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The aim of this paper is to introduce a new incremental procedure that can beused for numerical evaluation of the limit load. Existing incremental typemethods are based on parametrization of the energy by the loading parameter$\zeta\in[0,\zeta_{lim})$, where $\zeta_{lim}$ is generally unknown. In the newmethod, the incremental procedure is operated in terms of an inverse mappingand the respective parameter $\alpha$ is changing in the interval$(0,+\infty)$. Theoretically, in each step of this algorithm, we obtain aguaranteed lower bound of $\zeta_{lim}$. Reduction of the problem to a finiteelement subspace associated with a mesh $\mathcal T_h$ generates computablebound $\zeta_{lim,h}$. Under certain assumptions, we prove that $\zeta_{lim,h}$tends to $\zeta_{lim}$ as $h\rightarrow0_+$. Numerical tests confirm practicalefficiency of the suggested method.

A new incremental method of computing the limit load in deformation plasticity models