We study the asymptotic behaviour of the minimizers of the variational problem: min {∫a−a[ε2(u′)2(x)+W(u(x))]dx:u∈L1(−a,a),u≥0,∫a−au(x)dx=m,u(−a)=u(a)=c}, where m/2a∈(α,β) and W is a non-negative, continuous and non-convex function, with W(u) = 0 iff u∈{α,β}. We prove that the presence of the necking is related to the value c; more precisely, we have a “neck” if cβ.
Necking deformation in non linear elasticity / E. Mascolo; L. Migliaccio. - In: ASYMPTOTIC ANALYSIS. - ISSN 0921-7134. - STAMPA. - 9:(1994), pp. 149-161. [10.3233/ASY-1994-9204]
Necking deformation in non linear elasticity
MASCOLO, ELVIRA;
1994
Abstract
We study the asymptotic behaviour of the minimizers of the variational problem: min {∫a−a[ε2(u′)2(x)+W(u(x))]dx:u∈L1(−a,a),u≥0,∫a−au(x)dx=m,u(−a)=u(a)=c}, where m/2a∈(α,β) and W is a non-negative, continuous and non-convex function, with W(u) = 0 iff u∈{α,β}. We prove that the presence of the necking is related to the value c; more precisely, we have a “neck” if cβ.File in questo prodotto:
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