sum frac partial v partial x v ii boldsymbol nabla circ cdot boldsymbol sum ij frac partial ij partial x j mathbf e ijj mathbf e math math mathbf v math vector field math boldsymbol math second order tensor field math mathbf e math components orthonormal basis reference configuration inner product defined math boldsymbol boldsymbol b sum ij ij b ij operatorname trace boldsymbol boldsymbol b math clausius duhem inequality clausius duhem inequality used express second law thermodynamics elastic plastic materials inequality statement concerning irreversibility natural processes especially energy dissipation involved like balance laws
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