Evolving microstructures in relaxed continuum damage mechanics for the modeling of strain softening

A new relaxation approach is proposed which allows for the description of stress- and strain-softening at finite strains. The model based on construction a convex hull replacing originally non-convex incremental stress potential in turn represents damage terms classical (1?D) approach. This given as linear combination weakly strongly damaged phases thus, it homogenization microstructure bifurcated two phases. As result thereof, evolves convexified regime mainly by an increasing volume fraction phase. In contrast to previous relaxed formulations Gürses Miehe (2011) Balzani Ortiz (2012), where has been kept fixated after construction, here, phase allowed elastically unload upon further loading. At same time, its increases nonlinearly within regime. Thus, sense decreasing with strain can be modeled. major advantage that ensures mesh-independent structural simulations without requirement additional length-scale related parameters or nonlocal quantities, simplifies implementation using material subroutine interfaces. this paper, focus one-dimensional models fiber are combined microsphere allow three-dimensional dispersions appearing fibrous materials such soft biological tissues. Several numerical examples analyzed show overall response mesh-independence resulting calculations.