The paper deals with the problem of the growth and propagation of interfaces inside a continuum medium. The proposed formulation falls in the context of the Strong Discontinuities Approach [1] implemented by means of Elements with Embedded Discontinuities. It is presented a general thermodynamically consistent weak formulation starting from a mixed multi-fields Hu-Washizu functional based on an enriched kinematics. The continuum and the interface are ruled by different constitutive equations, defined by distinct free energy and dissipation functionals. Therefore, in principle, both the continuum and the interface can show dissipative behaviour. The strong form of the equilibrium and compatibility conditions is presented, with special attention to the equilibrium conditions at the interfaces. It can be satisfied in weak sense all over the enriched region of the continuum, not locally. However, a special choice of the interpolation of the enriched field can lead to a strong satisfaction of the equilibrium at the interface. Differently from other Statical Kinematical Optimal Nonsymmetric formulations in the literature [2] the constitutive tangent operator, and consequently the tangent stiffness operator, is symmetric. The non linear evolution problem at the interface is solved by means of a local algorithm, at the Finite Element level, that yields simultaneously the amplitude of the jump increment, the stress value at the Gauss points of the element and the traction on the interface surface. The algorithm generalizes the similar one due to Mosler [3]. Special interpolation functions of the enriched field are developed, able to model also not constant jumps. Consequently appropriate rules of numerical integration are needed, according to the order of the finite element for what concerns the integration on the enriched region, depending on the interpolation on the jump for what concerns the integration on the interface. Different possibilities are discussed in the paper and it is shown that the required number of quadrature points is larger than in the standard case due to additional geometrical mappings. Comparisons with recent developments [4] are finally discussed.

Modelling interfaces by the Strong Discontinuity Approach: new theoretical and computational developments

CONTRAFATTO, Loredana Caterina;CUOMO, Massimo;
2011-01-01

Abstract

The paper deals with the problem of the growth and propagation of interfaces inside a continuum medium. The proposed formulation falls in the context of the Strong Discontinuities Approach [1] implemented by means of Elements with Embedded Discontinuities. It is presented a general thermodynamically consistent weak formulation starting from a mixed multi-fields Hu-Washizu functional based on an enriched kinematics. The continuum and the interface are ruled by different constitutive equations, defined by distinct free energy and dissipation functionals. Therefore, in principle, both the continuum and the interface can show dissipative behaviour. The strong form of the equilibrium and compatibility conditions is presented, with special attention to the equilibrium conditions at the interfaces. It can be satisfied in weak sense all over the enriched region of the continuum, not locally. However, a special choice of the interpolation of the enriched field can lead to a strong satisfaction of the equilibrium at the interface. Differently from other Statical Kinematical Optimal Nonsymmetric formulations in the literature [2] the constitutive tangent operator, and consequently the tangent stiffness operator, is symmetric. The non linear evolution problem at the interface is solved by means of a local algorithm, at the Finite Element level, that yields simultaneously the amplitude of the jump increment, the stress value at the Gauss points of the element and the traction on the interface surface. The algorithm generalizes the similar one due to Mosler [3]. Special interpolation functions of the enriched field are developed, able to model also not constant jumps. Consequently appropriate rules of numerical integration are needed, according to the order of the finite element for what concerns the integration on the enriched region, depending on the interpolation on the jump for what concerns the integration on the interface. Different possibilities are discussed in the paper and it is shown that the required number of quadrature points is larger than in the standard case due to additional geometrical mappings. Comparisons with recent developments [4] are finally discussed.
978-84-87867-66-8
strong discontinuity; variational formulation; EED gauss quadrature; discontinuità forti; formulazione variazionale; quadratura di gauss
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11769/104397
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