A phase field model for stress‐based evolution of load‐bearing structures. (1st August 2018)

• Record Type: Journal Article
• Authors: Muench, I.; Gierden, C.; Wagner, W.
• Is Part Of: International journal for numerical methods in engineering. Volume 115:Number 13(2018)
• Page Start: 1580
• Page End: 1600
• Publication Date: 2018-08-01
• Subjects: phase field modeling -- stress optimization -- structural growth -- topology optimization -- variational method; Numerical analysis -- Periodicals; Engineering mathematics -- Periodicals; 620.001518
• DOI: 10.1002/nme.5909
• Languages: English
• ISSNs: 0029-5981

Abstract

Summary: We present a continuum‐type optimality algorithm for the evolution of load‐bearing solid structures with linear elastic material. The objective of our model is to generate structures with help of a sensitivity function accounting for equivalent stress. Similar to Evolutionary Structural Optimization, a threshold of equivalent stress is evaluated. However, we do not consider a material rejection ratio. The evolution process is governed by an Allen‐Cahn equation in the context of phase field modeling. The steady state of phase transition is the final geometry of the structure. The model accounts for the desired filling level, geometry of the design space, static loadings, and boundary conditions. Our variational approach drops conservation of mass and couples density as well as stiffness of the continuum by a sophisticated function to the phase field variable. Continuous regions of voids and material evolve from the initial state of homogeneously distributed material. The complexity of evolving structures depends on two numerical parameters, which we discuss in several examples.