloading cycling tests. The model is formulated within the general framework of Fracture Mechanics and is based on assuming that fracture at the FRP-to-concrete interface develops in (pure shear) mode II, as widely accepted in similar problems. Two alternative expressions of the bond-slip behavior are herein considered and their preliminary validation is finally proposed. The proposed results highlight the difference between the monotonic and the cyclic response; particularly, they show that the latter is characterized by a significantly lower force and displacement capacity.

Damage-Based Seismic Performance Evaluation of Reinforced Concrete Frames

A damage-based approach for the performance-based seismic assessment of reinforced concrete frame structures is proposed. A new methodology for structural damage assessment is developed that utilizes response information at the material level in each section fiber. The concept of the damage evolution is analyzed at the section level and the computed damage is calibrated with observed experimental data. The material level damage parameter is combined at the element, story and structural level through the use of weighting factors. The damage model is used to compare the performance of two typical 12-story frames that have been designed for different seismic requirements. A series of nonlinear time history analyses is carried out to extract demand measures which are then expressed as damage indices using the proposed model. A probabilistic approach is finally used to quantify the expected seismic performance of the building.

Strain and Damage-Based Analytical Methods to Determine the Kachanov–Rabotnov Tertiary Creep-Damage Constants

In the power generation industry, the goal of increased gas turbine efficiency has led to increased operating temperatures and pressures necessitating nickel-base superalloy components. Under these conditions, the tertiary creep regime can become the dominant form of creep deformation. In response, the classical Kachanov–Rabotnov coupled creep-damage constitutive model is often used to predict the creep deformation and damage of Ni-base superalloys. In this model, the secondary creep behavior can be determined through analytical methods while the tertiary creep behavior is often found using trial and error or numerical optimization. Trial and error may produce no constants. Numerical optimization can be computationally expensive. In this study, a strain-based and damage-based approach to determine the tertiary creep behavior of nickel-base superalloys has been developed. Analytically determined constants are found for a given nickel-base superalloy. Creep deformation and damage evolution curves are compared. Methods to deal with stress dependence are introduced and studied.

Modeling of concrete nonlinear mechanical behavior at high temperatures with different damage-based approaches

Heating of concrete leads to decrease of mechanical properties due to different damage processes: thermal strain gradients, chemical reactions, increase of vapour pressure (which is not taken and strain incompatibilities (between cement paste and aggregates, which is not taken into account explicitly here). This research project deals with comprehension of mechanical modeling (smeared cracking approach) on concrete’s behavior at high temperatures so as to be able to predict the previous mechanical damage processes and properties decreases. Two types of mechanical models are used: an isotropic elastic damage model (IED) and an orthotropic elasto-plastic damage model (OEPD). Transient thermal creep model (TTC) is also introduced. Different temperature rates are investigated and different virtual mechanical tests are performed (uniaxial tension, uniaxial compression, biaxial tension). The paper concludes, using numerical analysis and comparisons to experimental results, on relevances and performances of these different mechanical models.

Statistical damage model with strain softening and hardening for rocks under the influence of voids and volume changes

With regards to the composition of natural rocks including voids or pores, deformation behavior is strongly affected by variation in porosity. By using a statistical damage-based approach, the characteristics of strain softening and hardening under the influence of voids and volume changes are investigated in the present paper. Suppose that a rock consists of three parts: voids, a damaged part, and an undamaged part. The effects of voids and volume changes on rock behavior are first analyzed through determination of the porosity and an associated damage model is then developed. Later, a statistical evolution equation describing the influence of the damage threshold on the propagation condition of rock damage is formulated based on measurement of the mesoscopic element strength. A statistical damage constitutive model reflecting strain softening and hardening behavior for rocks loaded in conventional triaxial compression is further developed and a corresponding method for determining the model parameters is also provided. Theoretical results of this proposed model are then compared with those observed experimentally. Finally, several aspects of the present constitutive model, which affect the relevant behavior of rocks, are particularly discussed.

Towards Damage-Based Design Approach for RC Bridge Columns Under Combined Loadings Using Damage Index Models

This article investigates a damage-based design approach for circular reinforced concrete (RC) columns under combined bending, shear, and torsion using decoupled damage index models. The combination of bending moment, shear, axial, and torsional loading affects the structural performance of bridge columns with respect to strength, deformation capacity and progression of damage. The damage index model proposed here permits decoupling these combined actions according to various damage limit states. This work evaluates the interaction between bending and torsional damage indices in terms of progression of damage. It also investigates the effects of the transverse reinforcement ratios and shear span. Based on experimental and analytical results increase of torsion amplified the progression of damage. The increase in transverse reinforcement ratio was found to have delayed the progression of damage and to have changed the torsional dominated behavior to flexural dominated behavior under combined bending and torsion.

Creep crack growth simulations in 316H stainless steel

Virtual methods of predicting creep crack growth (CCG), using finite element analysis (FE), are implemented in a compact tension specimen, C(T). The material examined is an austenitic type 316H stainless steel at 550 °C, which exhibits power-law creep–ductile behaviour. A local damage-based approach is used to predict crack propagation and the CCG rate data are correlated with the C ∗ parameter. Two-dimensional elastic–plastic–creep analyses are performed under plane stress and plane strain conditions. Finite element CCG rate predictions are compared to experimental data and to the NSW and modified NSW (NSW–MOD) CCG models’ solutions, which are based on ductility exhaustion arguments. An alternative version of the NSW–MOD model is presented for direct comparison with the FE implementation. The FE predictions are found to be in agreement with the appropriate analytical solutions, and follow the trends of the experimental data at high C ∗ values. Accelerated cracking behaviour is observed experimentally at low C ∗ values, which is consistent with the standard plane strain NSW–MOD prediction. The FE model may be developed to predict this accelerated cracking at low C ∗ values so that the trends between CCG rates at high and low C ∗ values may be determined.