Differentiable physics simulation provides an avenue to tackle previously intractable challenges through gradient-based optimization, thereby greatly improving the efficiency of solving robotics-related problems. To apply differentiable simulation in diverse robotic manipulation scenarios, a key challenge is to integrate various materials in a unified framework. We present SoftMAC, a differentiable simulation framework that couples soft bodies with articulated rigid bodies and clothes. SoftMAC simulates soft bodies with the continuum-mechanics-based Material Point Method (MPM). We provide a novel forecast-based contact model for MPM, which effectively reduces penetration without introducing other artifacts like unnatural rebound. To couple MPM particles with deformable and non-volumetric clothes meshes, we also propose a penetration tracing algorithm that reconstructs the signed distance field in local area. Diverging from previous works, SoftMAC simulates the complete dynamics of each modality and incorporates them into a cohesive system with an explicit and differentiable coupling mechanism. The feature empowers SoftMAC to handle a broader spectrum of interactions, such as soft bodies serving as manipulators and engaging with underactuated systems. We conducted comprehensive experiments to validate the effectiveness and accuracy of the proposed differentiable pipeline in downstream robotic manipulation applications. Supplementary materials and videos are available on our project website at https://sites.google.com/view/softmac.

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