Peter Grassl

Concrete in compression: a plasticity theory with a novel hardening law

This paper deals with the modelling of the behaviour of plain concrete in triaxial compression using the theory of plasticity. The aim is to model the load resistance and the deformation capacity in uniaxial, biaxial and triaxial compression by means of few parameters, which can be determined easily. A novel hardening law based on a non-associated flow rule and the volumetric plastic strain as hardening parameter is combined with a yield surface proposed by Menetrey and William (1995). The novel hardening and softening law differs from a classic strain-hardening law, as instead of the length of the plastic strain vector only the volumetric component of the latter is used as a hardening parameter. Thus, the non-linearity of the plastic potential is utilized to describe the influence of multiaxial compression on the deformation capacity and no additional ductility measure is required. The implementation and calibration of the novel hardening law are discussed. The prediction of the model is compared to results of uniaxial, biaxial and triaxial compression tests. It is shown that with one set of calibration parameters a good prediction of the load resistance and the deformation capacity for all three types of compression tests can be achieved.

On a 2D hydro-mechanical lattice approach for modelling hydraulic fracture

A 2D lattice approach to describe hydraulic fracturing is presented. The interaction of fluid pressure and mechanical response is described by Biots theory. The lattice model is applied to the analysis of a thick-walled cylinder, for which an analytical solution for the elastic response is derived. The numerical results obtained with the lattice model agree well with the analytical solution. Furthermore, the coupled lattice approach is applied to the fracture analysis of the thick-walled cylinder. It is shown that the proposed lattice approach provides results that are independent of the mesh size. Moreover, a strong geometrical size effect on nominal strength is observed which lies between analytically derived lower and upper bounds. This size effect decreases with increasing Biots coefficient.

CDPM2: A damage-plasticity approach to modelling the failure of concrete

A constitutive model based on the combination of damage mechanics and plasticity is developed to analyse the failure of concrete structures. The aim is to obtain a model, which describes the important characteristics of the failure process of concrete subjected to multiaxial loading. This is achieved by combining an effective stress based plasticity model with a damage model based on plastic and elastic strain measures. The model response in tension, uni-, bi- and triaxial compression is compared to experimental results. The model describes well the increase in strength and displacement capacity for increasing confinement levels. Furthermore, the model is applied to the structural analyses of tensile and compressive failure.

Mesoscale analysis of failure in quasi-brittle materials: comparison between lattice model and acoustic emission data

Summary The purpose of this paper is to analyse the development and the evolution of the fracture process zone during fracture and damage in quasi‐brittle materials. A model taking into account the material details at the mesoscale is used to describe the failure process at the scale of the heterogeneities. This model is used to compute histograms of the relative distances between damaged points. These numerical results are compared with experimental data, where the damage evolution is monitored using acoustic emissions. Histograms of the relative distances between damage events in the numerical calculations and acoustic events in the experiments exhibit good agreement. It is shown that the mesoscale model provides relevant information from the point of view of both global responses and the local failure process.

Size Effect of Cohesive Delamination Fracture Triggered by Sandwich Skin Wrinkling

Because the observed size effect follows neither the strength theory nor the linear elastic fracture mechanics, the delamination fracture of laminate-foam sandwiches under uniform bending moment is treated by the cohesive crack model. Both two-dimensional geometrically nonlinear finite element analysis and one-dimensional representation of skin (or facesheet) as a beam on elastic-softening foundation are used. The use of the latter is made possible by realizing that the effective elastic foundation stiffness depends on the ratio of the critical wavelength of periodic skin wrinkles to the foam core thickness, and a simple description of the transition from shortwave to longwave wrinkling is obtained by asymptotic matching. Good agreement between both approaches is achieved. Skin imperfections (considered proportional to the the first eigenmode of wrinkling), are shown to lead to strong size dependence of the nominal strength. For large imperfections, the strength reduction due to size effect can reach 50%. Dents from impact, though not the same as imperfections, might be expected to cause as a similar size effect. Using proper dimensionless variables, numerical simulations of cohesive delamination fracture covering the entire practical range are performed. Their fitting, heeding the shortwave and longwave asymptotics, leads to an approximate imperfection-dependent size effect law of asymptotic matching type. Strong size effect on postpeak energy absorption, important for impact analysis, is also demonstrated. Finally, discrepancies among various existing formulas for critical stress at periodic elastic wrinkling are explained by their applicability to different special cases in the shortwave-longwave transition.

Evaluation of nonlocal approaches for modelling fracture near nonconvex boundaries

Integral-type nonlocal damage models describe the fracture process zones by regular strain profiles insensitive to the size of finite elements, which is achieved by incorporating weighted spatial averages of certain state variables into the stress–strain equations. However, there is no consensus yet how the influence of boundaries should be taken into account by the averaging procedures. In the present study, nonlocal damage models with different averaging procedures are applied to the modelling of fracture in specimens with various boundary types. Firstly, the nonlocal models are calibrated by fitting load–displacement curves and dissipated energy profiles for direct tension to the results of mesoscale analyses performed using a discrete model. These analyses are set up so that the results are independent of boundaries. Then, the models are applied to two-dimensional simulations of three-point bending tests with a sharp notch, a V-type notch, and a smooth boundary without a notch. The performance of the nonlocal approaches in modelling of fracture near nonconvex boundaries is evaluated by comparison of load–displacement curves and dissipated energy profiles along the beam ligament with the results of meso-scale simulations. As an alternative approach, elastoplasticity combined with nonlocal and over-nonlocal damage is also included in the comparative study.

A micromechanics-enhanced finite element formulation for modelling heterogeneous materials

Abstract In the analysis of composite materials with heterogeneous microstructures, full resolution of the heterogeneities using classical numerical approaches can be computationally prohibitive. This paper presents a micromechanics-enhanced finite element formulation that accurately captures the mechanical behaviour of heterogeneous materials in a computationally efficient manner. The strategy exploits analytical solutions derived by Eshelby for ellipsoidal inclusions in order to determine the mechanical perturbation fields as a result of the underlying heterogeneities. Approximation functions for these perturbation fields are then incorporated into a finite element formulation to augment those of the macroscopic fields. A significant feature of this approach is that the finite element mesh does not explicitly resolve the heterogeneities and that no additional degrees of freedom are introduced. In this paper, Hybrid-Trefftz stress finite elements are utilised and performance of the proposed formulation is demonstrated with numerical examples. The method is restricted here to elastic particulate composites with ellipsoidal inclusions but it has been designed to be extensible to a wider class of materials comprising arbitrary shaped inclusions.

Three-dimensional network model for coupling of fracture and mass transport in quasi-brittle geomaterials

Dual three-dimensional networks of structural and transport elements were combined to model the effect of fracture on mass transport in quasi-brittle geomaterials. Element connectivity of the structural network, representing elasticity and fracture, was defined by the Delaunay tessellation of a random set of points. The connectivity of transport elements within the transport network was defined by the Voronoi tessellation of the same set of points. A new discretisation strategy for domain boundaries was developed to apply boundary conditions for the coupled analyses. The properties of transport elements were chosen to evolve with the crack opening values of neighbouring structural elements. Through benchmark comparisons involving non-stationary transport and fracture, the proposed dual network approach was shown to be objective with respect to element size and orientation.

3D modelling of the influence of microcracking on mass transport in concrete

A three-dimensional lattice approach for modelling the coupling of fracture and transport was applied to micro-cracking induced by aggregate restrained shrinkage in concrete, which was idealised as a three phase material consisting of matrix, aggregates and interfacial transition zones. Shrinkage of the matrix and interfacial transition zones was modelled by applying incrementally a uniform eigenstrain. The influence of aggregate diameter and specimen thickness on cracking and transport properties was investigated. The results show that increasing aggregate diameter at constant volume fraction increases the crack widths and, therefore, permeability, which confirms previously obtained 2D modelling results.

Transport-Structural Modelling of Corrosion Induced Cracking

Transport of corrosion products into pores and cracks in concrete must be considered when predicting corrosion induced cracking in reinforced concrete structures, since this transport significantly delays the onset of cracking and spalling by reducing the amount radial displacement displacement imposed on the concrete at the steel/concrete interface. We aim to model this process by means of a transport-structural approach, whereby the transport part is driven by a pressure gradient generated by the volumetric expansion due to the transformation of steel into corrosion products. This pressure driven transport was introduced in an analytical axisymmetric thickwalled cylinder model and a numerical network approach. The influence of cracking and permeability on corrosion induced cracking process with increasing inner displacement is investigated with these two approaches.