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The maximum effective stress increases exponentially at lower values of anisotropy and reaches to an asymptotic value at higher values.

σ1′ = maximum effective stress, σ3′ = minimum effective stress, σ′ = normal stress, φ = friction angle, C = cohesion, τ = shear stress, α = fracture angle.

The objective was to produce a part with minimum thickness variation while keeping the maximum effective stress below the material ultimate stress during the forming process.

Numerical results for the maximum effective stress in the cylinder wall are also provided to illustrate applications of the newly derived solution.

An appropriate combination of a Ti film with a large thickness and SiO2 film with a small thickness can reduce the maximum effective stress (σmax) and provide an efficient barrier for copper diffusion into the Si wafer substrate.

Estimating the maximum effective stress that rocks have experienced, Pe,max, or the maximum burial depth for sedimentary rocks, Dmax, is important for many types of research, ranging from engineering applications to estimation of tectonic evolution.

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Numerous fracture criteria, based on strain and stress conditions, exist which can be used in finite element (FE) models of the shearing, for example, maximum effective strain, maximum shear stress, or combined stress and strain criteria (Cockcroft and Latham 1968; Johnson and Cook 1985).

The maximum shear stress range plane is defined as the critical plane, and the damage parameters are the maximum effective shear stress amplitude and the maximum effective normal stress, which are obtained by averaging the stress in the hemisphere volume around the maximum stress point.

It is defined as the ratio between the maximum effective vertical stress and the present effective vertical stress.

When a shale rock has been unloaded (e.g., due to uplift and erosion), the effective vertical stress supported by the shale at any time in the uplifting process should be less than the maximum effective vertical stress.

The over-consolidation ratio at any time in the uplifting process is the ratio of maximum effective vertical stress ((sigma_{{v{ hbox{max} }}}^{prime })) in the geological history to the effective vertical stress ((sigma_{v(t)}^{prime })) at the time of any burial depth in the uplifting process.

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