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Summation from to infinity and the definition of yield (2.42).
This latter threshold is based on the definition of yield based on crack interaction.
The constitutive elasto-plastic matrix and its components are derived by using the definition of yield surface, material functions and non-linear elastic behavior, as function of hardening parameters.
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The definition of yields on.
The definition of yields that (2.16).
Clearly the definition of yields that.
Using the smallness condition and (4.32) together with the definition of yields (4.38).
The definition of yields that for and every there exists such that for any (4.12).
The definition of α yields that α ( x n k, x ) ≥ 1 for all k.
Applying the definition of S yields sup ( y, z ) ∈ S λ T y − μ T z = max i = 1, …, 6 sup ( r i, p i ) ∈ S i λ T B i r i − μ T p i. (19).
In particular, (u_{j}(l)rightarrow u(l)) in (H^{1}) as (j rightarrowinfty), which, together with the definition of M yields that (Vert u_{j }(l Vert _{H^{1}}< M).
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com