Benchmarking Standard and Micromechanical Models for Creep and Shrinkage of Concrete Relevant for Nuclear Power Plants.

The creep and shrinkage of concrete play important roles for many nuclear power plant (NPP) and engineering structures. This paper benchmarks the standard and micromechanical models using a revamped and appended Northwestern University database of laboratory creep and shrinkage data with 4663 data sets. The benchmarking takes into account relevant concretes and conditions for NPPs using 781 plausible data sets and 1417 problematic data sets, which cover together 47% of the experimental data sets in the database. The B3, B4, and EC2 models were compared using the coefficient of variation of error (CoV) adjusted for the same significance for short-term and long-term measurements. The B4 model shows the lowest variations for autogenous shrinkage and basic and total creep, while the EC2 model performs slightly better for drying and total shrinkage. In addition, confidence levels at 5, 10, 90, and 95% are quantified in every decade. Two micromechanical models, Vi(CA)2T and SCK CEN, use continuum micromechanics for the mean field homogenization and thermodynamics of the water-pore structure interaction. Validations are carried out for the 28-day Young's modulus of concrete, basic creep compliance, and drying shrinkage of paste and concrete. The Vi(CA)2T model is the second best model for the 28-day Young's modulus and the basic creep problematic data sets. The SCK CEN micromechanical model provides good prediction for drying shrinkage.

Deformation of a prestressed liquid lens membrane.

This paper presents a complete model for analysis of the deformed shape of a prestressed circular axisymmetric membrane of a liquid lens. The governing equations are derived using the exact relation between displacements and the Green-Lagrange strains combined with the Saint Venant-Kirchhoff material law, which postulates a linear relation between the Green-Lagrange strains and the second Piola-Kirchoff stresses. A numerical solution based on minimization of potential energy is illustrated by an example, and the dependence of the maximum membrane deflection on material properties and initial prestress is analyzed. The theoretical model is then experimentally validated. It is shown that the model is suitable for large-strain analysis of liquid lens membranes and provides sufficiently accurate results that can be used in further analyses and simulations of imaging properties of active optical elements based on liquid lenses.

Calculation of nonlinearly deformed membrane shape of liquid lens caused by uniform pressure.

The paper discusses a numerical calculation of deformation of a circular axisymmetric membrane of a liquid lens caused by the pressure of an optical liquid. Since such deflections of the membrane are many times larger than the membrane thickness, a nonlinear model is applied and generalized relationships are derived that characterize the resulting shape with a high precision and permit an accurate analysis of imaging properties of the lens and of optical aberrations. By comparison with experimental data, it is shown that the presented model is suitable to describe the deformation of the membrane of the lens.

An over-nonlocal implicit gradient-enhanced damage-plastic model for trabecular bone under large compressive strains.

PURPOSE: Investigation of trabecular bone strength and compaction is important for fracture risk prediction. At 1-2% compressive strain, trabecular bone undergoes strain softening, which may lead to numerical instabilities and mesh dependency in classical local damage-plastic models. The aim of this work is to improve our continuum damage-plastic model of bone by reducing the influence of finite element mesh size under large compression. METHODOLOGY: This spurious numerical phenomenon may be circumvented by incorporating the nonlocal effect of cumulated plastic strain into the constitutive law. To this end, an over-nonlocal implicit gradient model of bone is developed and implemented into the finite element software ABAQUS using a user element subroutine. The ability of the model to detect the regions of bone failure is tested against experimental stepwise loading data of 16 human trabecular bone biopsies. FINDINGS: The numerical outcomes of the nonlocal model revealed reduction of finite element mesh dependency compared with the local damage-plastic model. Furthermore, it helped reduce the computational costs of large-strain compression simulations. ORIGINALITY: To the best of our knowledge, the proposed model is the first to predict the failure and densification of trabecular bone up to large compression independently of finite element mesh size. The current development enables the analysis of trabecular bone compaction as in osteoporotic fractures and implant migration, where large deformation of bone plays a key role.

A nonlocal constitutive model for trabecular bone softening in compression.

Using the three-dimensional morphological data provided by computed tomography, finite element (FE) models can be generated and used to compute the stiffness and strength of whole bones. Three-dimensional constitutive laws capturing the main features of bone mechanical behavior can be developed and implemented into FE software to enable simulations on complex bone structures. For this purpose, a constitutive law is proposed, which captures the compressive behavior of trabecular bone as a porous material with accumulation of irreversible strain and loss of stiffness beyond its yield point and softening beyond its ultimate point. To account for these features, a constitutive law based on damage coupled with hardening anisotropic elastoplasticity is formulated using density and fabric-based tensors. To prevent mesh dependence of the solution, a nonlocal averaging technique is adopted. The law has been implemented into a FE software and some simple simulations are first presented to illustrate its behavior. Finally, examples dealing with compression of vertebral bodies clearly show the impact of softening on the localization of the inelastic process.