Recent progress in microplane modelling of plain concrete

Despite determined efforts in mathematical modelling of multiaxial behaviour of plain concrete by many researchers, the existing models have not achieved a full description of this complex behaviour. Among these models, the microplane models have contributed important advances in the semi-multiscale modelling of multiaxial behaviour of concrete since their inception in the early 80s. Among several versions of microplane models for plain concrete, model M4 had the greatest success in modelling both the rate-dependent dynamic and quasistatic multiaxial behaviours of concrete. Yet, some problems still have persisted, such as (1) a spurious lateral contraction under uniaxial tension, and (2) an unrealistic damage prediction in tension. These problems resulted from the difficulty in reconciling the pressure sensitive ductile behaviour in compression of concrete with its brittle tensile behaviour. A new microplane model, called M7 as a successor to the earlier microplane models for plain concrete, overcomes the aforementioned problems while retaining all of its compressive data fitting prowess. The volumetric-deviatoric split, required in the previous modelling of the pressure sensitive compressive behaviour of concrete, is now removed from the elastic strains under both compression and tension, but retained in the formulation of compressive stress-strain boundaries (i.e, strain-dependent yield limits on the generic microplane). This allows the simulation of a much more realistic tensile behaviour including the correct damage (loading/unloading slope) and correct lateral contraction. It also means that a new compressive normal boundary is needed. It is defined in terms of the existing deviatoric and volumetric boundaries, which preserves the versatility of the model in fitting a wide range of experimental data. Model M7 has been tested in finite element simulations of a wide range of compressive, tensile, mixed mode fracture tests and vertex effect tests, as well as compression-tension load cycles. It has recently been extended to fiber reinforced concrete and rate dependent behaviour of plain concrete. Perforations of concrete walls by missiles in which enormous strain rates (on the order of 104s−1) are encountered have also been simulated successfully using the rate dependent extension of the model M7, whose robustness is thus demonstrated

Constructing Pauli pulse schemes for decoupling and quantum simulation

Dynamical decoupling is a powerful technique to suppress errors in quantum systems originating from environmental couplings or from unwanted inter-particle interactions. However, it can also be used to selectively decouple specific couplings in a quantum system. We present a simple and easy-to-use general method to construct such selective decoupling schemes on qubit and qudit networks by means of (generalized) Pauli operations. As these constructed schemes can suppress Hamiltonian interactions on general qudit networks selectively, they are well suited for purposes of approximate quantum simulation. Some examples are presented, demonstrating the use of our method and the resulting decoupling schemes.Comment: 11 pages, 5 figure

Endochronic theory, non-linear kinematic hardening rule and generalized plasticity: a new interpretation based on generalized normality assumption

A simple way to define the flow rules of plasticity models is the assumption of generalized normality associated with a suitable pseudo-potential function. This approach, however, is not usually employed to formulate endochronic theory and non-linear kinematic (NLK) hardening rules as well as generalized plasticity models. In this paper, generalized normality is used to give a new formulation of these classes of models. As a result, a suited pseudo-potential is introduced for endochronic models and a non-standard description of NLK hardening and generalized plasticity models is also provided. This new formulation allows for an effective investigation of the relationships between these three classes of plasticity models

Modelling Localisation and Spatial Scaling of Constitutive Behaviour: a Kinematically Enriched Continuum Approach

It is well known that classical constitutive models fail to capture the post-peak material behaviour, due to localisation of deformation. In such cases the concept of Representative Volume Element (RVE) on which classical continuum models rest ceases to exist and hence the smearing out of local inhomogeneities over the whole RVE is no longer correct. This paper presents a new approach to capturing localised failure in quasi-brittle materials, focusing on the kinematic enrichment of the constitutive model to describe correctly the behaviour of a volume element with an embedded localisation band. The resulting models possess an intrinsic length scale which in this case is the width of the embedded localisation band. The behaviour therefore scales with both the width of the localisation band and the size of the volume on which the model is defined. As a consequence, size effects are automatically captured in addition to the model capability in capturing behaviour at the scale of the localisation zone.Comment: Proceedings of Asian-Pacific Conference on Fracture and Strength 2014 and the International Conference on Structural Integrity and Failure, 9-12 December, Sydney, Australi

Size Effect in Fracture: Roughening of Crack Surfaces and Asymptotic Analysis

Recently the scaling laws describing the roughness development of fracture surfaces was proposed to be related to the macroscopic elastic energy released during crack propagation [Mor00]. On this basis, an energy-based asymptotic analysis allows to extend the link to the nominal strength of structures. We show that a Family-Vicsek scaling leads to the classical size effect of linear elastic fracture mechanics. On the contrary, in the case of an anomalous scaling, there is a smooth transition from the case of no size effect, for small structure sizes, to a power law size effect which appears weaker than the linear elastic fracture mechanics one, in the case of large sizes. This prediction is confirmed by fracture experiments on wood.Comment: 9 pages, 6 figures, accepted for publication in Physical Review

Meso-scale modelling of the size effect on the fracture process zone of concrete

The size effect on the fracture process zone in notched and unnotched three point bending tests of concrete beams is analysed by a meso-scale approach. Concrete is modelled at the meso-scale as stiff aggregates embedded in a soft matrix separated by weak interfaces. The mechanical response of the three phases is modelled by a discrete lattice approach. The model parameters were chosen so that the global model response in the form of load-crack mouth opening displacement curves were in agreement with experimental results reported in the literature. The fracture process zone of concrete is determined numerically by evaluating the average of spatial distribution of dissipated energy densities of random meso-scale analyses. The influence of size and boundary conditions on the fracture process zone in concrete is investigated by comparing the results for beams of different sizes and boundary conditions