Computational modeling of gradient hardening in polycrystals

A gradient hardening crystal plasticity model for polycrystals is introduced in Ekh et al. (2007). It is formulated in a thermodynamically consistent fashion and is capable of modeling a grain-size-dependent stress-strain response. In this contribution we extend that model to also include cross-hardening. A free energy is stated which includes contributions from the gradient of hardening along each slip direction. This leads to hardening stresses depending on the second derivative of the plastic slip. The governing equations for a nonlinear coupled system of equations is solved numerically with the help of a dual-mixed finite element method. The numerical results show that the macroscopic strength increases with decreasing grain size as a result of gradient hardening: Moreover, cross-hardening further enhances the strengthening gradient effect

Variationally consistent homogenisation of plates

Advanced fibre composite materials are often used for weight-efficient thin-walled designs, making a plate-based modelling approach suitable for their structural assessment. However, as the sub-structural geometrical features of these materials govern much of their behaviour, a multi-scale approach is necessary. A related challenge, however, is that the in-plane variation of these sub-structural features may be much larger than the total thickness of the material, whereby tailored homogenisation techniques for shell elements are needed. Existing frameworks for plate- and shell-based homogenisation are typically developed using second-order homogenisation in combination with the Hill–Mandel (macro-homogeneity) condition. However, it has been reported in the literature that this approach can lead to kinematic inconsistencies in the macro- to micro-scale transition. One inconsistency that is commonly reported, is the inability to correctly account for the macro-scale transverse shear behaviour on the sub-scale level. In this contribution, we show how the method of Variationally Consistent Homogenisation (VCH) can be used to develop a homogenisation framework for Reissner-Mindlin plate elements, which guarantees kinematically consistent prolongation and homogenisation operations. The homogenisation approach is demonstrated in four numerical examples, where it is shown that the method accurately homogenise the effective sectional plate stiffnesses of homogeneous and heterogeneous sub-structures

Mixed-effects models for health care longitudinal data with an informative visiting process: A Monte Carlo simulation study.

Electronic health records are being increasingly used in medical research to answer more relevant and detailed clinical questions; however, they pose new and significant methodological challenges. For instance, observation times are likely correlated with the underlying disease severity: Patients with worse conditions utilise health care more and may have worse biomarker values recorded. Traditional methods for analysing longitudinal data assume independence between observation times and disease severity; yet, with health care data, such assumptions unlikely hold. Through Monte Carlo simulation, we compare different analytical approaches proposed to account for an informative visiting process to assess whether they lead to unbiased results. Furthermore, we formalise a joint model for the observation process and the longitudinal outcome within an extended joint modelling framework. We illustrate our results using data from a pragmatic trial on enhanced care for individuals with chronic kidney disease, and we introduce user-friendly software that can be used to fit the joint model for the observation process and a longitudinal outcome

Finite deformation analysis of geomaterials

The mathematical structure and numerical analysis of classical small deformation elasto}plasticity is generally well established. However, development of large deformation elastic}plastic numerical formula-tion for dilatant, pressure sensitive material models is still a research area. In this paper we present development of the "nite element formulation and implementation for large deformation, elastic}plastic analysis of geomaterials. Our developments are based on the multiplicative decomposition of the deformation gradient into elastic and plastic parts. A consistent linearization of the right deformation tensor together with the Newtonmethod at the constitutive and global levels leads toward an ecient and robust numerical algorithm. The presented numerical formulation is capable of accurately modelling dilatant, pressure sensitive isotropic and anisotropic geomaterials subjected to large deformations. In particular, the formulation is capable of simulating the behaviour of geomaterials in which eigentriads of stress and strain do not coincide during the loading process. The algorithm is tested in conjunction with the novel hyperelasto}plastic model termed the B material model, which is a single surface (single yield surface, ane single ultimate surface and a$ne single potential surface) model for dilatant, pressure sensitive, hardening and softening geomaterials. It is speci"cally developed to model large deformation hyperelasto}plastic problems in geomechanics

Viscoelastic substitute models for seismic attenuation caused by squirt flow and fracture leak off

We have investigated viscoelastic substitute models for seismic attenuation caused by fluid pressure diffusion in fluid-saturated porous media. Fluid pressure diffusion may locally occur associated with fracture leak off and/or squirt flow. We use a homogenization scheme with numerical model reduction (NMR), recently established in the literature, and we derive the corresponding viscoelastic material properties that are apparent at a larger scale (i.e., the observer scale). Moreover, we find that the rheology of the resulting viscoelastic model is of the Maxwell-Zener type. Based on a series of numerical experiments, we find that this method is able to accurately and efficiently predict the overall attenuation and stiffness moduli dispersion for a range of scenarios without resolving the substructure problem explicitly. Computational homogenization, together with NMR, can be useful to simulate seismic wave propagation using a viscoelastic substitute model that accurately reproduces the energy dissipation and dispersion of a heterogeneous medium in which squirt flow and/or fracture leak-off occurs