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The localized strain softening behaviour of concrete has been modelled by two approaches: (i) the stiffness degrading model based on the total stress‐strain constitutive relationship, and (ii) the tangent softening model based on the incremental stress‐strain relationship. The models are implemented using a new softening initiation criterion proposed for application in multi‐dimensional finite element analysis. Parametric analyses on plain concrete beams, tested experimentally by other researchers, have been carried out to investigate the required numerical efforts, the mesh objectivity, and the energy dissipation characteristics of the structures. The stiffness degrading model is very stable even when applied with relatively coarse finite element meshes. However, the computational demand of this model is relatively high. The combination of a total stress‐strain constitutive relationship to compute the element responses, and an incremental relationship to formulate the stiffness matrix, appears to be computationally efficient and stable, provided that adequately refined finite element mesh is used to model the structure.

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 study is to experimentally investigate the large deformation compression characteristics of fused deposition modelling (FDM)-printed poly lactic acid (PLA), considering the combined effect of infill density and strain rate, and to develop a constitutive viscoplastic model that can incorporate the infill density to predict the experimental result.

The experimental approach focuses on strain rate-dependent (2.1 × 10⁻⁴, 2.1 × 10⁻³, and 2.1 × 10⁻² s⁻¹) compression testing for varied infill densities. Scanning electron microscopy (SEM) imaging of compressed materials is used to investigate deformation processes. A hyperelastic-viscoplastic constitutive model is constructed that can predict mechanical deformations at different strain rates and infill densities.

The yield stress of PLA increased with increase in strain rate and infill density. However, higher degree of strain-softening response was witnessed for the strain rate corresponding to 2.1 × 10⁻² s⁻¹. While filament splitting and twisting were identified as the damage mechanisms at higher strain rates, matrix crazing was observed as the primary deformation mechanism for higher infill density (95%). The developed constitutive model captured yield stress and post-yield softening behaviour of FDM build PLA samples with a high R² value of 0.99.

This paper addresses the need to analyse and predict the mechanical response of FDM print polymers (PLA) undergoing extensive strain-compressive loading through a hyperelastic-viscoplastic constitutive model. This study links combined effects of the printing parameter (infill density) with the experimental parameter (strain rate).

A concrete material model is presented. The model is based on non‐associated plasticity for the pre‐failure and ductile post‐failure regimes and fracture (smeared crack approach) for the brittle post‐failure regime. The implementation of the constitutive model in the 2‐D elements of a general purpose non‐linear incremental finite element code is discussed. Some important numerical features of the implementation are the implicit integration of the stress/strain relation and the use of an efficient symmetric stiffness formulation for the equilibrium iterations.

With the discussion on the linear relationship of determined material parameters, this study aims to propose a new method to analyze the deformation mechanism.

A modified constitutive model based on the hyperbolic sine Arrhenius equation has been established, which is applied to describe the flow behavior of Ti-6Al-4V alloy during the superplastic forming (SPF).

The modified constitutive model in this work has a good ability to describe the flow behavior for Ti-6Al-4V in SPF. Besides, a deformation map of titanium material is obtained based on the parameters. As the supplement, finite element models of high-temperature tensile tests are carried out as the application of the constitutive model.

The relationship between constitutive model parameters and forming mechanism is established, which is a new angle in rheological behavior research and constitutive model analysis.

The purpose of this paper is to develop a constitutive model in cyclic viscoplasticity of perfluoroelastomers that accounts for the Mullins effect and to determine adjustable parameters in the stress‐strain relations by fitting observations in mechanical tests.

A perfluoroelastomer with a complicated internal structure is modeled as an equivalent incompressible, permanent, non‐affine network of chains with constrained mobility. Its viscoplastic response at finite strains is treated as sliding of junctions between chains with respect to their reference positions. Damage accumulation is associated with acceleration of plastic flow of junctions driven by growth of free volume. Stress‐strain relations are derived by using the Clausius‐Duhem inequality.

Constitutive equations are developed that correctly describe the mechanical behavior of perfluoroelastomers under cyclic loading with stress‐ and strain‐controlled deformation programs and arbitrary numbers of cycles. Adjustable parameters in the stress‐strain relations are found by matching experimental data in uniaxial tensile tests. Numerical simulation demonstrates that the model adequately predicts characteristic features of the Mullins effect.

A constitutive model is derived that can be applied for description of the viscoplastic response in perfluoroelastomers at cyclic loading with complicated deformation programs and prediction of their time to failure under fatigue conditions.

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.

Shear-induced strain localization in granular materials has been a hot topic under intensive research during the last four decades. However, the micromechanical process and mechanisms underlying the initiation and development of shear bands are still not fully understood. The purpose of this paper is to eliminate this deficiency.

The paper carries out several two-dimensional distinct element method simulations to examine various global and local micromechanical quantities particular the energy dissipation and local stress and strain invariants with a special emphasis on the initiation and propagation of shear bands. Moreover, the effects of various influential variables including initial void ratio, confining stress, inter-particle friction coefficient, rolling resistance coefficient, specimen slenderness and strain rate on the pattern, scope and degree of shear bands are investigated.

Novel findings of the relationship between sliding and rolling dissipation band and shear band are achieved, indicating a plastic dissipation nature for the shear band. The high inter-particle sliding or rolling resistance, relative small initial void ratio, relative low confining stress and high strain rate facilitate the formation of shear band. In addition, the specimen slenderness affects the pattern of shear band.

In this paper, a comprehensive and deep investigation on shear band formation linked with localization of energy dissipation and strain invariants was presented. The new findings on particle scale during shear band formation helps to develop robust micromechanics-based constitutive models in the future.

There is not a unified modelling approach to finite element failure analysis of concrete dams. Different behaviours of a dam predicted by different fracture methods with various material constitutive models may significantly influence on the dam safety evaluation. The purpose of this paper is to present a general comparative investigation to examine whether the nonlinear responses of concrete dams obtained from different fracture modelling approaches are comparable in terms of crack propagation and failure modes.

Three fracture modelling approaches, including the extended finite element method with a cohesive law (XFEM-COH), the crack band finite element method with a plastic-damage relation (FEPD), and the Drucker-Prager (DP) elasto-plastic model, are chosen to analyse damage and cracking behaviour of concrete gravity dams under overloading conditions. The failure process and loading capacity of a dam are compared.

The numerical results indicate that the three approaches are all applicable to predict loading capacity and safety factors of gravity dams. However, both XFEM-COH and FEPD give more reasonable crack propagation and failure modes in comparison with DP. Therefore, when cracking patterns are the major concern for safety evaluation of concrete dams, it is recommended that XFEM-COH and FEPD rather than DP be used.

The comparison of cracking behaviours of concrete dams obtained from different fracture modelling approaches is conducted. The applicability of the modelling approaches for failure analysis of concrete dams is discussed, and from the results presented in this work, it is significant to consider the suitability of the selected fracture modelling approach for dam safety evaluation.

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.