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1

Damage standard models with a fixed convex

Cimetiere A., Halm D., Marigo J. J., Molines E.

Archives of Mechanics

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2005

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Vol. 57, nr 4

265--276

EN

The formal structure of a large class of standard damage models is being revisited. Particular attention is paid to the dependence of damage convex on the damage (internal) variables themselves. This dependence complicates the discussion about the existence and uniqueness conditions since the rate of internal variable is no longer a solution of a symmetric variational inequality. The alternative formulation is put forward involving a complementary set of internal variables. This method, leading to a fixed damage convex, brings back the rate response to an incremental behavior relevant to the generalized standard formalism. Some non-fixed convex models are replaced in the framework of damage models with fixed convex.

2

Dimensional analysis and asymptotic expansions of the equilibrium equations in nonlinear elasticity. Cz. 2, The two-dimensional von Karman model

Millet O., Hamdouni A., Cimetiere A.

Archives of Mechanics

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1998

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Vol. 50, nr 6

975-1001

EN

In the second part of this article, which is a continuation of [8] which dealt with a plate subjected to large loads, we consider a plate subjected to moderate applied forces level within the framework of nonlinear elasticity. We then apply the new constructive approach developed in the first part which needs no a priori assumption. For these moderate forces, we prove that the two-dimensional model we obtain by asymptotic expansions is the von Karman one. Finally the two-dimensional stress field in the plate is deduced from the three-dimensional constitutive equations without any a priori assumption.

3

Dimensional analysis and asymptotic expansions of the equilibrium equations in nonlinear elasticity. Cz. 1, The membrane model

Millet O., Hamdouni A., Cimetiere A.

Archives of Mechanics

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1998

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Vol. 50, nr 6

953-973

EN

In this paper, we develop a new asymptotic constructive approach in nonlinear plate theory. The dimensional analysis of the three-dimensional equilibrium equations naturally leads to dimensionless numbers which reflect the geometry of the structure and the magnitude of forces. These numbers also define the domain of validity of the two-dimensional models which will later be obtained by asymptotic expansions. For nonlinear plates, we prove that the two-dimensional models we obtain by asymptotic expansions are determined by the magnitude of the forces applied. In this first part, we consider a plate subjected to large loads. In this case, we prove that the nonlinear plate model we obtain by asymptotic expansions is a membrane model. In the second part of this article, we will consider a plate subjected to smaller applied forces.