Abstract: Many widely used materials, such as concrete, rocks,ceramics and polymers, have the feature of increasing shear strength as aresult of hydrostatic pressure increases. Structures made of thesepressure-dependent materials would typically hold the characteristic ofbetter stress limit in tension than in compression. In this case, the vonMises criterion is incompetent while the D-P criterion describedin terms of stress invariants is available as one of the simplest plasticityyield models. To take into account the asymmetrical compression and tensionbehaviors in the conceptual design of continuum structures, a practicabletopology optimization strategy for pressure-dependent materials based onD-P yield criterion is presented in this paper. By using theelement artificial relative densities as design variables, the optimizationproblem is formulated as to minimize the total material volume underD-P yield constraints on each element. In this optimizationmodel, the SIMP interpolation for element stiffness and the power-lawinterpolation for the local stress of porous microstructures are adopted. Inorder to circumvent the stress singularity phenomenon, the \varepsilon-relaxation strategy is applied for relaxing the local yield constraintsinvolved in the low-density elements. In this context, the sensitivity ofthe element constraints with respect to the design variables is efficientlyderived by the adjoint variable method. Then, the optimal design is obtainedby employing the gradient-based optimization algorithm. Finally, threenumerical examples with different strength limits in compression and tensionhave been solved to illustrate the validity of the proposed optimizationmodel as well as the efficiency of the numerical techniques. It is observedthat the optimal material distribution designed by the present method mayhave a significant difference compared with one designed by the conventionalvon Mises stress constraint approach. The obtained optimization solutionsare reasonable since they can make the best use of their strength inwithstanding the compression. The meaning of the proposed method forpressure-dependent material structures is thus demonstrated.