Institute of Fundamental Technological Research

Generalized continuum theories involve non-standard boundary conditions that are associated with the additional kinematic variables introduced in those theories, e.g., higher gradients of the displacement field or additional kinematic degrees of freedom. Accordingly, formulation of a contact problem for such a continuum necessarily requires that adequate contact conditions are formulated for the additional kinematic variables and/or for the respective generalized tractions. In this paper, we address several related open problems, namely, how to enhance the classic contact conditions to include the effects of the additional kinematic variables, how to link the enhanced contact model to the underlying microstructure of the solid, and how to do it in a consistent manner. As a first step towards a new class of contact models for generalized continua, a microblock contact model is derived for a Cosserat solid based on simple micromechanical considerations. To illustrate the non-trivial effects introduced by the non-standard boundary conditions, the problem of compression of an infinite strip with nonaligned microblocks is considered, and the analytical solution is derived for the corresponding boundary layers. A Hertz-like contact problem is also solved numerically with the focus on non-standard features of the solution and on the related size effects.

microstructure, contact problems, size effects, boundary layers, Cosserat continuum

A recently developed gradient-enhanced crystal-plasticity model is applied to predict the size effects in wedge indentation. In the model, the internal length scale is defined through standard quantities that appear in the underlying non-gradient hardening law. A careful calibration of the non-gradient hardening law is thus performed, and the model is validated against published experimental results. To this end, a comprehensive computational study of wedge indentation into a nickel single crystal is performed, and the obtained results show a good agreement with the experiment in terms of the load–penetration depth curves for three wedge angles, as well as in terms of the distributions of lattice rotation, GND density, and net Burgers vector. For the indentation depth of about 200 μm, as employed in the experiment, the predicted size effects are insignificant. Accordingly, the size effects are next studied for the indentation depth varied between 200 μm and 1 μm. As an intermediate result, apparently not published to date, the general 3D crystal plasticity model with anisotropic hardening is consistently reduced to a 2D plane-strain model in which plastic deformation is realized by three effective in-plane slip systems, each representing two crystallographic slip systems.

Indentation size effect, Geometrically necessary dislocations, Crystal plasticity, Gradient plasticity, Finite-element method

Several micromechanical and numerical approaches to estimating the effective properties of heterogeneous media are analyzed. First, micromechanical mean-field estimates of elastic moduli for selected metal matrix composite systems are compared with the results of finite element calculations performed for two simplified unit cells: spherical and cylindrical. Advantages and deficiencies of such numerical verification of analytical homogenization schemes are indicated. Next, predictions of both approaches are compared with available experimental data for two composite systems for tension and compression tests in the elastic-plastic regime using tangent and secant linearization procedures. In the examined range of strain and ceramic volume content, both the Mori-Tanaka averaging scheme and the generalized self-consistent scheme lead to reliable predictions when combined with the tangent linearization, while the use of secant moduli results in a too stiff response. It is also found that the mean-field predictions for a small ceramic volume content are very close to the results obtained from the finite-element analysis of a spherical unit cell.

Metal-matrix composites, Effective properties, Analytical estimates, Numerical homogenization, Nonlinear analysis

Cylindrical bolted steel tanks with H/D~1 can be made from very thin steel courses the thickness of which is determined by tension. The important issue is to stiffen the whole shell with intermediate stiffeners to prevent from stability loss in situations when the tank is empty and exposed to a strong wind. The FEM package Abaqus with nonlinear Riks algorithm was used for analysis. A parametric study programmed in python, internal Abaqus language was conducted to establish the influence of number and position of intermediate stiffeners on buckling resistance of the tank. After calculating nearly one thousands tasks, results were gathered with python script and compared with classic design recommendations proposed in Eurocode 3, DIN 18 800 Part 4 and AWWA D103-09. Simplified analytical approaches present in current standards are rather conservative and one may want to look for more sophisticated methods of analysis of tank shells presented in this paper for more economical design of such structures. From the comparison of the results obtained with different numerical strategies such as linear buckling analysis (LBA), geometrically nonlinear analysis of perfect (GNA) and imperfect (GNIA) structure a necessity of taking into account imperfections in GNA arises. Otherwise a capacity of the shell structure may be overestimated even over the value obtained from LBA.

Thin-walled steel tanks, Optimal stiffening ring location, Buckling, Finite element method, Python programming, Geometrical imperfections

Computational contact homogenization approach is applied to study friction anisotropy resulting from asperity interaction in elastic contacts. Contact of rough surfaces with anisotropic roughness is considered with asperity contact at the micro scale being governed by the isotropic Coulomb friction model. Application of a micro-to-macro scale transition scheme yields a macroscopic friction model with orientation- and pressure-dependent macroscopic friction coefficient. The macroscopic slip rule is found to exhibit a weak non-associativity in the tangential plane, although the slip rule at the microscale is associated in the tangential plane. Counterintuitive effects are observed for compressible materials, in particular, for auxetic materials.

Contact, Friction, Anisotropy, Roughness, Micromechanics

In the paper a general approach to modelling of anisotropic linear viscoelastic material properties is presented. Rychlewski's (1983) spectral decomposition theorem is used and one dimensional relaxation functions of linear viscoelasticity model is adopted to eigenvalues of stiffness tensor and named Kelvin relaxation functions. Proposed model was implemented in the FEM system Abaqus on the example of transversely isotropic and isotropic material. On the basis of experimental data available in literature, models were calibrated and verified. Constitutive relations were used in the complex boundary value problem modelling standard rutting test used in road sector to assess the resistance of asphalt mixtures to rutting.

constitutive modeling, viscoelasticity, finite element method, anisotropic materials, asphalt concretes