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This paper presents a comparison of various models for strain‐softening due to damage such as cracking or void growth, as proposed recently in the literature. Continuum‐based models expressed in terms of softening stress—strain relations, and fracture‐type models expressed in terms of softening stress—displacement relations are distinguished. From one‐dimensional wave propagation calculations, it is shown that strain‐localization into regions of finite size cannot be achieved. The previously well‐documented spurious convergence is obtained with continuum models, while stress—displacement relations cannot model well smeared‐crack situations. Continuum models may, however, be used in general if a localization limiter is implemented. Gradient‐type localization limiters appear to be rather complicated; they require solving higher‐order differential equations of equilibrium with additional bourdary conditions. Non‐local localization limiters, especially the non‐local continuum with local strain, in which only the energy dissipating variables are non‐local, is found to be very effective, and also seems to be physically realistic. This formulation can correctly model the transition between homogeneous damage states and situations in which damage localizes into small regions that can be viewed as cracks. The size effect observed in the experimental and numerical response of specimens in tension or compression is shown to be a consequence of this progressive transition from continuum‐type to fracture‐type formulations.

The purpose of this paper is to present a finite element model capable of describing both the diffuse damage mechanism which develops first during the loading of massive brittle structures and the failure process, essentially due to the propagation of a macro‐crack responsible for the softening behaviour of the structure. The theoretical developments for such a model are presented, considering an isotropic damage model for the continuum and a Coulomb‐type criterion for the localized part.

This is achieved by activating subsequently diffuse and localized damage mechanisms. Localized phenomena are taken into account by means of the introduction of a displacement discontinuity at the element level.

It was found that, with such an approach, the final crack direction is predicted quite well, in fact much better than the prediction made by the fracture mechanics type of models considering combination of only elastic response and softening.

The presented model has the potential to describe complex damage phenomena in a cyclic and/or non‐proportional loading program, such as crack closing and re‐opening, cohesive resistance deterioration due to tangential sliding, by using only a few parameters compared to the traditional models for cyclic loading.

Simple but also accurate models are needed to predict the failure response of concrete structures. Simplicity involves modelling assumptions while accuracy involves objectivity of both the experimentally identified model parameters and the numerica results. For concrete‐like heterogeneous and brittle materials, the modelling assumptions idealizing the material as a homogeneous continuum with classical linear or non‐linear behaviour, leads to some problems at the identification stage, namely the size effect phenomena. A continuum damage model, representing the non‐linear behaviour due to microcracking, is proposed here for predictive computations of structural responses. A Weibull based theory is used to determine, in a statistical sense, the value of the initial damage threshold. The essential influence of material heterogeneity on the damage evolution, is accounted for with a bi‐scale approach which is based on the idea of the non‐local continuum with local strain. It has already established that the non‐local approaches yield realistic failure predictions and the numerical results are convergent for subsequent mesh refinements. The applications presented here show the ability of the approach to predict the failure response of concrete structures without being obscured by size effect problems.

The purpose of the paper is to improve the calculability of a continuum damage failure model of composite laminates based on Tsai-Wu criteria.

A technique based on viscous regularization, a characteristic element length and fracture energies of fiber and matrix are used in the model.

The calculability of the material model is improved. The modified model can predict the behavior of composite structure better.

The convergence problem and the mesh softening problem are main concern in the calculability of numerical model. In order to improve the convergence, a technique based on viscous regularization of damage variable is used. Meanwhile, characteristic element length and fracture energies of fiber and matrix are added into the damage constitutive equation to reduce the mesh sensitivity of numerical results. Finally, a laminated structure with damages is implemented using a User Material Subroutine in ABAQUS/Standard. Mesh sensitivity and value of viscosity are discussed.

The purpose of this paper is to develop an improved analytical model for predicting the damage response of multi‐storey reinforced concrete frames modelled as an elastic beam‐column with two inelastic hinges at its ends.

The damage is evaluated in the hinges, using the concentrated damage concepts and a new member damage evaluation method for frame members, which leads to a meaningful global damage index of the structure. A numerical procedure for predicting the damage indices of the structures using matrix structural analysis, plastic theory and continuum damage model is also developed. The method is adequate for the prediction of the failure mechanisms.

Using the proposed framework numerical examples are finally included. From the obtained results, the advantages and limitation of the proposed model are observed.

The numeric model presented is useful to solve multi‐storey reinforced concrete frames using an inexpensive procedure that combines structural finite elements (beams) of low execution cost, with the moment‐curvature constitutive models deriving from classic stress‐strain ones. The proposed techniques give an inexpensive and reliability procedure to model the frame structures.

The purpose of this paper is to develop a progressive damage framework to predict the fatigue life of cord-reinforced rubber composite under cyclic loadings. Special attention has been paid to failure mechanisms, like cord–rubber interfacial debonding, and rubber matrix damage.

The constitutive modeling is based on the continuum damage mechanics (CDMs) and the thermodynamics of irreversible process. The damage in rubber is described by an istropic law, whereas elasto-plastic continuum model has been proposed for cord–rubber interphase layer. The numerical framework is implemented into commercial finite element code Abaqus/Standard via user subroutine (UMAT).

One of the most important findings obtained from reviewing various techniques is that meso-level fatigue damage modeling based on developed framework can simulate competitive damage scenarios, e.g. debonding, delamination or matrix failure.

A systematic framework for predicting failure in cord-reinforced rubber composite is formulated within the context of CDMs that can also be applied for industrial components, such as tires and airsprings.

Focuses on a finite element computational model for the Timoshenko beam which is idealized as an elasto‐plastic‐damage medium governed by Lemaitre’s continuum damage mechanics (CDM) model for ductile fracture. Response under monotonically increasing loading does not show any deviation from elasto‐plastic simulation. However, a marked difference in the residual stress field is noted by virtue of the unloading phase, in which the CDM model allows for stiffness degradation in contrast to classical elasto‐plasticity which requires unloading at the (frozen) initial stiffness of the material.

The purpose of this paper is to present a new simplified local remeshing procedure for the study of discrete crack propagation in finite element (FE) mesh. The proposed technique accounts for the generation and propagation of crack‐like failure within an FE‐model. Beside crack propagation, the technique enables the analysis of fragmentation of initially intact continuum. The capability of modelling fragmentation is essential in various structure‐structure interaction analyses such as projectile impact analysis and ice‐structure interaction analysis.

The procedure combines continuum damage mechanics (CDM), fictitious crack approach and a new local remeshing procedure. In the approach a fictitious crack is replaced by a discrete crack by applying delete‐and‐fill local remeshing. The proposed method is independent of mesh topology unlike the traditional discrete crack approach. The procedure is implemented for 3‐D solid elements in commercial finite element software Abaqus/Explicit using Python scripting. The procedure is completely automated, such that crack initiation and propagation analyses do not require user intervention. A relatively simple constitutive model was implemented strictly for demonstrative purposes.

Well known examples were simulated to verify the applicability of the method. The simulations revealed the capabilities of the method and reasonable correspondence with reference results was obtained. Material fragmentation was successfully simulated in ice‐structure interaction analysis.

The procedure for modelling discrete crack propagation and fragmentation of initially intact quasi‐brittle materials based on local remeshing has not been presented previously. The procedure is well suited for simulation of fragmentation and is implemented in a commercial FE‐software.

To provide a reinforced concrete model including bonding coupled to a classical continuum damage model of concrete, capable of predicting numerically the crack pattern distribution in a RC structure, subjected to traction forces.

A new coupling between bonding model and an alternative model for concrete cracking is proposed and analyzed. For concrete, proposes a damage‐like material model capable of combining two types of dissipative mechanisms: diffuse volume dissipation and localized surface dissipation.

One of the most important contributions is the capacity of predicting maximal and minimal spacing of macro‐cracks, even if the exact location of cracks remains undetermined. Another contribution is to reiterate on the insufficiency of the local damage model of concrete to handle this class of problems; much in the same manner as for localization problem which accompany strain‐softening behavior.

Bonding becomes very important to evaluate both the integrity and durability of a RC structure, or in particular to a reliable prediction of crack spacing and opening, and it should be integrated in future analysis of RC.

Shows that introduction of the influence of concrete heterogeneities in numerical analysis can directly affect the configuration of the crack pattern distribution. Use of a strong discontinuity approach provides additional cracking information like opening of macro‐cracks.

Traditionally, an armor-grade composite is based on a two-dimensional (2D) architecture of its fiber reinforcements. However, various experimental investigations have shown that armor-grade composites based on 2D-reinforcement architectures tend to display inferior through-the-thickness mechanical properties, compromising their ballistic performance. To overcome this problem, armor-grade composites based on three-dimensional (3D) fiber-reinforcement architectures have recently been investigated experimentally. The paper aims to discuss these issues.

In the present work, continuum-level material models are derived, parameterized and validated for armor-grade composite materials, having four (two 2D and two 3D) prototypical reinforcement architectures based on oriented ultra-high molecular-weight polyethylene fibers. To properly and accurately account for the effect of the reinforcement architecture, the appropriate unit cells (within which the constituent materials and their morphologies are represented explicitly) are constructed and subjected to a series of virtual mechanical tests (VMTs). The results obtained are used within a post-processing analysis to derive and parameterize the corresponding homogenized-material models. One of these models (specifically, the one for 0°/90° cross-collimated fiber architecture) was directly validated by comparing its predictions with the experimental counterparts. The other models are validated by examining their physical soundness and details of their predictions. Lastly, the models are integrated as user-material subroutines, and linked with a commercial finite-element package, in order to carry out a transient non-linear dynamics analysis of ballistic transverse impact of armor-grade composite-material panels with different reinforcement architectures.

The results obtained clearly revealed the role the reinforcement architecture plays in the overall ballistic limit of the armor panel, as well as in its structural and damage/failure response.

To the authors’ knowledge, the present work is the first reported attempt to assess, computationally, the utility and effectiveness of 3D fiber-reinforcement architectures for ballistic-impact applications.