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In this paper, we present a new united approach to formulate the equivalent micropolar constitutive relation of two-dimensional (2-D) periodic cellular material to capture its non-local properties and to explain the size effects in its structural analysis. The new united approach takes both the displacement compatibility and the equilibrium of forces and moments into consideration, where Taylor series expansion of the displacement and rotation fields and the extended averaging procedure with an explicit enforcement of equilibrium are adopted in the micromechanical analysis of a unit cell. In numerical examples, the effective micropolar constants obtained in this paper and others derived in the literature are used for the equivalent micropolar continuum simulation of cellular solids. The solutions from the equivalent analysis are compared with the discrete simulation solutions of the cellular solids. It is found that the micropolar constants developed in this paper give satisfying results of equivalent analysis for the periodic cellular material. Graphic abstract : [Figure not available: see fulltext.] [ABSTRACT FROM AUTHOR]

A modal analysis in linear elastic field for periodic masonry structures is proposed, based on continuous and discrete models. The continuum model is based on analytical homogenisation procedures, within the standard Cauchy and micropolar continuum theories, and the discrete model (DEM) describes masonry as a rigid skeleton. Both models are based on the assumptions of rigid blocks and mortar joints modelled as elastic interfaces. Modal analysis, performed with continuous and discrete models, has been carried on both at Representative Elementary Volume (REV) level and at masonry panel level, such as to evaluate masonry sensitivity to local microstructure and to characteristic length of REV compared with the masonry panel size. Hence, a parametric analysis is carried on to investigate the effect of (i) masonry texture (running versus header bond and other brick width-to-height ratios); (ii) size of heterogeneity; (iii) mortar elastic parameters; (iv) panel dimensions. Modal analysis is then carried on and compared also with a heterogeneous Finite Element Model (FEM) and a model already existent in literature (Brasile and Casciaro, 2009). The proposed modal analysis for masonry is a first step to investigate the dynamic behaviour of masonry panels. Comparisons between several models has been performed to verify the reliability of the proposed procedures and to use these different approaches for a future development in non-linear field. In addition, a modal analysis is performed to examine a full-scale masonry shear wall with constraints such as to simulate a single shear wall in a two-story masonry building, with the aim to provide a case of technical interest. [ABSTRACT FROM AUTHOR]

Borehole breakout denotes the failure in rock mass subjected to drilling, caused by stress concentrations exceeding the material strength. Depending on the material properties, the preexisting in situ stress state, and the borehole dimensions, different types of borehole breakout, such as spiral-shaped breakout or v-shaped breakout, are distinguished in the literature. In the present work, we address the influence of the material properties on the predicted borehole breakout mode in a comprehensive finite element study. To this end, we employ a gradient-enhanced micropolar damage-plasticity model based on the Mohr–Coulomb strength criterion, formulated in the finite strain regime, which is calibrated based on experimental results from plane strain compression tests on Red Wildmoor sandstone. In the numerical study, the influence of the in situ stress state, the material friction angle, plastic dilation, post peak residual strength, and the inherent material length scale parameters are investigated. Thereby, we demonstrate that depending on the material parameters, substantially different failure modes, characterized by strongly localized shear bands or diffuse failure zones, are predicted. It is shown that in particular the brittleness of the material in the post peak regime has a major influence on the predicted breakout type. Moreover, a statistical validation of the results is obtained by considering different random field distributions of the initial material strength. [ABSTRACT FROM AUTHOR]

Micromorphic continua are equipped with additional degrees of freedom in comparison to the classical continuum, representing microdeformations of the material points of a body. Secondary they are provided with a higher order gradient. Therefore, they are able to account for material size-effects and to regularize the boundary value problem, when localization phenomena arise. Arbitrary microdeformations are allowed for in the micromorphic continuum, while the special cases micropolar continuum and microstrain continuum merely allow for microrotation and microstrain, respectively. Amongst these cases, the micropolar case has been covered most extensively in the literature. One goal of this paper is to make the transition from a full micromorphic continuum to a micropolar or microstrain continuum, by varying the constitutive equations. To this end two different possibilities are presented for hyperelasticity with large deformations. This leads to four different material models, which are compared and illustrated by numerical examples. Another goal is to present a constitutive model encompassing the micromorphic, micropolar and microstrain continua as special cases and enabling arbitrary mixtures of micropolar and microstrain parts, allowing the representation of versatile material behaviour. [ABSTRACT FROM AUTHOR]

The aim of this paper is to present a critical comparative review of different models that may be adopted for modelling the mechanical behaviour of masonry, with particular attention to microstructured models. Several continuous and discrete models are discussed. Such models are based on the following assumptions: i) the structure is composed of rigid blocks; ii) the mortar is modelled as an elastic material or an elastic interface. The rigid block hypothesis is particularly suitable for historical masonry, in which stone blocks may be assumed as rigid bodies. For this type of masonry, mortar thickness is negligible if compared with block size, hence it can be modelled as an interface. Masonry-like materials may be modelled taking into account their heterogeneity by adopting a heterogeneous Finite Element Model (FEM) or a Discrete Element Model (DEM). The former seems to be more representative of masonry, but it is computationally onerous and results interpretation may be difficult; the latter is limited to rigid block assumption and mortar joints modelled as interfaces. For this reason, continuous equivalent models may be suitable to investigate masonry behaviour. Continuum equivalent models provide, in an analytical form, constitutive functions, but Cauchy model may be not suitable to describe masonry behaviour due to not negligible size of heterogeneity (block size) with respect to masonry panel size. For this reason, micropolar equivalent continuum may be adopted. By reference to the existing literature, a simple and effective DEM is adopted, in which masonry is modelled as a ‘skeleton’ having a behaviour depending on forces and moments transferred between blocks through the interfaces (mortar joints). Moreover for the micropolar equivalent continuum, an ad hoc enriched homogenised FEM is formulated by means of triangular elements. The proposed numerical models represent two possible simple approaches for solving heterogeneous problems. Such models are developed both by means of fast numerical routines and do not require specific computer codes, whereas the heterogeneous FEM may be studied by adopting a traditional FE code. DEM and heterogeneous FEM are adopted to verify reliability and application field of Cauchy and micropolar continua. Moreover, sensitivity of micropolar model to the Representative Elementary Volume (REV) chosen is discussed. For these purposes, ad hoc FE models are adopted, with constitutive functions obtained from an identification procedure (both for Cauchy and micropolar continua). An extensive comparison between DEM, heterogeneous FEM and equivalent homogenous FEM is presented in some meaningful cases, taking into account also the effect of heterogeneity size on models behaviour. [ABSTRACT FROM AUTHOR]

Results from experimental torsion and bending tests show the existence of a size effect, which conventional continuum models are unable to describe. Therefore, the incorporation of the micropolar media into numerical approaches for the analysis of materials with a complex microstructure looks necessary. So far, most studies utilize Cosserat continuum theory with 3D finite solid elements, even though, it covers only few beam elements developed within a linear strain–displacement relationship, and therefore only works in a small deformation regime. In this study, the authors aim to develop a size-dependent 3D continuum beam element based on the absolute nodal coordinate formulation (ANCF) with microstructure inclusions. Comparing analytical solutions within the Cosserat continuum model and models based on the proposed and already existing 3D micropolar solid elements, one can see a good correlation between them, with a faster convergence rate for the developed ANCF beam element. That allows exploiting the developed beam element within the non-linear deformation range, which is usually bypassed because of high computational costs, thus, accounting fully for differences between two media descriptions. [ABSTRACT FROM AUTHOR]

In this work, a novel framework for modeling quasi-brittle crack propagation and shear band dominated failure of cohesive-frictional materials like concrete, mortar, rock, tough ceramics, energetic materials, but also granular materials like sands or powders in terms of a unified continuum approach is proposed. It is based on a combination of the gradient-enhanced continuum with gradients of internal variables for representing quasi-brittle cracking, and the micropolar continuum, accounting for the deformation of the microstructure. For developing the gradient-enhanced micropolar framework, the set of balance equations and the kinematic relations are derived, and the constitutive relations are established in a general manner. The framework is formulated in a geometrically exact setting, based on the thermodynamically sound theory of hyperelasto-plasticity, and the numerical implementation by means of the finite element method is discussed. For assessing the approach, realizations of this new approach in terms of constitutive models for particular materials are developed. They are applied to numerical benchmark examples, investigating various loading conditions, and the obtained results are validated by means of a comparison with experiments from the literature. [ABSTRACT FROM AUTHOR]

Rock formation such as shale normally has a layered structure where the rock blocks interact with each other by their interfaces like head joints and bed joints. In practical geological conditions, such interfaces are often rough and able to result in dilatancy and volume change of the overall geological structure. The dilatancy can be an important effect and cannot be neglected in determining the practical mechanical behavior of the layered rock. The purpose of this paper is to study the dilatancy effect on the mechanical behavior of layered rock structures with rough interfaces. Interfaces with various roughness are defined to evaluate the dilatancy effect. To estimate the stiffness properties of rough surfaces, a dilatancy model known as the contact density model is used. The current problem involves the size effect of the interface which must not be neglected, thus, a homogenized micropolar continuum is taken into consideration. According to the principle of energy equivalence, a homogenization method is used to get the constitutive parameters of the micropolar model. The present problem is analyzed by using finite element numerical codes to show the validity of the dilatancy models in combination with micropolar theory for a layered rock structure. • Increasing roughness and length of layered rock interfaces induce dilatancy effect. • Increasing roughness induced dilatancy affects shear strains and relative rotation. • A scale effect can be captured by changing the size of the rock block. • The Cauchy continuum also shows a dilatancy effect with a symmetry shear strain. [ABSTRACT FROM AUTHOR]

Hard-magnetic soft materials (HMSMs), as a sub-class of magneto-active polymers, consist of a polymeric matrix filled with particles of high remnant magnetic induction. The application of external magnetic flux on HMSMs induces a moment on its material particles. From the angular momentum balance law, it is deduced that the Cauchy stress tensor in these materials cannot be symmetric. Therefore, the micropolar continuum theory, with inherent asymmetric stress tensor, is a rational candidate for modeling the deformation of these materials. In the present contribution, an HMSM is modeled as a three-dimensional micropolar continuum body, which is subjected to external magnetic stimuli. The moment resulting from the interaction of the internal and external magnetic fluxes plays the role of a body couple in the micropolar formulation. After developing the main formulation, due to the highly nonlinear nature of the governing equations, the weak form of the equations and its linearization to perform numerical simulations is presented. To demonstrate the capability and performance of the developed formulations, several examples are provided. It is shown that the present formulation can successfully predict the deformation of HMSMs under various loading and boundary conditions. [ABSTRACT FROM AUTHOR]

Abstract: In this work a generalized continuum formulation is introduced which is based on a theoretical framework of a generalized deformation description proposed by Sansour (1998) [25]. That is the deformation field is composed by macro- and micro-components according to the consideration that the generalized continuum consists of a macro- and micro-continuum. It is demonstrated that by specific definition of the topology of the micro-space this generalized deformation formulation allows for the derivation of a generalized variational principle together with corresponding strain measures and underlying equilibrium equations. The approach makes use of a macroscopic rotation field which is considered to be element of the Lie group SO(3) and independent of the macroscopic displacement field. In that way the formulation incorporates three additional rotational degrees of freedom and is closely related to the Cosserat continuum. In contrast to the conventional Cosserat continuum the proposed generalized formulation allows to describe multiple scale effects associated with multiple micro-structural directions, possibly with a different magnitude for each one. The approach considers a geometrically exact description of finite deformation within the macro-continuum, but as a first step linearises the deformation within the micro-continuum. The constitutive law is defined at the microscopic level and the geometrical specification of the micro-continuum is the only material input which goes beyond that needed in a classical description. Various meshfree computations demonstrate that this model is able to address fundamental physical phenomena which are related to the underlying micro-structure of the material, in particular scale-effects and oriented material behaviour. Clear differences are revealed between a classical and the non-classical formulation. [Copyright &y& Elsevier]

Abstract: The asymptotic homogenization of periodic beam lattices is performed in an algorithmic format in the present contribution, leading to a micropolar equivalent continuum. This study is restricted to lattices endowed with a central symmetry, for which there is no coupling between stress and curvature. From the proposed algorithms, a versatile simulation code has been developed, relying on an input file giving the lattice topology and beam properties, and providing as an output the equivalent stiffness matrix of the effective continuum. The homogenized moduli are found in close agreement with the moduli obtained from finite element simulations performed over extended lattices. The obtained results are exploited to design and calculate a lattice endowed with a hierarchical double scale microstructure, leading to a dominant micropolar effect under bending at the macroscopic scale. [Copyright &y& Elsevier]

SUMMARY Recently, the shear behavior of a cohesionless granular strip that is in contact with a very rough surface of a moving bounding structure has been numerically investigated by several authors by using a micropolar hypoplastic continuum model. It was shown that the micropolar boundary conditions assumed along the interface have a strong influence on the deformations within the granular layer. In previous investigations, only interface friction angles for very rough bounding structures were assumed. In contrast, the focus of the present paper is on the influence of the interface roughness on the deformation behavior of the granular strip when the interface friction angle is lower than the peak friction angle of the granular material. In addition to the interface friction angle, particular attention is also paid to the influence of the mean grain diameter, the solid hardness, the initial void ratio, and the vertical stress on the maximum horizontal shear displacement within the granular layer before sliding is started. Copyright © 2011 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Abstract: The goal of this manuscript is to set up a novel methodology for the calculation of the effective mechanical properties of biological membranes viewed as repetitive networks of elastic filaments, based on the discrete asymptotic homogenization method. We will show that for some lattice configurations, flexional effects due to internal structure mechanisms at the unit cell scale lead to additional flexional effects at the continuum scale, accounted for by an internal length associated to a micropolar behavior. Thereby, a systematic methodology is established, allowing the prediction of the overall mechanical properties of biological membranes for a given network topology, as closed form expressions of the geometrical and mechanical micro-parameters. The peptidoglycan and the erythrocyte have been analyzed using this methodology, and their effective moduli are calculated and recorded versus the geometrical and mechanical lattice parameters. A classification of lattices with respect to the choice of the equivalent continuum model is proposed: The Cauchy continuum and a micropolar continuum are adopted as two possible effective medium, for a given beam model. The relative ratio of the characteristic length of the micropolar continuum to the unit cell size determines the relevant choice of the equivalent medium. In most cases, the Cauchy continuum is sufficient to model membranes in most of their configurations. The peptidoglycan network may exhibit a re-entrant hexagonal lattice, for which micropolar effects become important. This is attested by the characteristic length becoming larger than the beam length for such configurations. The homogenized moduli give accurate results for both membranes, as revealed by comparison with experimental measurements or simulation results from the literature at the network scale. A first insight into the nonlinear mechanical behavior of the hexagonal and triangular networks is lastly investigated using a perturbative method. [Copyright &y& Elsevier]

In this paper, the concept of hypo-elasticity is generalized to the micropolar continuum theory, and the general forms of the constitutive equations of the micropolar hypo-elastic materials are presented. A new co-rotational objective rate whose spin is the micropolar gyration tensor is introduced which describes the deformation of the material in view of an observer attached to the micro-structure. As special case, simplified versions of the proposed constitutive equations are given in which the same fourth-order elasticity tensors are used as in the micropolar linear elasticity. A 2-D finite element formulation for large elastic deformation of micropolar hypo-elastic media based on the simplified constitutive equations in conjunction with Jaumann and gyration rates is presented. As an example, buckling of a shallow arc is examined, and it is shown that an increase in the micropolar material parameters results in an increase in the buckling load of the arc. Also, it is shown that micropolar effects become important for deformations taking place at small scales. [ABSTRACT FROM AUTHOR]

Abstract: Configurational forces and couples acting on a dynamically evolving fracture process region as well as their balance are studied with special emphasis to microstructure and dissipation. To be able to investigate fracture process regions preceding cracks of mode I, II and III we choose as underlying continuum model the polar and micropolar, respectively, continuum with dislocation motion on the microlevel. As point of departure balance of macroforces, balance of couples and balance of microforces acting on dislocations are postulated. Taking into account results of the second law of thermodynamics the stress power principle for dissipative processes is derived. Applying this principle to a fracture process region evolving dynamically in the reference configuration with variable rotational and crystallographic structure, the configurational forces and couples are derived generalizing the well-known Eshelby tensor. It is shown that the balance law of configurational forces and couples reflects the structure of the postulated balance laws on macro- and microlevel: the balance law of configurational forces and configurational couples are coupled by field variable, while the balance laws of configurational macro- and microforces are coupled only by the form of the free energy. They can be decoupled by corresponding constitutive assumption. Finally, it is shown that the second law of thermodynamics leads to the result that the generalized Eshelby tensor for micropolar continua with dislocation motion consists of a non-dissipative part, derivable from free and kinetic energy, and a dissipative part, derivable from a dissipation pseudo-potential. [Copyright &y& Elsevier]

One of the research direction of Horst Lippmann during his whole scientific career was devoted to the possibilities to explain complex material behavior by generalized continua models. A representative of such models is the Cosserat continuum. The basic idea of this model is the independence of translations and rotations (and by analogy, the independence of forces and moments). With the help of this model some additional effects in solid and fluid mechanics can be explained in a more satisfying manner. They are established in experiments, but not presented by the classical equations. In this paper the Cosserat-type theories of plates and shells are debated as a special application of the Cosserat theory. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, the concept of hyper-elasticity in the micropolar continuum theory is investigated. The restrictions on the fourth-order elasticity tensors are investigated. Using the representation theorems, a general form of constitutive equations for micropolar hyper-elastic isotropic materials is presented. As some special cases, generalizations of the neo-Hookean and Mooney-Rivlin type materials to the micropolar continuum theory are presented. The generalized constitutive equations reduce to those of the microplar linear elasticity theory when the deformations are infinitesimal. Also, Updated Lagrangian finite element formulations for the micropolar hyper-elastic materials are presented. Considering two planar examples, it is shown that an increase in the micropolar parameter results in the reduction of the deformation of the bodies. Also, it is shown that for a specimen with very small dimensions, e.g. in the micron level, the micropolar effects are more sensible. Furthermore, it is shown that the influence of the micropolar parameters is dependent not only on the size of the body, but also to its geometry and loading conditions. For the problems in which the deformation is very close to a homogeneous state, the micropolar effects are negligible. [Copyright &y& Elsevier]

Abstract: The natural Lagrangian stretch and wryness tensors of the non-linear Cosserat continuum are expressed in terms of the general finite rotation vector. These expressions are then specialized for seven particular definitions of the rotation vectors known in the literature. It is expected that some of the vectorially parameterized strain measures derived here may be more convenient than others in specific applications. [Copyright &y& Elsevier]

We discuss the general linear six-parametric theory of plates based on the direct approach. We consider the plate as a deformable surface. Each material point of the surface can be regarded as an infinitesimal small rigid body with six degrees of freedom. The kinematics of the plate is described by using the vector of translation and the vector of rotation as the independent variables. The relations between the equilibrium conditions of a three-dimensional micropolar plate-like body and the two-dimensional equilibrium equations of the deformable surface are established. Using the three-dimensional constitutive equations of a micropolar material we discuss the determination of the effective stiffness tensors appearing in the two-dimensional constitutive equations. [ABSTRACT FROM AUTHOR]

Abstract: We discuss three different ways of defining the strain measures in the non-linear micropolar continuum: (a) by a direct geometric approach, (b) considering the strain measures as the fields required by the structure of local equilibrium conditions, and (c) requiring the strain energy density of the polar-elastic body to satisfy the principle of invariance under superposed rigid-body deformations. The geometric approach (a) generates several two-point deformation measures as well as some Lagrangian and Eulerian strain measures. The ways (b) and (c) allow one to choose those Lagrangian strain measures which satisfy the additional mechanical requirements. These uniquely selected relative strain measures are called the natural ones. All the strain measures discussed here are formulated in the general coordinate-free form. They are valid for unrestricted translations, stretches and changes of orientations of the micropolar body, and are required to identically vanish in the absence of deformation. The relation of the Lagrangian stretch and wryness tensors derived here to the ones proposed in the literature is thoroughly discussed. [Copyright &y& Elsevier]

Abstract: In this paper, the concept of energy pairs in the micropolar continuum is introduced. A brief review of the micropolar continuum theory is presented for using in the subsequent derivations. A mathematical Lagrangian strain and a wryness tensor for the micropolar continuum are introduced. Using the first law of thermodynamics and for isothermal processes, the power of deformation is obtained and the energy pairs in the Eulerian and Lagrangian descriptions are defined. Also, the micropolar stress and couple stress tensors which are energy pairs to the micropolar Lagrangian strain and wryness measures are determined. [Copyright &y& Elsevier]

Abstract: In this contribution, the Desai hierarchical model is extended to the case of 3D elasto-plastic two-phase micropolar continuum. An unconditionally stable implicit Euler backward algorithm for integration of the constitutive relations is developed and presented in detail. The regularizing effect of the introduction of a length parameter to the classical Desai model is demonstrated by means of several case studies of single phase and two-phase porous media. [Copyright &y& Elsevier]

Based on the restudies of existing polar continuum theories rather complete systems of basic balance laws and equations for micropolar continuum theory are presented. In these new systems not only the additional angular momentum, surface moment and body moment produced by the linear momentum, surface force and body force, respectively, but also the additional velocity produced by the angular velocity are considered. The new coupled balance laws of linear momentum, angular momentum and energy are reestablished. From them the new coupled local and nonlocal balance equations are naturally derived. Via contrast it can be clearly seen that the new results are believed to be rather general and complete. [ABSTRACT FROM AUTHOR]

In the present contribution, the capabilities of classical and higher order damage-plasticity continuum models in their ability to predict complex shear failure of concrete is assessed. To this end, a classical local formulation of the popular Concrete Damage-Plasticity model by Grassl and Jirásek (2006a) with mesh-adjusted softening modulus is compared to a higher order gradient-enhanced formulation by Poh and Swaddiwudhipong (2009) and a recently proposed gradient-enhanced micropolar formulation by Neuner et al. (2020a) by means of challenging 3D finite element simulations of a transverse shear test. The transverse shear test is characterized by an anchor channel embedded in a concrete slab, which is loaded transversely to its axis until failure. A comparison with experimental results highlights the limitations of classical local formulations, whereas higher order continuum approaches show great potential in particular for modeling the structural post-peak response. • Classical and higher-order damage-plasticity models for concrete are reviewed • 3D finite element analysis of a challenging transverse shear test on anchor channels • Shortcomings of predictive capabilities of classical models are demonstrated • The capabilities of higher-order models are highlighted • Post-peak behavior is best predicted by a gradient-enhanced micropolar model [ABSTRACT FROM AUTHOR]

Nonlocal effects permeate most microstructured materials, including granular media, metals and foams. The quest for predictive nonlocal mechanical theories with well-defined internal length scales has been ongoing for more than a century since the seminal work of the Cosserats. We present here a novel framework for the nonlocal analysis of material behavior, which bypasses the need to define any internal length scale. This is achieved by extending the Data-Driven paradigm in mechanics, originally introduced for simple continua, into generalized continua. The problem is formulated directly on a material data set, comprised of higher-order kinematics and their conjugate kinetics, which are identified from experiments or inferred from lower scale computations. The case of a micropolar continuum is used as a vehicle to introduce the framework, which may also be adapted to strain-gradient and micromorphic media. Two applications are presented: a micropolar elastic plate with a hole, which is used to demonstrate the convergence properties of the method, and the shear banding problem of a triaxially compressed sample of quartz sand, which is used to demonstrate the applicability of the method in the case of complex history-dependent material behavior. • Development of a Data-Driven framework for weakly nonlocal continua • Novel metric in phase space guarantees optimal convergence properties. • Enforced thermodynamic consistency through generalized dissipation inequality. • Application in shear banding of granular materials. [ABSTRACT FROM AUTHOR]

A continuum theory of rigid suspensions is introduced. Balance laws and constitutive equations of micropolar continuum theory are modified and extended for the characterization of dense rigid suspensions. Thermodynamic restrictions are imposed. The general theory is specialized to the case of dense rigid fiber and spherical suspensions. Dilute suspensions in Newtonian fluids are obtained as special cases. Motions of rigid fiber suspensions in viscometric flows are determined as applications of the theory. [ABSTRACT FROM AUTHOR]

The article presents a study which aimed to derive the effective mechanical properties of trabecular bone using a micromechanical approach. The study discussed the homogenisation method for the treatment of elementary cells and internal nodes, which is based on the asymptotic development of static and kinematic variables under consideration. The construction of an anisotropic micropolar for trabecular bone from the homogenisation of the underlying trabecular microstructure is discussed.

• A micropolar gradient-enhanced framework for cohesive-frictional materials. • Mesh-objective representation of non-associated plasticity and material failure. • The GMCDP model, a micropolar gradient-enhanced constitutive model for concrete. • Application of the proposed framework to 3D large scale finite element simulations. • Validation of the GMCDP model based on experimental results. Continuum models based on the combination of the theories of plasticity and damage mechanics pose a powerful framework for representing the highly nonlinear material behavior of cohesive-frictional materials. However, non-associated plastic flow rules for representing the inelastic volumetric expansion of such materials may result in unstable material behavior and, accordingly, strongly mesh-dependent results in finite element simulations. Regularization techniques such as the gradient-enhanced continuum or similar nonlocal approaches, which work well for regularizing mode I failure, are often not sufficient as a remedy. In contrast to the latter, the theory of the micropolar continuum represents a suitable framework for regularizing non-associated plastic flow and shear band dominated failure properly, but it fails to do so for mode I failure. Hence, in the present contribution, a combination of the theories of the micropolar continuum and the gradient-enhanced continuum for regularizing both shear band dominated failure and mode I failure is presented. By incorporating a 3D damage-plasticity model for concrete into the proposed framework, it is demonstrated that the proposed model constitutes a physically sound and numerically stable approach for modeling the nonlinear material behavior of concrete in both the pre-peak and the post-peak regime for a broad variety of loading conditions. [ABSTRACT FROM AUTHOR]

For micropolar media we present a new definition of the local material symmetry group considering invariant properties of the both kinetic energy and strain energy density under changes of a reference placement. Unlike simple (Cauchy) materials, micropolar media can be characterized through two kinematically independent fields, that are translation vector and orthogonal microrotation tensor. In other words, in micropolar continua we have six degrees of freedom (DOF) that are three DOFs for translations and three DOFs for rotations. So the corresponding kinetic energy density nontrivially depends on linear and angular velocity. Here we define the local material symmetry group as a set of ordered triples of tensors which keep both kinetic energy density and strain energy density unchanged during the related change of a reference placement. The triples were obtained using transformation rules of strain measures and microinertia tensors under replacement of a reference placement. From the physical point of view, the local material symmetry group consists of such density-preserving transformations of a reference placement, that cannot be experimentally detected. So the constitutive relations become invariant under such transformations. Knowing a priori a material's symmetry, one can establish a simplified form of constitutive relations. In particular, the number of independent arguments in constitutive relations could be significantly reduced. [ABSTRACT FROM AUTHOR]