Relaxed Incremental Variational Formulation for Damage at Large Strains with Application to Fiber-Reinforced Materials and Materials with Truss-like Microstructures
Homogenized stress-strain response for a microtruss material using a relaxed incremental damage formulation
DFG_Deutsche_Forschungsgemeinschaft_research_fellowship_project_BA_2823_6-1
Associated people
D. Balzani (TU Dresden), in cooperation with M. Ortiz (CALTECH Pasadena)
Abstract
In this project incremental variational formulations for damage at finite strains are developed. The classical continuum damage mechanics serves as a basis where a stress-softening term depending on a scalar-valued damage function is prepended an effective hyperelastic strain energy function, which describes the virtually undamaged material. Since loss of convexity is obtained at some critical deformations a relaxed incremental stress potential is constructed which convexifies the original non-convex problem. The resulting model can be interpreted as the homogenization of a micro-heterogeneous material bifurcated into a strongly and weakly damaged phase at the microscale. A one-dimensional relaxed formulation is derived and based thereon, models for fiber-reinforced materials are constructed. Moreover, these models are used for the computational homogenization of materials with truss-like microstructures as e.g. cellular materials.
References