This article addresses numerical simulation of the mechanical behaviour of materials comprising heterogeneous ductile micro-structures in the presence of voids using a multi-scale approach considering plasticity processes. This kind of material has been used in several applications as structural solutions. Therefore, for safety reasons, studies about stress analysis of porous ductile materials are essential to understand their mechanical behaviour. Numerical modelling is performed in micro-structures using the concept of representative volume element (RVE) where the matrix is considered as an ideally plastic material governed by the von Mises model with isotropic hardening, while inclusions are adopted as very stiff elastic materials. Also, fracture and contact finite elements are used to model the phase debonding. Different distributions of voids and inclusions are assumed in the RVE domain to investigate their influences on the proposed analyses. We conclude, for instance, that the concentration of voids in the RVE decreases its loading capacity. On the other hand, we show in the numerical examples that the RVEs containing random distributions of voids present loading capacity improved when compared to the RVEs containing symmetric distributions of voids. Moreover, the results show that the insertion of reinforcements into porous ductile media has limited efficiency when dealing with high values of loading.

本文使用考虑塑性过程的多尺度方法对包含异质延展微结构的材料在存在空隙的情况下的力学行为进行数值模拟。这种材料已作为结构解决方案用于多种应用。因此，出于安全原因，多孔延性材料的应力分析研究对于了解其力学行为至关重要。使用代表性体积元 (RVE) 的概念在微观结构中进行数值建模，其中矩阵被视为理想的塑性材料，由具有各向同性硬化的 von Mises 模型控制，而夹杂物被用作非常坚硬的弹性材料。此外，断裂和接触有限元用于模拟相分离。在 RVE 域中假设空隙和夹杂物的不同分布，以研究它们对拟议分析的影响。例如，我们得出结论，RVE 中空隙的浓度会降低其负载能力。另一方面，我们在数值示例中表明，与包含空隙对称分布的 RVE 相比，包含空隙随机分布的 RVE 具有更高的承载能力。此外，结果表明，在处理高载荷值时，将增强材料插入多孔延性介质的效率有限。我们在数值示例中表明，与包含空隙对称分布的 RVE 相比，包含空隙随机分布的 RVE 的承载能力有所提高。此外，结果表明，在处理高载荷值时，将增强材料插入多孔延性介质的效率有限。我们在数值示例中表明，与包含空隙对称分布的 RVE 相比，包含空隙随机分布的 RVE 的承载能力有所提高。此外，结果表明，在处理高载荷值时，将增强材料插入多孔延性介质的效率有限。