Gianluca Cusatis

Lattice Discrete Particle Model for Fiber-Reinforced Concrete. I: Theory

The lattice discrete particle model (LDPM) is a mesoscale model for heterogeneous materials. Developed for concrete, it simulates material mesostructure by modeling coarse aggregate particles and their surrounding mortar as polyhedral cells. A tetrahedralization of the particle centers generates a lattice framework where each lattice member is associated with a triangular-shaped plane of contact (facet) between two cells. Compatibility equations are formulated by describing the deformation of an assemblage of particles through rigid-body kinematics. Equilibrium equations are obtained through the force and moment equilibrium of each cell. The material behavior is assumed to be governed by a vectorial constitutive law imposed at the facets. A natural extension for this discrete model is to include the effect of dispersed fibers as discrete entities within the mesostructure. The LDPM incorporates this effect by modeling individual fibers randomly placed within the framework according to a given fiber volume fraction. The number and orientation of the fibers crossing each facet is computed and the contribution of each fiber to the facet response is formulated on the basis of a previously established micromechanical model for fiber-matrix interaction. The theory for the developed model, entitled the LDPM-F, is discussed herein. A subsequent companion paper will address model calibration and validation through the numerical simulation of experimental test results.

Lattice Discrete Particle Model for Fiber-Reinforced Concrete. II: Tensile Fracture and Multiaxial Loading Behavior

In Part I of this two-part study, a theory is provided for the extension of the lattice discrete particle model (LDPM) to include fiber reinforcing capability. The resulting model, LDPM-F, is calibrated and validated in the present paper by comparing numerical simulations with experimental data gathered from the literature. The analyzed experiments include direct tension, confined and unconfined compression, and notched three-point bending tests.

Spectral Stiffness Microplane Model for Quasibrittle Composite Laminates—Part I: Theory

The paper presents the spectral stiffness microplane model, which is a general constitutive model for unidirectional composite laminates, able to simulate the orthotropic stiffness, prepeak nonlinearity, failure envelopes, and, in tandem with the material characteristic length, also the post-peak softening and fracture. The framework of the microplane model is adopted. The model exploits the spectral decomposition of the transversely isotropic stiffness matrix of the material to define orthogonal strain modes at the microplane level. This decomposition is a generalization of the volumetric-deviatoric split already used by Bauant and co-workers in microplane models for concrete, steel, rocks, soils, and stiff foams. Linear strain-dependent yield limits (boundaries) are used to provide bounds for the normal and tangential microplane stresses, separately for each mode. A simple version, with an independent boundary for each mode, can capture the salient aspects of the response of a unidirectional laminate, although a version with limited mode coupling can fit the test data slightly better. The calibration of model parameters, verification by test data, and analysis of multidirectional laminates are postponed for the subsequent companion paper. DOI: 10.1115/1.2744036

Asymptotic expansion homogenization of discrete fine-scale models with rotational degrees of freedom for the simulation of quasi-brittle materials

Discrete fine-scale models, in the form of either particle or lattice models, have been formulated successfully to simulate the behavior of quasi-brittle materials whose mechanical behavior is inherently connected to fracture processes occurring in the internal heterogeneous structure. These models tend to be intensive from the computational point of view as they adopt an “a priori” discretization anchored to the major material heterogeneities (e.g. grains in particulate materials and aggregate pieces in cementitious composites) and this hampers their use in the numerical simulations of large systems. In this work, this problem is addressed by formulating a general multiple scale computational framework based on classical asymptotic analysis and that (1) is applicable to any discrete model with rotational degrees of freedom; and (2) gives rise to an equivalent Cosserat continuum. The developed theory is applied to the upscaling of the Lattice Discrete Particle Model (LDPM), a recently formulated discrete model for concrete and other quasi-brittle materials, and the properties of the homogenized model are analyzed thoroughly in both the elastic and the inelastic regime. The analysis shows that the homogenized micropolar elastic properties are size-dependent, and they are functions of the RVE size and the size of the material heterogeneity. Furthermore, the analysis of the homogenized inelastic behavior highlights issues associated with the homogenization of fine-scale models featuring strain-softening and the related damage localization. Finally, nonlinear simulations of the RVE behavior subject to curvature components causing bending and torsional effects demonstrate, contrarily to typical Cosserat formulations, a significant coupling between the homogenized stress–strain and couple-curvature constitutive equations.

High-Order Microplane Theory for Quasi-Brittle Materials with Multiple Characteristic Lengths

AbstractThe heterogeneous internal structure of quasi-brittle materials governs several aspects of their behavior, especially in the nonlinear range. Size and spacing of weak spots (e.g., aggregate-matrix interfaces, flaws, and slip planes) where failure is likely to occur are two of the most important material characteristic lengths that can be used to characterize the micro- and meso-structure of these materials. Discrete (lattice and particle) models can be conveniently used to directly model these geometrical features, but they tend to be computationally expensive, and consequently, the derivation of macroscopic continuum-based approximations is often highly beneficial. The current study demonstrates that the continuum macroscale approximation of discrete fine-scale models leads naturally to a high-order microplane theory characterized by multiple characteristic lengths. The average weak spot spacing is shown to be associated with strain gradient effects; whereas the average weak spot size is shown to...

Capacity of Rectangular Cross Sections under Biaxially Eccentric Loads

This paper seeks to present an analytical procedure for the determination of moment contures for rectangular reinforced concrete cross sections under assigned axial loads. The moment contours represent horizontal sections of the failure surface for assigned axial loads. The analytical approximation is obtained through a function of the type suggested by Bresler, in which, however the power exponent is not fixed but calculated on the basis of the interaction diagrams for load eccentricities along axes parallel to the axes of symmetry and to a diagonal of the rectangular cross section. Calculation of these interaction diagrams is made easy by the equivalence between their dimensionless expressions and the interaction diagrams of an equivalent square cross section of unit length side. Analytical proof of this equivalence is provided. A comparison of this procedure with interaction diagrams obtained through direct numerical integration shows that the proposed method is accurate and conservative.

A multiscale framework for the simulation of the anisotropic mechanical behavior of shale

Summary Shale, like many other sedimentary rocks, is typically heterogeneous and anisotropic and is characterized by partial alignment of anisotropic clay minerals and naturally formed bedding planes. In this study, a micromechanical framework based on the lattice discrete particle model is formulated to capture these features. Material anisotropy is introduced through an approximated geometric description of shale internal structure, which includes representation of material property variation with orientation and explicit modeling of parallel lamination. The model is calibrated by carrying out numerical simulations to match various experimental data, including the ones relevant to elastic properties, Brazilian tensile strength, and unconfined compressive strength. Furthermore, parametric study is performed to investigate the relationship between the mesoscale parameters and the macroscopic properties. It is shown that the dependence of the elastic stiffness, strength, and failure mode on loading orientation can be captured successfully. Finally, a homogenization approach based on the asymptotic expansion of field variables is applied to upscale the proposed micromechanical model, and the properties of the homogenized model are analyzed. Copyright

Analysis of the behavior of ultra high performance concrete at early age

Abstract Ultra high performance concretes (UHPCs) are cementitious composite materials with high level of performance characterized by high compressive strength, high tensile strength and superior durability. These are reached by a low water-to-binder ratio, optimized aggregate size distribution, thermal activation, and fiber reinforcement. In the past couple of decades, more and more UHPCs have been developed and found their ways into practice. Thus, the demand for computational models capable of describing and predicting relevant aging phenomena to assist design and planning is increasing. This paper presents the early age experimental characterization as well as the results of subsequent simulations of a typical UHPC matrix. Performed and simulated tests include unconfined compression, splitting (Brazilian), and three-point-bending tests. The computational framework is constructed by coupling a hygro-thermo-chemical (HTC) theory and a comprehensive mesoscale discrete model with formulated aging functions. The HTC component allows taking into account various types of curing conditions with varying temperature and relative humidity and predicting the level of concrete aging. The mechanical component, the Lattice Discrete Particle Model (LDPM), permits the simulation of the failure behavior of concrete at the length scale of major heterogeneities. The aging functions relate the mesoscale LDPM mechanical properties in terms of aging degree, defined in this work as the ratio between the quasi-static elastic modulus at a certain age and its asymptotic value. The obtained results provide insights into UHPC early age mechanisms yielding a computational model for the analysis of aging UHPC structures.

Integrated Experimental and Computational Characterization of Shale at Multiple Length Scales

Shale is known as a hydrocarbon source rock and is emerging as a potentially key component of the worldwide energy landscape via the recent development of hydraulic fracturing technique. A fundamental understanding of the fracturing behaviors of intact shale is the basis of any technological innovation aiming at increasing extraction efficiency. Considering the highly heterogeneous and fine-grained nature of shale, investigation and characterization should be conducted at multiple length scales. Through a brief overview of the experimental and computational studies for mechanical characterization of shale at different scales, this study investigates the possibility of integrating experimental and computational characterization research into a unified multiscale framework. Such multiscale framework is needed to predict macroscale shale fracturing behavior from the microscopic events. As preliminary results, an experimental characterization campaign of Marcellus shale at the macroscopic level and a micromechanical discrete model for predicting the mechanical behaviors of anisotropic shale are also presented.

Automatic parameter identification of discrete mesoscale models with application to the coarse-grained simulation of reinforced concrete structures

In this study, the analysis of reinforced concrete structures is performed by adopting a coarse-grained approximation of a recently developed meso-scale model for concrete, the Lattice Discrete Particle Model (LDPM). The coarse-grained system is obtained by scaling the particle size with a “coarsening factor” > 1. The coarse system cannot reproduce all aspects of the mechanics of the fine system, consequently, the coarse-scale model parameters need to be calibrated from the behavior of the fine-scale system by matching some aspects, e.g. the macroscopic stress-strain/load-displacement curves under different loading conditions, of the fine scale response. The coarse-scale parameters are optimized by the least-square minimization procedure. The effectiveness of the procedure is verified by comparing full fine-scale solutions and coarse-grained solutions for cases of interest in which the full meso-scale problem can be actually solved.