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This paper presents a new approach to topology optimization that is based on observations of natural biological systems in which growth processes are initialized during high mechanical loading. A compliance parameter is introduced that serves as an internal variable and for which evolution equations are derived using the variational principle of the minimum of the dissipation potential. The well-known problem of checkerboarding is faced with regularization techniques on the Helmholtz free energy. The final procedure uses only the Helmholtz free energy as input. Several numerical examples are given for demonstration purposes. © 2015, Springer-Verlag Berlin Heidelberg.