Vision-based tactile sensors require high-fidelity simulation for reinforcement learning, yet existing approaches struggle to provide accurate mechanical stress fields within GPU-accelerated robotics platforms. We present TaCauchy, an extensible Finite Element Method (FEM) framework that integrates rigorous physics-based force computation into Isaac Sim. Built on the Unified Incremental Potential Contact (UIPC) solver, TaCauchy directly computes Cauchy stress tensors from hyperelastic constitutive laws and projects them onto contact surfaces to obtain traction forces and pressure distributions, providing mechanical ground truth from first principles rather than empirical estimation. Our framework features automatic mesh generation with geometry-aware adaptive refinement and a modular sensor interface enabling rapid integration of diverse sensors (GelSight Mini, DIGIT, 9DTact) with minimal configuration. Performance benchmarks demonstrate 33.40 FPS for single environments and 555 FPS aggregate throughput across 60 parallel environments, with stress extraction overhead under 1 ms. Physical validation experiments show strong agreement between simulated and real tactile responses across force ranges from 1.2556 N to 4.7332 N, achieving SSIM above 0.93, confirming the framework's capability to provide accurate, physically-grounded force supervision for downstream robotic manipulation tasks.

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