Many widely used materials, such as concrete, rocks, ceramics and polymers, have the feature of increasing shear strength as a result of hydrostatic pressure increases. Structures made of these pressure-dependent materials would typically hold the characteristic of better stress limit in tension than in compression. In this case, the von Mises criterion is incompetent while the D-P criterion described in terms of stress invariants is available as one of the simplest plasticity yield models. To take into account the asymmetrical compression and tension behaviors in the conceptual design of continuum structures, a practicable topology optimization strategy for pressure-dependent materials based on D-P yield criterion is presented in this paper. By using the element artificial relative densities as design variables, the optimization problem is formulated as to minimize the total material volume under D-P yield constraints on each element. In this optimization model, the SIMP interpolation for element stiffness and the power-law interpolation for the local stress of porous microstructures are adopted. In order to circumvent the stress singularity phenomenon, the ε-relaxation strategy is applied for relaxing the local yield constraints involved in the low-density elements. In this context, the sensitivity of the element constraints with respect to the design variables is efficiently derived by the adjoint variable method. Then, the optimal design is obtained by employing the gradient-based optimization algorithm. Finally, three numerical examples with different strength limits in compression and tension have been solved to illustrate the validity of the proposed optimization model as well as the efficiency of the numerical techniques. It is observed that the optimal material distribution designed by the present method may have a significant difference compared with one designed by the conventional von Mises stress constraint approach. The obtained optimization solutions are reasonable since they can make the best use of their strength in withstanding the compression. The meaning of the proposed method for pressure-dependent material structures is thus demonstrated.%基于描述材料力学行为的Drucker—Prager（D—P）屈服准则，研究丁压力相关材料连续体结构拓扑优化发计问题的数学模型和数值算法．以单元材料人工密度为设计变量，结合SIMP惩罚模型和多孔微结构局部应力插值模型，建立了以材料体积最小化为目标、考虑材料D—P屈服条件约束的优化问题数学模型．利用ε-松弛方法消除奇异解现象，采用伴随法有效推导约束函数灵敏度计算公式，运用基于梯度的连续变量优化算法迭代求解优化问题．数值算例验证了优化模型的正确性及数值算法的有效性，并通过与vonMises应力约束优化结果的比较，说明了材料的压力相关特性会对结构最优拓扑产生重要影响．该方法设计出的最优拓扑由于充分利用了压力相关材料的抗压能力，因而更为合理和实际．
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