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Various phenomena (phase transformations, chemical reactions, and friction)under high pressures in diamond anvil cell are strongly affected by fields ofall components of stress and plastic strain tensors. However, they could not bemeasured. Even measured pressure distribution contains significant error. Here,we suggest coupled experimental-analytical-computational approaches utilizingsynchrotron X-ray diffraction, to solve an inverse problem and find all thesefields and friction rules before, during, and after $\alpha$-$\omega$ phasetransformation in strongly plastically predeformed Zr. Due to advancedcharacterization, the minimum pressure for the strain-induced $\alpha$-$\omega$phase transformation is changed from 1.36 to 2.7 GPa. It is independent of thecompression-shear path. The theoretically predicted plastic strain-controlledkinetic equation is verified and quantified. Obtained results openopportunities for developing quantitative high-pressure/stress science,including mechanochemistry, material synthesis, and tribology.

Tensorial stress-plastic strain fields in $\alpha$-$\omega$ Zr mixture, transformation kinetics, and friction in diamond anvil cell