Influence of anisotropy, rate-dependence and microstructure on the stability of finitely strained solids

One of the fundamental issues confronting engineers involves designing against failure. Based on the intended purpose for each structural component, a different failure criterion is often proposed. The concepts of bifurcation and stability play an important role in analyzing failure. In this work, attention is focused on the influence of anisotropy, rate-dependence and microstructure on the stability of finitely strained solids.; In the first part, motivated by problems in metal forming, the influence of material anisotropy on surface roughness is studied. The development of strain induced surface roughness limits the formability of alloys with a desired high quality surface finish. Surface roughness appearing in the form of same orientation surface waviness on the traction-free surfaces is a surface bifurcation instability. The general theory for surface bifurcation is applied to a homogeneously strained, anisotropic, rate-independent, elastoplastic half-space in order to study the influence of material anisotropy on the onset of surface instabilities.; The second part is motivated by the need of introducing rate-dependency in order to explain certain instability phenomena. The proposed linear stability criterion captures the onset of instability in time-dependent paths of rate-sensitive, cohesive, frictional materials subjected to finite straining. The criterion predicts that a solid is initially unstable if there exists a unit norm perturbation in the velocity field whose time derivative is positive. For solids with an associated flow rule, it is shown that the exclusion of instability in a trajectory, coincides in the limit with stability of the corresponding rate-independent solid in the sense of Hill.; The last part is motivated by failure problems in microstructured materials subjected mainly to compressive loading. Of interest are the theoretical predictions for the onset of failure in finitely strained, rate-independent solids with periodic microstructures. For these materials, one can define in macroscopic space, a microscopic failure surface, corresponding to the first bifurcation instability, and a macroscopic failure surface, corresponding to the first long wavelength instability. The regions where the two surfaces coincide is of significant interest, since a macroscopic localized mode of deformation appears in the post-bifurcation regime.