Matrix differential equation and higher‐order numerical methods for problems of non‐linear creep, viscoelasticity and elasto‐plasticity

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Abstract
The constitutive equation is assumed in a very general form which includes as special cases non‐linear creep, incremental elasto‐plasticity as well as viscoelasticity represented by a chain of n standard solid models. Subdividing the structure into N finite elements, the problem of structural analysis is formulated with a system of 6N(n + 1) ordinary non‐linear first‐order differential equations in terms of the components of stresses and strains in the elements. This formulation enables one to apply Runge–Kutta methods or the predictor–corrector methods.

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