Macroscopic Finite Element Model Research Articles

Experimental and multi-scale numerical investigation of ultra-high performance fiber reinforced concrete (UHPFRC) with different coarse aggregate content and fiber volume fraction

This study investigates the influence of the coarse aggregate content and steel fiber volume fraction on the mechanical properties of UHPFRC. On the meso-scale, according to Mori-Tanaka homogenization method and progressive damage theory, the equivalent damage constitutive model of UHPFRC composite is established. On the macro-scale, the mesoscopic equivalent properties of UHPFRC material are input into the finite element model corresponding to the test for numerical simulation, and the mesoscopic material properties are coupled with the macroscopic finite element model to study the influence of mesoscopic components of UHPFRC on its macroscopic mechanical properties. The compression, tension and four-point bending numerical simulation results of UHPFRC show that the predicted results of the multi-scale numerical model are in good agreement with the test results. It is also found that with the increase of fiber volume fraction, the compressive strength, tensile strength and four-point bending strength of UHPFRC increase first and then decrease. The improvement effect of coarse aggregate on the properties of UHPFRC is not as obvious as that of fiber, and the increase of fiber volume fraction has a significant enhancement effect on the ductility and post peak toughness of UHPFRC slab.

Revisiting the demagnetization curves of Dy-diffused Nd-Fe-B sintered magnets

The grain boundary diffusion process (GBDP) is now widely used to increase coercivity in Nd-Fe-B sintered magnets with a more efficient use of heavy rare earth elements (Dy, Tb). This process leads to a typical core-shell structure for the grains consisting of (Nd,Dy)2Fe14B shells at the outer grain regions and Nd2Fe14B cores. The thickness of the (Nd,Dy)2Fe14B shells decreases from the diffusion surface to the magnet core. This inhomogeneous distribution in Dy content gives rise to a coercivity gradient within the magnet and leads therefore to a reduced squareness of the demagnetization curve. The purpose of this work is to provide a quantitative understanding of the influence of composition profiles after GBDP on the shape of the demagnetization curve of Nd-Fe-B sintered magnets diffused with the Dy63Co37 (at. %) intermetallic compound. SEM/X-EDS analyses along the Fisher diffusion model allow the estimation of the Dy concentration in grains and at different depths. Then, after ascribing to the grains some critical values for the switching field that are related to the local Dy content, a macroscopic finite element model is implemented to provide a better understanding of the grain reversal sequence in the graded magnets tested in closed-circuit. Grain reversal patterns show that demagnetization starts from the less coercive grains in the magnet core, remains constricted in this zone thanks to a shielding effect from the external surface, and then propagates towards outer layers via magnetostatic interactions. When the coercivity gradient is large, the coercivity of the whole magnet measured in closed-circuit could be 100–200 kA/m lower than the value expected without considering magnetostatic interactions, suggesting that the shielding effect from the diffusion affected layers could be limited and counterbalanced by magnetostatic interactions.

Pseudo-dynamic response and analytical evaluation of blind bolted CFT frames with BRBs

This paper presents the experimental and analytical studies on the blind bolted end plate concrete-filled steel tube (CFT) composite frames with buckling-restrained braces (BRBs). A series of pseudo-dynamic tests (PDTs) on two 2/3-scaled two-story, one-bay blind bolted end plate CFT (BECFT) composite frames with BRBs showed that the novel dual system exhibited good hysteretic behavior and high ductility. The moment capacity, initial rotational stiffness, rotation capacity and the mathematical moment-rotation model of a BECFT composite joint were systematically analyzed and modified to some extent. Meanwhile, the shear force-deformation relation of a CFT panel zone was suggested and checked for its applicability. Furthermore, the macroscopic finite element (FE) model incorporating semi-rigid characteristic of the joint and shear response of the panel zone was developed by OpenSees program. The numerical analytical results would match better with experimental data when the FE model took the gusset plate stiffness into account in comparison with other models neglecting this case. Both experimental and FE analytical results indicated that the BRBs were in elastic state to provide great lateral stiffness and resistance under small earthquakes, and they yield first to stably dissipate energy under severe earthquakes. The combination of BECFT composite frames with BRBs will extend the feasibility of the novel dual system in high- or even super high-rise buildings.

Micromechanical modeling of the contact stiffness of an osseointegrated bone\u2013implant interface

BackgroundThe surgical success of cementless implants is determined by the evolution of the biomechanical properties of the bone–implant interface (BII). One difficulty to model the biomechanical behavior of the BII comes from the implant surface roughness and from the partial contact between bone tissue and the implant. The determination of the constitutive law of the BII would be of interest in the context of implant finite element (FE) modeling to take into account the imperfect characteristics of the BII. The aim of the present study is to determine an effective contact stiffness left( {K_{c}^{text{FEM}} } right) of an osseointegrated BII accounting for its micromechanical features such as surface roughness, bone–implant contact ratio (BIC) and periprosthetic bone properties. To do so, a 2D FE model of the BII under normal contact conditions was developed and was used to determine the behavior of K_{c}^{text{FEM}}.ResultsThe model is validated by comparison with three analytical schemes based on micromechanical homogenization including two Lekesiz’s models (considering interacting and non-interacting micro-cracks) and a Kachanov’s model. K_{c}^{text{FEM}} is found to be comprised between 1013 and 1015 N/m3 according to the properties of the BII. K_{c}^{text{FEM}} is shown to increase nonlinearly as a function of the BIC and to decrease as a function of the roughness amplitude for high BIC values (above around 20%). Moreover, K_{c}^{text{FEM}} decreases as a function of the roughness wavelength and increases linearly as a function of the Young’s modulus of periprosthetic bone tissue.ConclusionsThese results open new paths in implant biomechanical modeling since this model may be used in future macroscopic finite element models modeling the bone–implant system to replace perfectly rigid BII conditions.

Using spectral-based representative volume element crystal plasticity simulations to predict yield surface evolution during large scale forming simulations

Abstract We present a new approach to predict the evolution of anisotropic yield functions by coupling large scale forming simulations with crystal plasticity-spectral based virtual experiments, realizing a multi-scale model for metal forming. Employing a fast spectral method solver enables us to conduct on-the-fly full-field virtual experiments to evolve the yield surface at each integration point of the macroscopic finite element model. As illustrative example, two advanced anisotropic yield functions, namely Yld2000-2D and Yld2004-18p, are used in finite element simulations of deep drawing for a 2090-T3 aluminum alloy sheet. The simulated earing profiles are compared to the experimental ones as well as to simulations with non-evolving yield functions. It is found that the prediction of the earing is improved for the case of the evolving Yld2000-2D yield function. The evolution of the plastic anisotropy during cup drawing is systematically analyzed, showing that the evolution of anisotropy can have considerable effect on the prediction accuracy of the macroscopic simulations.

Microstructure-based multiscale modeling of large strain plastic deformation by coupling a full-field crystal plasticity-spectral solver with an implicit finite element solver

We present a fully embedded implementation of a full-field crystal plasticity model in an implicit finite element (FE) framework, a combination which realizes a multiscale approach for the simulation of large strain plastic deformation. At each integration point of the macroscopic FE model a spectral solver, based on Fast Fourier Transforms (FFTs), feeds-in the homogenized response from an underlying full-field polycrystalline representative volume element (RVE) model which is solved by using a crystal plasticity constitutive formulation. Both, a phenomenological hardening law and a dislocation density based hardening model, implemented in the open source software DAMASK, have been employed to provide the constitutive response at the mesoscale. The accuracy of the FE-FFT model has been benchmarked by one-element tests of several loading scenarios for an FCC polycrystal including simple tension, simple compression, and simple shear. The multiscale model is applied to simulate four application cases, i.e., plane strain deformation of an FCC plate, compression of an FCC cylinder, four-point bending of HCP bars, and beam bending of a dual-phase steel. The excellent capabilities of the model to predict the microstructure evolution at the mesoscale and the mechanical responses at both macroscale and mesoscale are demonstrated.

Parametrically Homogenized Constitutive Models (PHCMs) for Multi-scale Predictions of Fatigue Crack Nucleation in Titanium Alloys

This paper develops a bottom-up and top-down multi-scale modeling framework for predicting fatigue crack nucleation in structures of titanium alloys, e.g., Ti-7Al. A parametrically homogenized constitutive model (PHCM) and a parametrically homogenized crack nucleation model (PHCNM) are developed from computational homogenization of crystal plasticity finite element simulation results performed on microstructural statistically equivalent RVEs. Bayesian inference and machine-learning methods are employed to derive microstructure-dependent functional forms of PHCM and PHCNM coefficients. The PHCM is augmented with uncertainty quantification to account for model reduction errors and microstructural uncertainty. Macroscopic finite element models for Ti-7Al test specimens are created by matching correlation functions of microtexture in electron back-scatter diffraction scans. Nucleation hot-spots are identified by PHCNM in macroscopic simulations of stress-controlled dwell loading, then top–down microscopic simulations are performed to probe into the crack nucleation process. The computed distributions of nucleation lives and locations follow experimentally observed characteristics of the dwell effect in Ti alloys.

Direct Macroscopic Modeling of Grain Structure and Macrosegregation with a Cellular Automaton–Finite Element Model

Grain structure and macrosegregation are two main factors determining mechanical properties of components and are strongly coupled during alloy solidification. A two-dimensional (2D) cellular automaton (CA)–finite element (FE) model is developed to achieve a direct macroscopic modeling of grain structure and macrosegregation during the solidification of binary alloys. With the conservation equations of mass, momentum, energy, and solute solved by a macroscopic FE model and the grain structure described by a microscopic CA model, a two-way coupling between the CA and FE models is applied. Furthermore, the effect of the fluid flow on the dendrite tip growth velocity is considered by modified dendrite tip growth kinetics. The CAFE model is applied to a quasi-2D benchmark solidification experiment of a Sn–3.0wt.%Pb alloy, and the grain structure and macrosegregation are predicted simultaneously. It is demonstrated that the model has a capacity to describe the undercooling ahead of the growth front. The growth directions of columnar grains, grain sizes, and columnar-to-equiaxed transition (CET) position are obviously modified by the fluid flow, and obvious segregated channels almost aligned with the orientations of the columnar grains are found. Qualitatively good agreement is obtained between the predicted segregation profiles and experimental measurements.

Seismic tests and numerical investigation of blind-bolted moment CFST frames infilled with thin-walled SPSWs

This paper aims to investigate the seismic response of blind-bolted moment concrete-filled steel tubular (CFST) frames infilled with thin-walled steel plate shear walls (SPSWs). Tests of two-storey blind-bolted circular or square CFST frames with thin-walled SPSWs subjected to horizontal low-cyclic loading were performed. Macroscopic finite element (FE) models of the specimens were primarily established by fibre beam-column elements, zero-length springs, and truss elements. The numerical simulation results were verified by the experimental data. A parametric analysis was conducted to analyse the influence of the axial load level, material strength, and height-thickness ratio of the steel plate etc. on the hysteresis behaviour and energy dissipation of blind-bolted moment CFST frames with thin-walled SPSWs. In addition, the mechanics of the semi-rigid frame with SPSWs were compared with the pinned and rigid frames with SPSWs using mechanical analysis model and FE model. The experimental and analytical results show that the blind-bolted moment CFST frames with SPSWs connected to the beams only exhibit preferable hysteretic response, ductility and energy dissipation. The peak strength, initial stiffness and energy dissipation of blind-bolted moment CFST frames infilled with thin-walled SPSWs can be significantly affected by the axial load level as well as the steel plates' yield strength, height-thickness ratio, aspect ratio, and connection type.

A Tensile Constitutive Relationship and a Finite Element Model of Electrospun Nanofibrous Mats.

It is difficult to establish a numerical model for a certain structure of electrospun nanofibrous mats, due to their high porosity and non-linear characteristics, that can fully consider these characteristics and describe their mechanical behaviors. In this paper, an analytical method of meso-mechanics was adopted to establish the tensile constitutive relationship between a single fiber and mats from fiber-web microstructures. Meanwhile, a macroscopic finite element model was developed and verified through uniaxial tensile stress-strain experimental data of silk fibroin (SF)/polycaprolactone (PCL) nanofibrous mats. The compared results show that the constitutive relation and finite element model could satisfactorily express elastic-plastic tensile mechanical behaviors of the polymer. This model helps regulate the microstructure of nanofibrous mats to meet the mechanical requirements in engineering applications.

The Bearing Capacity Calculation Method of Cracked Reinforced Concrete Column at High Temperature

Introduction: This paper presents results from a set of numerical studies on the cracked reinforced concrete column at high temperature. Methods: The macroscopic finite element model used in the accounts analysis for high temperature properties of constitutive materials. The validity of the model is established by comparing the predictions from numerical analysis with the data measured in the fire test. Result and Conclusion: Data from the test indicated that the temperature of rebar in column with cracks is 57% ~ 130% higher than that without cracks under the same condition, and different types of crack had significant influence on the bearing capacity of column. These results from parametric studies were utilized to propose ultimate bearing capacity of cracked reinforced concrete column.

Gas Breakthrough Pressure (GBP) through Claystones: Correlation with FIB/SEM Imaging of the Pore Volume

This contribution uses six claystone samples imaged by FIB/SEM (Focused Ion Beam/Scanning Electron Microscopy), within micrometric volumes located in the clay matrix; their 3D connected pore network is identified down to 17-22 nm pore size. All samples are gently dried to minimize damage, and several are impregnated with Poly(Methyl MethAcrylate) (PMMA) resin to avoid further damage during FIB/SEM observations. Three pore volumes out of six are connected between two parallel end surfaces through crack-like pores; two are not connected between any two parallel end surfaces; only one sample has a connected pore network distinct from cracks.By assuming varied pathways for gas to migrate by capillarity through the connected pore volumes (either by taking the shortest path, or through the largest path, or through the most frequent pore size, or by simulating the ingress of a non wetting fluid), we determine the Gas Breakthrough Pressure (GBP) through the initially fully liquid saturated claystone, from these micrometric volumes. The scale change (from the micrometric to the macroscopic scale) is assumed possible without changing the GBP value, and clay/water interactions are not accounted for. By comparison with GBP values measured in the laboratory on centimetric-sized claystone samples, it is concluded that breakthrough occurs most probably by capillary digitation; micro-cracks are the most probable pathways for gas, so that gas does not progress in a homogeneous manner through the claystone, as standard macroscopic finite element models would represent it. For intact claystone, predictions based on the capillary ingress of a non wetting fluid provide a GBP value ranging between 7-14 MPa.

(Invited) Thermo-Chemo-Mechanical Response of Solid Oxide Cells during Reduction and Cooling

Thermal expansion mismatch among the materials used in a Solid Oxide Cell (SOC) generates in-plane strain within the SOC layers during the cooling process following sintering. These residual stresses induce cell curvature for asymmetric cells, challenging the stacking process, but more importantly they may also result in more fragile cells. Furthermore, the composite nature of some of the layers results in the development of local micro-strain in each constituent phase of the composite. Both types of strain undergo major changes upon heating and reduction of the NiO-containing fuel electrode, and upon subsequent temperature changes during dynamic operation. Surprisingly fast deformation is observed upon reduction causing relaxation of residual stresses at a rate that is ~104 times faster than creep during operation. The origins of this newly discovered chemo-mechanical response, termed accelerated creep, are discussed. To assess and optimize the reliability of SOCs during operation, the stress field and its thermo-chemical and temporal evolution must be known. In this work the stresses are measured in-situ before, during and after reduction by use of X-ray diffraction. Two different techniques are used to measure the stresses (elastic strains): i) The biaxial stresses in the cell plane are determined from the variation in spacing between lattice planes as a function of the angle of the lattice plane normal to the cell plane, and ii) the micro-strain is assessed from the widening of the Bragg peaks due to local stress. Utilizing diffraction peaks from different phases of the Ni(O)-YSZ/YSZ half-cell it is possible to determine both the in-plane stress at different SOC layers as well as the microstrain in each constituent phase of the composite Ni(O)-YSZ support layer. As an example, the evolution of the in-plane stress in the YSZ electrolyte layer upon thermo-chemical conditioning (heating to 700 °C, reduction, and subsequent cooling to 25 °C) of the Ni(O)-YSZ/YSZ half-cell is shown in the Figure. The compressive stress in the electrolyte layer decreases with increasing temperature, due to the larger thermal expansion coefficient of the NiO-YSZ layer compared to YSZ. Very fast and nearly complete stress relaxation was observed upon reduction of the NiO-YSZ support. Compressive stress builds up again in the electrolyte upon cooling, but at a slightly slower rate. The residual stresses of the two above-mentioned types i) and ii) have been measured in the YSZ electrolyte and Ni(O)-YSZ support layer as a function of temperature for different reduction temperatures. Furthermore, the stresses in the half-cell are assessed by use of a macroscopic finite element model, taking into account the elastic response and creep of each layer. The local stresses in the different phases of the Ni-YSZ composite are modelled by use of a 3D microstructural reconstruction combined with finite element modeling. Figure 1

An evolving plane stress yield criterion based on crystal plasticity virtual experiments

This paper presents a new hierarchical multi-scale framework that allows taking into account evolution of the plastic anisotropy during sheet forming processes. The evolution of crystallographic texture, which is identified as the main source of the plastic anisotropy, is predicted by the ALAMEL crystal plasticity model. An extension to the phenomenological anisotropic plane-stress yield criterion BBC2008 is proposed, which provides adaptive updates of the local anisotropy in the integration points of the macroscopic finite element model. To this end, the BBC2008 is systematically recalibrated to data provided by the crystal plasticity virtual experiment framework (VEF). An enhanced identification algorithm is proposed. The new algorithm exploits comprehensive material characterization delivered by the VEF.The deep drawing of cylindrical cups is used as a benchmark case. An industrial-grade aluminium alloy AA6016 is chosen for the test case. The experimental part of the study includes X-ray diffraction measurements of the texture as well as mechanical testing, which comprises uniaxial tensile tests, a bulge test and the deep drawing of cylindrical cups. A noticeable through-thickness gradient in terms of both the texture and the plastic anisotropy is identified in the initial material. This issue is taken into consideration in the study.Three groups of simulations have been performed, in which (i) the BBC2008 was calibrated by means of the mechanical tests, (ii) the BBC2008 was calibrated by means of the VEF based on the initial texture, but kept constant throughout the simulation, and (iii) the BBC2008 was systematically recalibrated by means of the VEF to reflect the effects of texture evolution. The earing profiles measured in the experimentally drawn cups are compared to the ones predicted by the simulations. It is found that the cup profile predictions by (i) are clearly inferior compared to both (ii) and (iii). However, in the considered process (iii) provides only a moderate improvement over the results of (ii). The explanation of this limited impact of the anisotropy evolution is based on the analysis of the evolved texture and associated plastic anisotropy.

Parameter identification of rockfall protection barrier components through an inverse formulation

Rockfall barriers are key protection systems in mountainous regions worldwide. They are designed to intercept and capture falling rocks. Most systems are composed of flexible steel wire-nets connected to wire-rope cables which are in turn attached to steel posts and anchored to the ground. Additional energy dissipating devices can be connected to the cables to enhance the performance of the barriers. The composition and geometrical arrangement of wires forming net components and cables are a severe limitation to realistic finite element (FE) modeling of rockfall barriers. Detailed models are computationally expensive. Therefore, macroscopic models reflecting the system behavior on a coarser scale, i.e., the global behavior, need to be derived. In this work, macroscopic FE models pertaining to the modeling of the wire-ring net and the spiral cables have been developed and investigated. Material plasticity, damage initiation and ductile damage are taken into account. The non-linear force displacement response obtained in laboratory tests has been successfully reproduced by introducing additional parameters. An inverse optimization process based on the multi-island genetic algorithm is used for the determination of model parameters. The developed numerical approach succeeds in modeling rockfall barrier connections in a manner that is more refined than previous attempts, yet of low computational expense. The accuracy of this approach is verified by the match between simulation and test results of a full scale rockfall barrier prototype that was tested according to the ETAG027 standard.

Generalized bridging domain method for coupling finite elements with discrete elements

The concurrent coupling of finite elements and discrete elements is an effective DOF reduction methodology for reproducing the granular flow phenomenon as discrete element method does. In this paper, we present a novel coupling strategy named the generalized bridging domain method. This method introduces independent functions to weight the material properties of the continuum and those of the discrete element model, and then the equilibrium of each new model is guaranteed by imposing compensation forces. The compensation force of continuum is determined by force and displacement compatibility requirements of continuum with respect to discrete elements, and vice versa. Utilizing different weighting functions, four typical coupling methods, the bridging domain method, edge-to-edge coupling, separate domain coupling, and separate edge coupling, are obtained. Additionally, a new integration algorithm with multiple time steps is developed for the separate edge coupling. The numerical performance of the separate domain coupling, where displacement compatibility condition of continuum and that of discrete elements are individually enforced by the Lagrange multiplier method, has been investigated in detail. Results of several numerical examples show that the separate domain coupling outperforms other methods in avoiding spurious reflection and the separate edge coupling is effective enough for coupling finite elements with discrete elements. Due to the truncation of high frequency waves, there exists energy loss but at an acceptable level if the waves can be resolved by the macroscopic finite element model.

Microscale Fiber Network Alignment Affects Macroscale Failure Behavior in Simulated Collagen Tissue Analogs

A tissue's microstructure determines its failure properties at larger length scales, however, the specific relationship between microstructure and macroscopic failure in native and engineered soft tissues (such as capsular ligaments, aortic aneurysms, or vascular grafts) has proven elusive. In this study, variations in the microscale fiber alignment in collagen gel tissue analogs were modeled in order to understand their effects on macroscale damage and failure outcomes. The study employed a multiscale finite-element (FE) model for damage and failure in collagen-based materials. The model relied on microstructural representative volume elements (RVEs) that consisted of stochastically-generated networks of discrete type-I collagen fibers. Fiber alignment was varied within RVEs and between layers of RVEs in a macroscopic FE model of a notched dogbone geometry. The macroscale stretch and the microscale response of fibers for each of the differently aligned cases were compared as the dogbone was uniaxially extended to failure. Networks with greater fiber alignment parallel to the direction of extension failed at smaller strains (with a 6-22% reduction in the Green strain at failure), however, at greater grip forces (a 28-60% increase) than networks with fibers aligned perpendicular to the extension. Alternating layers of crisscrossed network alignments (aligned ±45 deg to the direction of extension) failed at smaller strains but at greater grip forces than those created using one fiber alignment type. In summary, variations in microscale structure via fiber alignment produced different macroscale failure trends. To conclude, these findings may be significant in the realm of tissue engineering and in soft tissue biomechanics.

Factors governing the fire response of concrete beams reinforced with FRP rebars

This paper presents results from a set of numerical studies on the influence of critical factors on the fire response of concrete beams reinforced with FRP rebars. The macroscopic finite element model used in the analysis accounts for high temperature properties of constitutive materials, realistic load and restraint conditions, as well as temperature induced slip between FRP rebars and concrete. The validity of the model is established by comparing predictions from numerical analysis with measured data in fire test. Results from parametric studies indicate that rebar type, concrete cover thickness, and fire scenario have significant influence on the fire response of concrete beams reinforced with FRP rebars, while the presence of axial restraint in the beam has moderate influence on fire resistance. These results from parametric studies are utilized to propose an optimum insulation scheme for enhancing the fire response of concrete beams reinforced with FRP rebars.

Study on the Inwall Crack Extension and Fatigue Life Evaluation for Deep-Sea Steel Catenary Riser under Wave and Current Action

Aimed at deep-sea steel catenary risers(SCRs) transporting supercritical or dense CO2, this paper uses the macroscopic pipeline-transporting finite element model and the microscopic pipewall crack growth model to numerically simulate corrosive-inwall-defect-induced crack extension along radial direction for the deep-sea riser which is subjected to wave and current loads. Meanwhile, based on linear elastic fracture mechanics and fatigue crack extension theory, the effect of wave height on the fatigue life of the pipewall at touchdown zone is discussed. The above-mentioned study in this paper is expected to give a good reference to the similar study for oil&gas SCRs.

Concurrent and Hierarchical Multiscale Analysis for Layer-Thickness Effects of Nanoscale Coatings on Interfacial Stress and Fracture Behavior

To investigate the effects of coating layer thickness on stress and the debonding behavior near the interface of coating layer and substrate, multiscale analysis is a must since molecular dynamics (MD) simulations can only be performed on models with thicknesses of about tens of nanometers on common computers, but the real thicknesses of such layers are around 300–1200 nm. In this work, generalized particle dynamics (GP) modeling for Al coated on Fe is first developed by using an atomistic domain near the layer interface and having high-scale particles far from that region to reduce degrees of freedom. Results show that the thicker coatings experience lower local average shearing stresses for a given shear strain. However, it is found that when the layer thickness reaches a large value, further increase of the layer thickness will not greatly benefit the reduction of the stress, thereby not increasing the allowable load. This trend is consistent with the simulation for Al2O3 coated on Fe by a hierarchical multiscale analysis which is formulated by proposing a nanoscale-based key variable, Gdb, called debonding energy density. This variable, defined by the debonding energy per unit area, is used to characterize material bonding strength in realizing that failure originates from the atomistic and nanoscale. The difference and connection of this low-scale fracture variable, Gdb, with crack energy release rate, GIC, in traditional fracture mechanics is illustrated and how Gdb can be easily determined through atomistic simulation is exemplified. To make the new variable effective in engineering applications, Gdb is used as input to a macroscopic scale finite element model. The obtained layer-thickness effect directly confirms the existence of a critical thickness, predicted by the GP method. This work is an effort in developing material failure theory from lower scales where material fracture originates but with applications in continuum scale via both hierarchical and concurrent multiscale analyses.