Zdenko Tonković

On the Calculation of Stress Intensity Factors and J-Integrals Using the Submodeling Technique

In the present paper, calculations of the stress intensity factor (SIF) in the linear elastic range and the J-integral in the elastoplastic domain of cracked structural components are performed by using the shell-to-solid submodeling technique to improve both the computational efficiency and accuracy. In order to validate the submodeling technique, several numerical examples are analyzed. The influence of the choice of the submodel size on the SIF and the J-integral results is investigated. Detailed finite element (FE) solutions for elastic and fully plastic J-integral values are obtained for an axially cracked thick-walled pipe under internal pressure. These values are then combined, using the General Electric/Electric Power Research Institute (GE/EPRI) method and the reference stress method (RSM), to obtain approximate values of the J-integral at all load levels up to the limit load. The newly developed analytical approximation of the reference pressure for thick-walled pipes with external axial surface cracks is applicable to a wide range of crack dimensions.

On nonisothermal elastoplastic analysis of shell components employing realistic hardening responses

Abstract In the present paper, efficient numerical algorithms for elastoplastic analysis of shell-like structural components will be proposed employing nonisothermal, realistic, highly nonlinear hardening responses. The closest point projection integration algorithm is presented using a Reissner–Mindlin type kinematic shell model, completely formulated in tensor notation. Further, a consistent elastoplastic tangent modulus is derived, which ensures high convergence rates in the global iteration approach. The integration algorithm has been implemented into a layered assumed strain isoparametric finite element, which also enables geometrical nonlinearities including finite rotations. The nonisothermal elastoplastic response of a circular cylindrical shell and a box column under axial compression is analysed. Under the assumption of an adiabatic process, the increase in temperature is computed during elastoplastic deformation. Robustness and numerical stability of the proposed algorithms are demonstrated.

C1 continuity finite element formulation in second-order computational homogenization scheme

The paper describes a second-order two-scale computational homogenization procedure for modeling of heterogeneous materials at small strains. The Aifantis theory of linear elasticity has been described and implemented into the two dimensional C1 continuity triangular finite element formulation. The element has been verified on several patch tests and the computational efficiency of numerical integration of the element stiffness matrix has been tested as well. Furthermore, the C1 two dimensional triangular finite element based on full second gradient continuum is formulated and used for the macrolevel discretization in the frame of a multiscale scheme, where the RVE is discretized by the C0 quadrilateral finite element. The application of generalized periodic boundary conditions and the microfluctuation integral condition on RVE has been investigated. The presented numerical algorithms have been implemented into FE software ABAQUS via user subroutines and verified on a pure bending problem. The comparability of RVE size to the length scale parameter of gradient elasticity has been proved, and elastoplastic behavior of heterogeneous material has been also considered. The results obtained show good numerical efficiency of the proposed algorithms.

A new formulation of numerical algorithms for modelling of elastoplastic cyclic response of shell-like structures

Abstract An efficient computational strategy for modelling of cyclic elastoplastic deformation of shell structures employing the Reissner–Mindlin type kinematic model has been proposed. A realistic highly nonlinear hardening model in multi-component form has been applied. The closest point projection algorithm, completely formulated in tensor notation, is presented. A consistent tangent modulus is derived and its symmetrized form preserves the quadratic rate of asymptotic convergence of the global iteration schemes, as the numerical examples illustrate. The integration algorithm has been implemented into the layered assumed strain isoparametric finite element, which also permits the simulation of geometrical nonlinearity including finite rotations.

Microplane Model for Steel and Application on Static and Dynamic Fracture

AbstractThe behavior of materials and structures is strongly influenced by the loading rate. Compared with quasi-static loading structures loaded by high loading rate and impact acts in a different way. First, there is a strain-rate influence on strength, stiffness, and ductility, and, second, there are inertia effects activated. Both influences are clearly shown in experiments. Although steel does not exhibit significant strain rate sensitivity, the dynamic fracture of steel is highly sensitive on loading rates. In this paper, the static and dynamic fracture of steel is numerically studied on a compact tension specimen (CTS), which is loaded under loading rates up to 100  m/s. First, the proposed microplane model for steel is discussed and verified for monotonic and cyclic quasi-static loading. Subsequently, three-dimensional (3D) finite element dynamic fracture analysis is carried out. It is shown that the resistance of steel (apparent strength and toughness) increases progressively after the critical s...

Second-Order Computational Homogenization Scheme Preserving Microlevel C1 Continuity

The paper deals with a new second-order computational homogenization procedure for modeling of heterogeneous materials at small strains, where C1 continuity is preserved at the microlevel. The multiscale model is based on the Aifantis theory of gradient elasticity. The C1 two dimensional triangular finite element used for the discretization of macro-and microlevel is described. Contrary to the C1 - C0 transition, here besides the displacements, the displacement gradients are included into the boundary conditions on the representative volume element (RVE). According to the second order continuum at microlevel, the relevant homogenization relations are derived. Finally, the performance of the algorithms derived is investigated. Dependency of homogenized stresses on mesh density and microstructural parameter l are examined in simple loading cases.

Experimental and Numerical Investigation of Fatigue Behaviour of Nodular Cast Iron

This paper presents an experimental and numerical study on two different types of the nodular cast iron EN-GJS-400-18-LT. The experimental procedure includes symmetrical and unsymmetrical strain controlled tests on the cylindrical specimens as well as crack initiation and propagation tests on the compact tension and single edged notched specimens. Different loading regimes are applied, and monitoring of the crack length during the tests is performed by an optical system. Within the framework of numerical investigations an efficient algorithm for modelling of cyclic plasticity is examined. Experimental results show that two material types have significantly different the crack behaviour.

Second-Order Computational Homogenization Approach Using Higher-Order Gradients at Microlevel

Realistic description of heterogeneous material behavior demands more accurate modeling at macroscopic and microscopic scales. To observe strain localization phenomena and material softening occurring at the microstructural level, an analysis on the microlevel is unavoidable. Multiscale techniques employing several homogenization schemes can be found in literature. Widely used second-order homogenization requires C1 continuity at the macrolevel, while standard C0 continuity has usually been hold at microlevel. However, due to the C1-C0 transition macroscale variables cannot be defined fully consistently. The present contribution is concerned with a multiscale second-order computational homogenization employing C1 continuity at both scales under assumptions of small strains and linear elastic material behavior. All algorithms derived are implemented into the FE software ABAQUS. The numerical efficiency and accuracy of the proposed computational strategy is demonstrated by modeling three point bending test of the notched specimen.

Boundary Conditions in a Multiscale Homogenization Procedure

This paper is concerned with a second-order multiscale computational homogenization scheme for heterogeneous materials at small strains. A special attention is directed to the macro-micro transition and the application of the generalized periodic boundary conditions on the representative volume element at the microlevel. For discretization at the macrolevel the C1 plane strain triangular finite element based on the strain gradient theory is derived, while the standard C0 quadrilateral finite element is used on the RVE. The implementation of a microfluctuation integral condition has been performed using several numerical integration techniques. Finally, a numerical example of a pure bending problem is given to illustrate the efficiency and accuracy of the proposed multiscale homogenization approach.

Modeling of Material Deformation Responses Using Gradient Elasticity Theory

Realistic description of material deformation responses demands more accurate modeling at both macroscopic and microscopic scales. Multiscale techniques employing several homogenization schemes are mostly used, in which a transition between nonlocal and local continuum formulations has been performed. Therein the transition of state variables is not defined fully consistently. In the present contribution a novel multiscale approach is proposed, where the same nonlocal theories at both scales are coupled, and discretisation is performed only by means of the \(C^{1}\) finite element based on the strain gradient theory. The advantage of the new computational procedure is discussed in comparison with the approach using a local concept at microlevel. Employing the strain gradient continuum theory, a damage model for quasi-brittle materials is proposed and embedded into the \(C^{1}\) continuity triangular finite element. The softening response of homogeneous materials under assumption of isotropic damage law is considered. The regularization superiority over the conventional implicit gradient enhancement procedure is demonstrated.