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The temperature increase induced by radioactive waste decay generates the thermal pressurisation around the excavation damage zone (EDZ), and the excess pore pressure could induce fracture re-opening and propagation. Shear strain localisation in band mode leading to the onset of micro-/macro-cracks can be always evidenced before the fracturing process from the lab experiments using advanced experimental devices. Hence, the thermal effects on the rock behaviour around the EDZ could be modelled with the consideration of development of shear bands. A coupled local 2nd gradient model with regularisation technique is implemented, considering the thermo-hydro-mechanical (THM) couplings in order to well reproduce the shear bands. Furthermore, the thermo-poro-elasticity framework is summarized to validate the implemented model. The discrepancy of thermal dilation coefficient between solid and fluid phases is proved to be the significant parameter leading to the excess pore pressure. Finally, an application of a heating test based on Eurad Hitec benchmark exercise with a drift supported by a liner is studied. The strain localisation induced by thermal effects is properly reproduced. The plasticity and shear bands evolutions are highlighted during the heating, and the shear bands are preferential to develop in the minor horizontal principal stress direction. Different shear band patterns are obtained with changing gap values between the drift wall and the liner. A smaller gap between the wall and the liner can limit the development of shear bands.HighlightsThe formulation of a coupled local 2nd gradient model considering the thermo-hydro-mechanical (THM) couplings.Validation of the model with comparison with analytical solution of thermo-elastic problem.The prediction of strain localisation pattern induced by thermal effects around a large scale drift.The analysis of the gap distance (between the drift wall and the liner) on the strain localisation process under the thermal loading.

A smoothed particle hydrodynamics code based on micropolar continua for geomaterials is developed for problems involving large deformation and shear strain localization. Two typical geotechnical problems, i.e., biaxial compression test and sand column collapse, are simulated using classical and micropolar model to demonstrate the performance of the newly proposed method. A parameter study is given on the scale effect in the micropolar continua.

This paper presents results of investigation of multifunctional β-Ti alloy Gum Metal subjected to tension at various strain rates. Digital image correlation was used to determine strain distributions and stress-strain curves, while infrared camera allowed for us to obtain the related temperature characteristics of the specimen during deformation. The mechanical curves completed by the temperature changes were applied to analyze the subsequent stages of the alloy loading. Elastic limit, recoverable strain, and development of the strain localization were studied. It was found that the maximal drop in temperature, which corresponds to the yield limit of solid materials, was referred to a significantly lower strain value in the case of Gum Metal in contrast to its large recoverable strain. The temperature increase proves a dissipative character of the process and is related to presence of ω and α″ phases induced during the alloy fabrication and their exothermic phase transformations activated under loading. During plastic deformation, both the strain and temperature distributions demonstrate that strain localization for higher strain rates starts nucleating just after the yield limit leading to specimen necking and rupture. Macroscopically, it is exhibited as softening of the stress-strain curve in contrast to the strain hardening observed at lower strain rates.

Thin fiber networks are widely represented in nature and can be found in man-made materials such as paper and packaging. The strength of such materials is an intricate subject due to inherited randomness and size-dependencies. Direct fiber-level numerical simulations can provide insights into the role of the constitutive components of such networks, their morphology, and arrangements on the strength of the products made of them. However, direct mechanical simulation of randomly generated large and thin fiber networks is characterized by overwhelming computational costs. Herein, a stochastic constitutive model for predicting the random mechanical response of isotropic thin fiber networks of arbitrary size is presented. The model is based on stochastic volume elements (SVEs) with SVE size-specific deterministic and stochastic constitutive law parameters. The randomness in the network is described by the spatial fields of the uniaxial strain and strength to failure, formulated using multivariate kernel functions and approximate univariate probability density functions. The proposed stochastic continuum approach shows good agreement when compared to direct numerical simulation with respect to mechanical response. Furthermore, strain localization patterns matched the one observed in direct simulations, which suggests an accurate prediction of the failure location. This work demonstrates that the proposed stochastic constitutive model can be used to predict the response of random isotropic fiber networks of arbitrary size.

In this study, calculations are carried out for the plastic deformation of amorphous metallic glass films resting on rough substrates. It is found that plastic strain localization in the amorphous film is controlled by the synergistic interplay between substrate constraint and interfacial debonding. For the polymer substrate with low stiffness and yield stress, film-substrate interfacial debonding has negligible influence on plastic deformation of amorphous film. However, in the case of metal substrate with high stiffness and yield stress, debonding of the film-substrate interface promotes plastic strain localization in the amorphous film, leading to low plastic dissipation. The interface morphology plays an important role in development of shear bands in the amorphous film; high degree of interface waviness enables formation of multiple shear bands in the amorphous film, delaying strain localization and promoting plastic dissipation. We have further unraveled the effect of adding a buffer layer in the structure consisting of the amorphous film and rough substrate. The wavy interface is capable of generating inhomogeneous plastic deformation of the buffer layer, which activates strain localization bands in the amorphous film. The buffer layer with high stiffness suppresses strain localization in the amorphous film.

Abstract Metallic materials exhibit pronounced strain localization during damage and failure, posing a challenge in damage mechanics when predicting the change in the size of the strain localization zone. In this study, uniaxial tensile tests were carried out to observe changes in the size of the strain localization zone during the loading of aluminum and low-carbon steel. The initial and final states of the two metallic materials during deformation localization were compared. The strain localization zone shrank gradually with the increase in the load, which agrees with existing electronic speckle pattern interferometry (ESPI) results. This experimental phenomenon was further analyzed theoretically. By establishing the relationship between the material characteristic length and the damage, the variation of the material characteristic length was revealed, and the form of the nonlocal kernel function with a varying characteristic length was determined. The results demonstrated that within the framework of nonlocal damage theory, the nonlocal kernel function with a varying characteristic length can be used to satisfactorily simulate the gradual shrinkage of the strain localization zone of metallic materials with the damage evolution. Therefore, this study provides an effective theoretical tool for predicting the size of the strain localization zone.

The present paper aims at providing a comprehensive investigation of the abilities and limitations of strain gradient crystal plasticity (SGCP) theories in capturing different kinds of localization modes in single crystals. To this end, the small deformation Gurtin-type SGCP model recently proposed by the authors, based on non-quadratic defect energy and the uncoupled dissipation assumption, is extended to finite deformation. The extended model is then applied to simulate several single crystal localization problems with different slip system configurations. These configurations are chosen in such a way as to obtain idealized slip and kink bands as well as general localization bands, i.e., with no particular orientation with respect to the initial crystallographic directions. The obtained results show the good abilities of the applied model in regularizing various kinds of localization bands, except for idealized slip bands. Finally, the model is applied to reproduce the complex localization behavior of single crystals undergoing single slip, where competition between kink and slip bands can take place. Both higher-order energetic and dissipative effects are considered in this investigation. For both effects, mesh-independent results are obtained, proving the good capabilities of SGCP theories in regularizing complex localization behaviors. The results associated with higher-order energetic effects are in close agreement with those obtained using a micromorphic crystal plasticity approach. Higher-order dissipative effects led to different results with dominant slip banding.

This paper presents a finite element approach for modelling three-dimensional crack propagation in quasi-brittle materials, based on the strain injection and the crack-path field techniques. These numerical techniques were already tested and validated by static and dynamic simulations in 2D classical benchmarks [Dias et al., in: Monograph CIMNE No-134. International Center for Numerical Methods in Engineering, Barcelona, (2012) ; Oliver et al. in Comput Methods Appl Mech Eng 274:289–348, (2014) ; Lloberas-Valls et al. in Comput Methods Appl Mech Eng 308:499–534, (2016) ] and, also, for modelling tensile crack propagation in real concrete structures, like concrete gravity dams [Dias et al. in Eng Fract Mech 154:288–310, (2016) ]. The main advantages of the methodology are the low computational cost and the independence of the results on the size and orientation of the finite element mesh. These advantages were highlighted in previous works by the authors and motivate the present extension to 3D cases. The proposed methodology is implemented in the finite element framework using continuum constitutive models equipped with strain softening and consists, essentially, in injecting the elements candidate to capture the cracks with some goal oriented strain modes for improving the performance of the injected elements for simulating propagating displacement discontinuities. The goal-oriented strain modes are introduced by resorting to mixed formulations and to the Continuum Strong Discontinuity Approach (CSDA), while the crack position inside the finite elements is retrieved by resorting to the crack-path field technique. Representative numerical simulations in 3D benchmarks show that the advantages of the methodology already pointed out in 2D are kept in 3D scenarios.

3D discrete-element modeling is used to analyze passive pressure applied by dense soil to a retaining wall. The soil particles have spherical shapes with the radii selected from the normal distribution. The calculation of tangential forces between the particles takes into account the sliding friction and rolling resistance. The surface roughness of the retaining wall has influence on localization of shear strains in the granular medium and on the pressure applied to the wall by the granular material. The calculation results are compared with the classical solution of the limit state theory.

In this work, the crack tip strain localization in a face centered cubic single crystal subject to both monotonic and cyclic loading was investigated. The effect of constraint was implemented using T -stress and strain accumulation was studied for both isotropic and anisotropic elastic cases with the appropriate application of remote displacement fields in plane strain. Modified boundary layer simulations were performed using the crystal plasticity finite element framework. The consideration of elastic anisotropy amplified the effect of constraint level on stress and plastic strain fields near the crack tip indicating the importance of its use in fracture simulations. In addition, to understand the cyclic stress and strain behavior in the vicinity of the crack tip, combined isotropic and kinematic hardening laws were incorporated, and their effect on the evolution of yield curves and plastic strain accumulation were investigated. With zero-tension cyclic load, the evolution of plastic strain and Kirchhoff stress components showed differences in magnitudes between isotropic and anisotropic elastic cases. Furthermore, under cyclic loading, ratcheting was observed along the localized slip bands, which was shown to be affected by T -stress as well as elastic anisotropy. Negative T -stress increased the accumulation of plastic strain with number of cycles, which was further amplified in the case of elastic anisotropy. Finally, in all the cyclic loading simulations, the plastic strain accumulation was higher near the 55 0 slip band.