AutoMat: automatic differentiation for generalized standard materials on GPUs

We propose a universal method for the evaluation of generalized standard materials that greatly simplifies the material law implementation process. By means of automatic differentiation and a numerical integration scheme, AutoMat reduces the implementation effort to two potential functions. By moving AutoMat to the GPU, we close the performance gap to conventional evaluation routines and demonstrate in detail that the expression level reverse mode of automatic differentiation as well as its extension to second order derivatives can be applied inside CUDA kernels. We underline the effectiveness and the applicability of AutoMat by integrating it into the FFT-based homogenization scheme of Moulinec and Suquet and discuss the benefits of using AutoMat with respect to runtime and solution accuracy for an elasto-viscoplastic example.

Self-consistent, polycrystal rate-independent crystal plasticity modeling for yield surface determination

The evolution of the macroscopically observed yield surface has been the subject of many studies due to its significant effect on the numerical simulation of metal forming processes. Although macroscopic models exist that aim to define this evolution accurate data for calibration as well as validation of these models are difficult to obtain. One common approach is to use crystal plasticity simulations for analyzing the mesoscopic behavior followed by a homogenization scheme for gathering the aggregate behavior. In this study a similar approach is followed the difference being the choice of the crystal plasticity and homogenization methods. A rate-independent crystal plasticity framework where all slip system activities are solved implicitly using a backward Euler approach in combination with an interior point method for constrained optimization is used for single crystal behavior. The aggregate behavior is obtained using a self-consistent analytical homogenization scheme. The results of the homogenization scheme are compared against full-field crystal plasticity finite element simulations. The determination of the yield surface is done by considering the macroscopic behavior where the strain rate direction and magnitude changes over a threshold during stress-based loading.

Rigorous Estimates for Effective Creep-coefficients of Microcracked Masonry Accounting for Cracks Interactions

Based on the association of finite elements homogenization method and a rigorous homogenization scheme accounting for crack interactions, this paper provides rigorous predictions for the local and effective properties of microcracked viscoelastic masonry with or without creep of bricks. For the sake of simplicity, viscoelastic brick and mortar are assumed to follow the Generalized Maxwell rheological model and to be respectively safe and microcracked. In the mortar, the distribution of microcracks orientations is assumed to be random. Two steps are followed. The first one is based on the identification at the short and long terms of an approximate analytical creep function for the mortar. This step relies on the coupling between the Griffith’s brittle fracture theory and a rigorous homogenization scheme - the Ponte Castañeda & Willis model - accounting for crack interaction instead of the dilute scheme adopted previously in Rekik et al. Two cases are considered: open and closed cracks. The first step allows to avoid recourse to 'heavy' numerical inversion of the Laplace-Carson transform. The second one provides overall creep coefficients of masonry by means of periodic homogenization carried out by finite elements method. For open cracks state, time-dependent crack density is investigated. The proposed model is validated by comparison with an analytical one available for a compressed masonry wall with "standard" viscoelastic mortar joints. Effect induced by microcracks is also highlighted by comparison with uncracked masonry. At last, results provided by the proposed model can be considered to be rigorous solution improving on dilute estimates for the creep behavior of microcracked mortar and demonstrating the interest to not neglect both cracks interactions and creep of bricks units.

AN ALTERNATIVE TO PERIODIC HOMOGENIZATION FOR DENTIN ELASTIC STIFFNESS

Dentin, the main tissue of the tooth, is made of tubules surrounded by peri-tubular dentin (PTD), embedded in a matrix of inter-tubular dentin (ITD). The PTD and the ITD have different relative fractions of collagen and hydroxyapatite crystals. The ITD is typically less rigid than the PTD, which can be seen as a set of parallel hollow cylindrical reinforcements in the ITD matrix. In this paper, we extend Hashin and Rozen’s homogenization scheme to a nonuniform distribution of hollow PTD cylinders, determined from image analysis. We relate the transverse isotropic elastic coefficients of a Representative Elementary Volume (REV) of dentin to the elastic and topological properties of PTD and ITD. The model is calibrated against experimental data. Each sample tested is consistently characterized by Environmental Scanning Electron Microscopy (ESEM), nanoindentation and Resonant Ultrasound Spectroscopy (RUS), which ensures that macroscopic mechanical properties measured are correlated with microstructure observations. Despite the high variability of microstructure descriptors and mechanical properties, statistical analyses show that Hashin’s bounds converge and that the proposed model can be used for back-calculating the microscopic Poisson’s ratios of dentin constituents. Three-point bending tests conducted in the laboratory were simulated with the Finite Element Method (FEM). Elements were assigned transverse isotropic elastic parameters calculated by homogenization. The tubule orientation and the pdf of the ratio inner/outer tubule radius were determined in several zones of the beams before testing. The remainder of the micro-mechanical parameters were taken equal to those calibrated by RUS. The horizontal strains found experimentally by Digital Image Correlation (DIC) were compared to those found by FEM. The DIC and FEM horizontal strain fields showed a very good agreement in trend and order of magnitude, which verifies the calibration of the homogenization model. By contrast with previous studies of dentin, we fully calibrated a closed form mechanical model against experimental data and we explained the testing procedures. In elastic conditions, the proposed homogenization scheme gives a better account of microstructure variability than micro–macro dentin models with periodic microstructure.