Computational Mechanics

Computational mechanics comprises all types of computer modeling of the mechanical behavior of materials. In this contribution we concentrate on new developments in modeling based on the finite element method (FEM), especially deformation analyses based on numerical homogenization techniques (self-consistent embedding procedure, matricity model), simulations of real microstructural cut-outs, damage analyses of artificial and real microstructures, and multiscale modeling aspects. The limit flow stresses for transverse loading of metal matrix composites reinforced with continuous fibers and for uniaxial loading of spherical particle reinforced metal matrix composites are investigated by recently developed embedded cell models in conjunction with the finite element method. A fiber of circular cross section or a spherical particle is surrounded by a metal matrix, which is again embedded in the composite material, with the mechanical behavior to be determined iteratively in a self-consistent manner. Stress-strain curves have been calculated for a number of metal matrix composites with the embedded cell method and verified with literature data of a particle reinforced Ag/58vol.%Ni composite and for a transversely loaded uniaxially fiber reinforced Al/46vol.%B composite. Good agreement has been obtained between experiment and calculation, and the embedded cell model is thus found to well represent metal matrix composites with randomly arranged inclusions. Systematic studies of the mechanical behavior of fiber- and particle-reinforced composites with plane strain and axisymmetric embedded cell models are carried out to determine the influence of fiber or particle volume fraction and matrix strain-hardening ability on composite strengthening levels. Results for random inclusion arrangements obtained with self-consistent embedded cell models are compared with strengthening levels for regular inclusion arrangements from conventional unit cell models. It is found that with increasing inclusion volume fractions pronounced differences in composite strengthening exist between all models. Finally, closed-form expressions are derived to predict composite strengthening for regular fiber arrangements and for realistic random fiber or particle arrangements as a function of matrix hardening and particle volume fraction. The impact of the results on effectively designing technically relevant metal matrix composites reinforced by randomly arranged strong inclusions is emphasized. Atomistic modeling such as Monte Carlo (MC) simulations and molecular dynamics (MD) methods, dislocation theoretical modeling, and continuum mechanical methods are applied in order to provide insight into the mechanical behavior of materials. Simulations are presented graphically in a systematic manner for different material systems and are compared with experimental results. Finally, it will be shown that the results can be used to predict the future behavior of materials presently in service and even to design new materials.