Non-local Continuum Damage Model Research Articles

Multi-layer continuum model for adhesive films with knitted carrier

Film adhesives are a form of composite consisting of two constituents i.e. fibrous carrier and matrix. The fracture surfaces are usually dominated by the carrier-matrix de-bonding, but it also co-exists with a minor failure related to resin closer to the adhesive–adherend interface. This investigation aims at a realistic representation of the failure modes. For this, a 3D multi-layer approach of a FM 300-2 adhesive is defined where a non-local Continuum Damage Model (CDM) is developed accounting for the proper matrix mechanism defined with lower fracture energies. The carrier-matrix de-bonding was implemented by an in-built Cohesive Zone Model (CZM) at the interfaces of the matrix-carrier layers. For the characterization and validation, the modelling was tested with the Mode I fracture response of the adhesive in joints (butt joint, BJ, and double cantilever beam specimen, DCB) and bulk form (tensile tests). Numerical results with CZM-CDM implementation agreed with the experimental data in terms of load response and representation of the failure mechanisms, when correct material constants are applied. The multi-layer damage model was able to define strength and fracture properties of the matrix phase by the prediction of failure initiation in the BJ test. Consequently, the mechanism was able to reproduce the local damage path that occurred close to the adhesive–adherend interface.

A Review on Nonlocal Theories in Fatigue Assessment of Solids.

A review of nonlocal theories utilized in the fatigue and fracture modeling of solid structures is addressed in this paper. Numerous papers have been studied for this purpose, and various nonlocal theories such as the nonlocal continuum damage model, stress field intensity model, peridynamics model, elastic-plastic models, energy-based model, nonlocal multiscale model, microstructural sensitive model, nonlocal lattice particle model, nonlocal high cycle fatigue model, low cycle fatigue model, nonlocal and gradient fracture criteria, nonlocal coupled damage plasticity model and nonlocal fracture criterion have been reviewed and summarized in the case of fatigue and fracture of solid structures and materials.

A nonlocal continuum damage model for timber: Development, implementation, and application

The phenomenological constitutive modelling of timber requires complex anisotropic failure criteria or a combination of failure surfaces that adequately capture different failure modes ranging from brittle to ductile. Additionally, localization of strain/damage (associated with softening of the material) adds another layer of complexity to constitutive modelling of timber by rendering finite element (FE) simulations sensitive to size and orientation of the FE mesh. A generic three-dimensional (3D) nonlocal integral continuum damage constitutive law was developed for timber. The proposed model took advantage of symmetric attenuation function that consistently treats transition from local to nonlocal state while alleviating the boundary effects in the finite support domains. The developed nonlocal constitutive law was implemented in ABAQUS for FE simulation of timber. Values for interaction radius of the nonlocal model are proposed, and the model was verified against a wide range of experimental data. It is shown that the proposed nonlocal FE model captures load-carrying capacity and different failure modes of timber and effectively restores the objectivity of the results, whereas the FE model without strong localization limiters considerably underestimates the load-carrying capacity.

Non-local continuum damage model for poro-viscoelastic porous media

We present a novel poro-damage-viscoelastic model for predicting the failure response of fluid-saturated porous geomaterials. The Generalized Maxwell model is introduced for the representation of the viscoelastic behavior of the solid skeleton, which is achieved by a standard Prony-series type expansion. Damage regularization is obtained by an non-local integral-type formulation and damage behavior is described by Mazars model with the modified von Mises-type equivalent strain measure. The poromechanics parameters (Biot’s coefficient, Biot’s modulus) are functions of damage, and the fluid flow obeys Darcy’s seepage law in the entire domain, while the permeability is assumed to be anisotropic and strain dependent. The coupled system is discretized in time using a backward Euler scheme. The non-linear system is linearized using a Newton Raphson scheme and solved monolithically every time step. A consistent Jacobian matrix and residual vector are derived analytically. Several numerical examples are studied in order to investigate the performance of the proposed approach, including (i) a column undergoing hysteresis from cyclic loading, stress relaxation, creep and variable strain rate loading tests and (ii) fluid-driven fracturing in a 2D poro-viscoelastic domain. The numerical time-dependent results exhibit mesh insensitivity for all field variables, and confirm the feasibility and applicability of the proposed non-local damage model for simulating hydraulic fracture. • A non-local damage model for poro-viscoelastic saturated porous media is proposed. • Von-Mises strain measure is used to drive the non-local integral type damage growth. • Damage-response includes nonlinear Biot’s coefficients and anisotropic permeability. • A mixed FEM solution is developed, including a monolithic iterative solution. • Analytically derived Jacobian is used to drive the non-linear solution of equations. • Benchmark problems include poro-viscoelastic column and hydraulic fracture problems. • Objective mesh-independent and oscillation free numerical results are presented. • The model has the potential to represent time-dependent damage in several rock types.

An interactive orthotropic non-local damage model for progressive failure analysis of composite laminates

In this study, the non-local continuum damage model is further developed for progressive failure analysis of laminated composites. Characterized by two internal length scales, an orthotropic non-local integral strategy is implemented to model the constrained matrix damage along fiber direction. The introduction of spatial averaging may avoid spurious strain localization and thus ensure the physically-meaningful energy dissipation during damage evolution process. Compared to standard damage descriptions, the pathological mesh sensitivity and mesh orientation bias are effectively alleviated, leading to objective and accurate solutions. Moreover, an interactive damage transfer scheme is proposed to capture the strong interaction between matrix cracking and interface delamination, so that faithful predictions on the complex failure mechanisms of composite laminates are guaranteed. Performance of the present model and its superiority over conventional methods are demonstrated through several numerical examples, including the typical tensile failure of notched and unnotched laminates.

Timber beams with openings: Laboratory testing and nonlocal finite element modelling

Introducing openings in joists of flooring systems is usually necessary to pass through building services without increasing the floor-to-floor height. The openings reduce the stiffness and limits the ultimate load-carrying capacity of the timber beams by promoting tensile stresses perpendicular to the grain and longitudinal splitting shear stresses. Furthermore, quasi-brittle failure of the timber in shear and tension (promoted by openings) leads to localisation of strain, spurious numerical sensitivities and ultimately poor or erroneous damage initiation and failure load predicted by finite element (FE) models. In this paper, a nonlocal continuum damage model is proposed and implemented to alleviate the FE mesh dependency and strain localisation problems in failure analysis of the timber beams with openings. Benchmark experimental results obtained from bending test on Laminated Veneer Lumber (LVL) and Glued Laminated Timber (GLT or glulam) beams with openings are briefly presented and then accuracy of the implemented nonlocal FE model is validated against the benchmark test results and experimental data available in the literature. It is demonstrated that the proposed nonlocal model can effectively resolve the spurious mesh sensitivity and accurately capture the failure modes and peak load-carrying capacity of timber beams with openings.

Development of a multiphysics model of synergistic effects between environmental exposure and damage in woven glass fiber reinforced polymeric composites

Extending the application of fiber-reinforced polymer (FRP) composite materials into the automotive, aerospace and military manufacturing is a significant advance in recent years. However, few extending have been achieved in civil infrastructure and building construction industry. This gap is partly due to (i) the lack of multiphysics and multiscale models unifying degradation-deformation damage phenomena to assess the safety and durability of newly adopted or proposed material and structural systems, and (ii) no available computational models that are succinctly fundamental and directly interactable with other digital files from architecture designer or manufacturer. To begin addressing this gap, this paper presents a structure level multiphysics model that uses the UV and moisture deterioration variables homogenized from a micromechanics model to integrate a nonlocal continuum damage model in a curvilinear coordinate system. This model links the application of analysis to the architecture or manufacturing digital model by enabling more accurate predictions of mechanical performance. An example of the model is presented for analysis of a group of glass fiber-reinforced polymer (GFRP) composite plates in SFMOMA Façade System, the first and largest architectural application of fiber reinforced polymer (FRP) in the United States.

Virtual characterization of nonlocal continuum damage model parameters using a high fidelity finite element model

A virtual finite element framework is presented to provide the transition from a high fidelity model to a more computationally efficient continuum model for simulating fibre-dominated damage behavior in composite laminates subjected to tensile loadings. The high fidelity method in LS-DYNA is based on the use of cohesive interface elements to simulate both intra-laminar matrix cracks and delamination. Applied to IM7/8552 carbon fibre reinforced plastic laminates in over-height compact tension (OCT) tests, this modeling strategy is used to determine the effective damage parameters for the nonlocal continuum damage model, CODAM2, implemented as MAT219 in LS-DYNA. The prediction of CODAM2 is thoroughly assessed against quantitative and qualitative results obtained from the high fidelity model. Furthermore, the characterized CODAM2 model is applied to simulations of large-scale OCT, open–hole tension (OHT) and center-notched tension (CNT) specimens and results are compared to corresponding experimental data. Due to its nonlocal feature to track the crack trajectory without the need to align the mesh with fibre orientation, the continuum damage model CODAM2 is able to accurately predict the structural response in all large-scale OCT, OHT and CNT test cases with significant computational efficiency.

A nonlocal continuum damage model for brittle fracture

The objective of this paper is to develop a nonlocal continuum damage model for brittle fracture. A nonlocal damage conjugate force tensor is obtained from the “local” one, using an integral-type regularization technique, and the thermodynamic equations are formulated in a nonlocally generalized standard manner. A nonlocal damage model is developed based on a recently developed “local” model, which can rigorously handle damage anisotropy, distinct tensile and compressive damage behavior, and damage deactivation, so that the nonlocal model not only handles brittle fracture well but also possesses the advantageous features of the “local” model. A fully explicit integration scheme for the present model is developed and then implemented in Abaqus/Explicit via VUMAT. The present model is validated through: 1. simulating cyclic uniaxial tests on a SiC–SiC woven composite; 2. calibrating its associated material parameters via single edge notched bend (SENB) tests on concrete beams. Its versatility is demonstrated through simulating a mixed-mode fracture test on a double edge notched (DEN) specimen. It is found to be capable of producing realistic fracture paths and capturing size effects in real materials. A wide variety of mechanical behavior can be incorporated into the present model in the future.

A meshless approach to non-local damage modelling of concrete

A non-linear continuum damage mechanics model for concrete constructions is analysed using a radial point interpolation meshless method (RPIM). The fundamental mathematical relations and the material model are fully characterized. The 2D plane stress RPIM formulation is extended to a rate-independent standard (local) damage model considering both tension and compression static states. Additionally, in this work, the local damage formulation is modified considering a non-local constitutive damage criterion with regard to a Helmholtz free energy potential. Here, the internal variational fields, such as local and non-local damage variables, are determined by a return-mapping damage algorithm. Due to the non-linear nature of the phenomenon, a displacement controlled Newton-Raphson iterative approach is adopted to attain the non-linear damage solution. In the end, the performance of the proposed non-local damage model is evaluated using an experimental test of a notched-three-point bending beam available in the literature. The obtained solution shows that the meshless methods are capable to effectively analyse concrete structures assuming a non-linear non-local continuum damage model.

Effective calibration and validation of a nonlocal continuum damage model for laminated composites

A combined experimental and numerical approach is presented to calibrate the parameters of a previously developed nonlocal damage model used to simulate the inelastic response of laminated composites within a macroscopic modelling framework. In this approach, a limited number of physically-based damage parameters are obtained by conducting tests on notched specimens while employing the Digital Image Correlation (DIC) technique. These parameters are then used to calibrate a non-local sub-laminate based damage mechanics model, CODAM2. Compared to available ply-based approaches; the sub-laminate damage model reduces the computational time significantly while capturing the overall damage behaviour of the laminate. The damage model is implemented as a built-in material model in the commercial finite element code, LS-DYNA (MAT_219) and also in the open-source object oriented finite element code, OOFEM. To validate this approach, experiments were conducted on notched tensile specimens with varying notch-tip radii that result in a range of behaviour from stable to unstable damage growth as this radius increases. The calibrated damage model was used to predict this transition.

From diffuse damage to sharp cohesive cracks: A coupled XFEM framework for failure analysis of quasi-brittle materials

Abstract Failure of quasi-brittle materials is governed by crack formation and propagation which can be characterized by two phases: (i) diffuse material degradation process with initial crack formation and (ii) severe localization of damage leading to the propagation of large cracks and fracture. While continuum damage mechanics provides an excellent framework to describe the first failure phase, it is unable to represent discontinuous displacement fields. In sharp contrast, cohesive zone models are poorly suited for describing diffuse damage but can accurately resolve discrete cracks. In this manuscript, we propose a coupled continuous/discontinuous approach to model the two failure phases of quasi-brittle materials in a coherent way. The proposed approach involves an integral-type nonlocal continuum damage model coupled with an extrinsic discrete interface model. The transition from diffuse damage to macroscopic cohesive cracks is made through an equivalent thermodynamic framework established in multidimensional settings, in which the dissipated energy is computed numerically and weakly matched. The method is implemented within the extended finite element framework, which allows for crack propagation without remeshing. A few benchmark problems involving straight and curved cracks are investigated to demonstrate the applicability and robustness of the coupled XFEM cohesive-damage approach. Force–displacement responses, as well as predicted propagation paths, are presented and shown to be in close agreement with available experimental data. Furthermore, the method is found to be insensitive to various damage threshold values for damage–crack transition, yielding energetically consistent results.

Implementation of a parallel finite-element library: Test case on a non-local continuum damage model

This paper presents an efficient method to implement a damage law within an explicit time-integration scheme, in an open-source object-oriented finite-element framework. The hybrid object/vector design of the framework and implementation choices are detailed in the special case of non-local continuum damage constitutive laws. The computationally demanding aspect of such constitutive laws requires efficient algorithms, capable of using High Performance Computing (HPC) clusters. The performance of our approach is demonstrated on a numerically and physically challenging 3D dynamic brittle-fragmentation test case. An almost perfect scalability is achieved on parallel computations. The global dynamics and energy terms are in good agreement with classical cohesive models’ predictions.

Simulation of finite-width process zone in concrete-like materials by means of a regularized extended finite element model

Experimental tests carried out on concrete specimens show that a fracture process zone with finite width develops in front of the crack tip. Currently, the only way of modelling a finite-width process zone is to adopt a non-local continuum damage model. This choice, however, precludes the description of macro-cracks, which emerge during the late stage of the cracking process. The eXtended Finite Element Method is a powerful tool for modelling the cracking process. The proposed eXtended Finite Element approach can simulate in a unified and smooth way both the formation of a process zone with finite width and its subsequent collapse into a macro-crack. Weak points of existing formulations, such as the necessity of ad hoc strategies in order to get mesh-independent results, and the sudden loss of stiffness at the transition from the continuous to the discontinuous regime, are overcome. In the case of tensile cracking, effectiveness is tested through comparisons with numerical and experimental results.

Criteria for mesh refinement in nonlocal damage finite element analyses

Abstract The strain softening behavior due to the development of damage is well known to produce unrealistic mesh sensitivity in standard finite element applications. In the present paper, a nonlocal continuum damage model is used to regularize the problem. The accuracy of the nonlocal finite element results is assessed introducing a nonlocal error estimator based on the “mechanical error” concept brought about by Ladeveze. To account for the dissipative nature of the problem, a time-step incremental error estimator is also proposed and comparatively tested. It is shown how the obtained information about the error distribution can be used for the accuracy assessment of different meshes. It is also shown how mesh refinement in the late stage of damage growth could be effectively driven by the estimate of the process zone width, based on the analytical derivation of the localization width.

Criteria for mesh refinement in nonlocal damage finite element analyses

The strain softening behavior due to the development of damage is well known to produce unrealistic mesh sensitivity in standard finite element applications. In the present paper, a nonlocal continuum damage model is used to regularize the problem. The accuracy of the nonlocal finite element results is assessed introducing a nonlocal error estimator based on the “mechanical error” concept brought about by Ladevèze. To account for the dissipative nature of the problem, a time-step incremental error estimator is also proposed and comparatively tested. It is shown how the obtained information about the error distribution can be used for the accuracy assessment of different meshes. It is also shown how mesh refinement in the late stage of damage growth could be effectively driven by the estimate of the process zone width, based on the analytical derivation of the localization width.