Importance

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Abstract

For each (ij)-th tensor component, an equation ΔF₁^(ij) using ε₁ is computed based on a function W(F) of an inputted tensor amount F and a value (F=F̂) of F. For each (kl)-th tensor component, an equation ^˜ΔF₂^(kl) using ε₁ and ε₂ is computed based on the value (F=F̂) of F. For each combination of an (ij)-th and a (kl)-th component, a function W(F̂+ΔF₁^(ij)+^˜ΔF₂^(kl)) is computed using the computed equations ΔF₁^(ij) and ^˜ΔF₂^(kl). For each (ij)-th component, a coefficient of ε₁ in the function W(F̂+ΔF₁^(ij)+^˜ΔF₂^(kl)) is removed, and stress, based on a first order derivative with respect to the amount F of the function W(F), is computed. For each combination of an (ij)-th and a (kl)-th component, a coefficient of ε₁·ε₂ in the function W(F̂+ΔF₁^(ij)+^˜ΔF₂^(kl)) is removed, and a material Jacobian, based on a second order derivative with respect to the amount F of the function W(F), is computed.

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First Claim