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Highlights • A new thermodynamics-based constitutive model employing a new way for coupling damage and plasticity is proposed. • The proposed model uses a single set of identifiable parameters. • The proposed model can predict the macro-mechanical behaviour of porous rocks together with the onset and modes of localisation under different confining pressures. Abstract This study presents the development of a thermodynamics-based constitutive model for describing the macro-mechanical behaviour of porous rocks. The model formulation is developed within the well-established framework of generalised thermodynamics, or thermodynamics with internal variables (TIV), in order to guarantee the thermodynamics admissibility of the results. A new way for coupling different mechanisms of energy dissipation is proposed within the framework of TIV, so that the essential aspects of macro-mechanical behaviour of porous rocks ranging from brittle to ductile, dilation and compaction, as well as various modes of localised failure, under shearing at a wide range of confining pressures are correctly captured. The pressure sensitive behaviour of porous rocks is captured by introducing a shift stress in the formulation of the yield function, through the concept of 'frozen elastic energy' or non-dissipative part of the plastic work, which is stored within the material during loading. The proposed model allows the investigation of several important aspects of macro-mechanical behaviour of porous rocks at both material and specimen levels. [ABSTRACT FROM AUTHOR]

Rock response to confining pressure and strain rate can change dramatically from very brittle to ductile. Capturing this transition is crucial for a correct prediction of rock mass failure due to blasting, explosion or drilling in mining. In this work, a new constitutive model that accounts for the effects of both confining pressure and strain rate on the nominal strength and post peak behaviour is proposed for dry intact rocks and other similar geological materials. The key features of the proposed constitutive model are the employment of a single loading function that evolves from initial yielding to ultimate failure during damaging and the rate-dependent enhancement so that the strain rate effects can be faithfully described at different confining pressures. The model can adequately capture both the brittle and ductile responses as well as the brittle-ductile transition as a result of both strain rate and confining pressure. [ABSTRACT FROM AUTHOR]

Highlights: [•] A new approach to bridge the scales in modelling localised failure is proposed. [•] We enrich the kinematics of constitutive models with localised mode of deformation. [•] The resulting constitutive models possess two different scales of behaviour. [•] Size effects induced by localised failure are properly captured with models based on this approach. [ABSTRACT FROM AUTHOR]

Fallas localizadas en geomateriales están precedidas y se dan en conjunto con deformaciones intensas y cambios micro estructurales irreversibles del material en una región de tamaño finito, pero pequeña. Corte, compactación y bandas de dilatación observables en suelos y rocas porosas son ejemplos típicos de fenómenos que conducen a fallas localizadas. Ha sido experimentalmente demostrado que el ancho h de la banda de localización es una cantidad física relacionada con la micro estructura del material. Por otro lado, métodos numéricos para la resolución de problemas de valor en la frontera usualmente introducen otra longitud de escala H como un resultado de la discretización espacial del dominio considerado en partes más pequeñas sobre el cual la respuesta constitutiva del material está definida en términos de relaciones incrementales de tensión-deformación. Mientras h como cantidad física está fija, H varía con la resolución de la discretización numérica. Dado que h escala con la micro estructura del material y por lo tanto es usualmente mucho más pequeño que la resolución de la discretización numérica, el caso H > h es considerado en este estudio, por ejemplo el comportamiento en falla gobernado por una banda de localización de ancho h inserta en una masa elástica de lado nominal H. Se presenta un marco de modelamiento constitutivo general para conectar estas dos escalas, y las respuestas correspondientes del material dentro y fuera de la zona de localización. Se demuestra como esta estrategia puede ayudar a obtener soluciones con significado físico que son independientes de la discretización espacial en análisis numéricos. Análisis numéricos de falla localizada en materiales cuasi frágiles son además usados para destacar las características y aplicabilidad de la estrategia propuesta. [ABSTRACT FROM AUTHOR]

Abstract: Most constitutive models for quasi-brittle materials ignore the fact that the measurable fracture energy represents more than one dissipative mechanism, including those from the creation of new surface areas and frictions between surfaces. Specifically, these models “see” the measurable fracture energy as one that comes only from the creation of new surface area. However, experimental deduction by Bažant indicates that the frictional dissipation is not at all negligible, even in mode I failure, where it contributes an energy loss of around 50–75% to the total dissipation budget. Here we study the consequences of this simplification by adopting simple local and nonlocal damage models, which include a new powerful parameter that represents the measurable partition of the dissipation. It is found that the oversight of frictional dissipation can lead to a critical over-prediction of both the magnitude and the spreading of damage. [Copyright &y& Elsevier]

Abstract: We present a damage model for softening materials with evolving nonlocal interactions. The thermodynamic implications and the material stability issue are addressed. The proposed nonlocal averaging scheme provides the obtained constitutive models with an evolving nonlocal interaction which is activated only when damage occurs. In the analysis of structures made of quasi-brittle materials, this feature helps not only to overcome some issues with the incorrect initiation of damage but also to better control the evolving size of the active fracture process zone. This is an essential feature that is usually not considered in depth in many existing nonlocal approaches to the continuum modelling of quasi-brittle fracture. Numerical examples are given to demonstrate features of the proposed modelling approach. [Copyright &y& Elsevier]

Abstract: In the present study we consider an adaptation of Nguyen’s model [G.D. Nguyen, A thermodynamic approach to constitutive modelling of concrete using damage mechanics and plasticity theory, D.Phil. Thesis, Dept. of Engng. Sci., University of Oxford, 2005] for brittle materials to the case of ductile rupture. We focus our attention on the formulation of a consistent tangent stiffness matrix which is essential for the efficiency and convergence of the implementation within a finite element framework. We demonstrate the capability of the model to generate mesh-independent results and to follow the rupture process very close to failure. Rupture analysis of thin plates of different geometry is presented (symmetric double notch-edged specimen, asymmetric double notch-edged specimen, double notch-edged specimen containing a hole). Further modifications are outlined required to simulate crack growth and paths under the conditions of creep and fatigue. [Copyright &y& Elsevier]

Abstract: The paper presents an approach to constitutive modelling of concrete using damage mechanics and plasticity theory. The thermodynamic formulation, and parameter identification of a non-local coupled damage-plasticity model are presented in this study. The particular focus is the calibration of model parameters. It is shown that both the local parameters and the parameters governing the non-local interaction can be determined from experimental data reliably and consistently. A novel procedure is developed for parameter identification, using the separation of total dissipation energy into additive parts corresponding to different dissipation mechanisms. The relationship between the local and non-local parameters is also addressed, helping to obtain model responses consistent with the fracture energy of the material. The application of the model and the calibration procedure proposed in this study to the numerical failure analysis of concrete structures is illustrated through a series of real structural tests, showing both the performance of the model and the consistency of the proposed calibration procedure. [Copyright &y& Elsevier]

Abstract: This paper focuses on the development of a thermodynamic approach to constitutive modelling of concrete materials, with emphasis on the use of non-local damage models. Effort is put on the construction of a consistent and rigorous thermodynamic framework, which readily allows the incorporation of non-local features into the constitutive modelling. This is an important feature in developing non-local constitutive models based on thermodynamics. Examples of non-local constitutive models derived from this framework and numerical examples are given to demonstrate the promising features of the proposed approach. [Copyright &y& Elsevier]

In this study, new theoretical and experimental stress-strain-damage correlation procedures for hard rock constitutive models are proposed. The damage-plasticity modelling framework is first supplied with the unified yield-failure criterion to describe the failure behaviour of granite under triaxial compression. This unified criterion allows the initial yield surface to evolve to a final failure surface through the utilisation of an appropriate damage evolution law. This evolution automatically captures the quasi-brittle behaviour of rocks under shearing at low confining pressure and ductile response under high confining pressure, as well as the transition from quasi-brittle to ductile reactions. In this theoretical sense, damage and plasticity are tightly coupled to govern the behaviour of rocks under different confining pressures without requiring any separate formulations for softening or hardening. Next, an innovative experimental correlation procedure is proposed to better link the experimental damage measure to stress states throughout triaxial loading. By obtaining full stress, strain and acoustic emission damage results from testing it was possible to construct a series of evolving yield surfaces from experiment. These surfaces, coupled with experimental damage evolution with respect to accumulated plastic strain, provide a comprehensive data set to a constitutive model for calibration. The results of numerical simulation show that this new method to incorporate coupled stress-strain-damage evolution characteristics directly from experiment removes the need for trial and error curve fitting. Also, by maintaining a closer link to detailed experimental results, the model is easier to calibrate and can be relied upon to predict the damage and stress states for compressive stress regimes. Finally, it is shown that the theoretical and experimental procedures can capture the key behaviours of granite under a range of confining pressures. [ABSTRACT FROM AUTHOR]