• Computers and Concrete
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• v.5 no.4
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• pp.417-434
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• 2008

This paper deals with damage induced anisotropy modeling for concrete-like materials. A thermodynamics based constitutive relationship is presented coupling anisotropic damage and elasticity, the main idea of the model being that damage anisotropy is responsible for the dissymmetry tension/compression. A strain written damage criterion is considered (Mazars criterion extended to anisotropy in the initial model). The biaxial behavior of a family of anisotropic damage model is analyzed through the effects of yield surface modifications by the introduction of new equivalent strains.

• Journal of the Society of Naval Architects of Korea
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• v.48 no.3
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• pp.200-206
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• 2011

The mechanical properties of the most widely used cryogenic materials, i.e. austenitic stainless steel (ASS), aluminum alloy and invar steel, strongly depend on temperatures and strain rates. These phenomena show very complicated non-linear behaviors and cannot be expressed by general constitutive equation. In this study, an unified constitutive equation was proposed to represent the effect of temperature and strain rate on the materials. The proposed constitutive equation has been based on Tomita/Iwamoto and Bodner/Partom model for the expression of 2nd hardening due to martensite phase transformation of ASS. To simulate ductile fracture, modified Bodner/Chan damage model was additionally applied to the model and the model validity was verified by comparison of experimental and simulation results.

• Transactions of Materials Processing
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• v.33 no.1
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• pp.18-35
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• 2024

In the present work, the evolution rules for the internal variables including continuum damage factors are obtained using the thermodynamic framework, which are in turn facilitated to derive the elastic-plastic constitutive relation for the particulate composites. Using the Mori-Tanaka scheme, the homogenization on state and internal variables such as back-stress and damage factors is carried out to procure the rate independent plasticity relations. Moreover, the degradation of mechanical properties of constituents is depicted by the distinctive damages such that the phase and interfacial damages are treated individually accordingly, whereas the kinematic hardening is depicted by combining the Armstrong-Frederick and Phillips' back-stress evolutions. On the other hand, the present constitutive relation for each phase is expressed in terms of the respective damage-free effective quantities, then, followed by transformation into the damage affected overall nominal relations using the aforementioned homogenization concentration factors. An emphasis is placed on the qualitative analyses for strain localization by observing the perturbation growth instead of the conventional bifurcation analyses. It turns out that the proposed constitutive model offers a wide range of strain localization behavior depending on the evolution of various internal variable descriptions.

• International Journal of Concrete Structures and Materials
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• v.2 no.2
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• pp.123-136
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• 2008

A new plastic-damage constitutive model applicable to lightweight concrete (LWC) and normal weight concrete (NWC) is proposed in this paper based on both continuum damage mechanics and plasticity theories. Two damage variables are used to represent tensile and compressive damage independently. The effective stress is computed in the Drucker-Prager multi-surface plasticity framework. The stress is then computed by multiplication of the damaged part and the effective part. The proposed model is coded as a user material subroutine and incorporated in a finite element analysis software. The constitutive integration algorithm is implemented by adopting the operator split involving elastic predictor, plastic corrector and damage corrector. The numerical study shows that the algorithm is efficient and robust in the finite element analysis. Experimental investigation is conducted to verify the proposed model involving both static and dynamic tests. The very good agreement between the numerical results and experimental results demonstrates the capability of the proposed model to capture the behaviors of LWC and NWC structures for static and impact loading.

• Coupled systems mechanics
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• v.4 no.4
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• pp.337-364
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• 2015

In this paper we present methodology for parameters identification of constitutive model which is able to present behavior of a connection between two members in a structure. Such a constitutive model for frame connections can be cast in the most general form of the Timoshenko beam, which can present three failure modes. The first failure mode pertains to the bending in connection, which is defined as coupled plasticity-damage model with nonlinear softening. The second failure mode is seeking to capture the shearing of connection, which is defined as plasticity with linear hardening and nonlinear softening. The third failure mode pertains to the diffuse failure in the members; excluding it leads to linear elastic constitutive law. Theoretical formulation of this Timoshenko beam model and its finite element implementation are presented in the second section. The parameter identification procedure that will allow us to define eighteen unknown parameters is given in Section 3. The proposed methodology splits identification in three phases, with all details presented in Section 4 through three different examples. We also present the real experimental results. The conclusions are stated in the last section of the paper.

• Journal of the Korea Concrete Institute
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• v.14 no.2
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• pp.239-248
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• 2002

A constitutive model unifying plasticity and crack damage mode)s was developed to address the cyclic behavior of reinforced concrete planar members. The stress of concrete in tension-compression was conceptually defined by the sum of the compressive stress developed by the strut-action of concrete and the tensile stresses developed by tensile cracking. The plasticity model with multiple failure criteria was used to describe the isotropic damage of compressive crushing affected by the anisotropic damage of tensile cracking. The concepts of the multiple fixed crack damage model and the plastic flow model of tensile cracking were used to describe the tensile stress-strain relationship of multi-directional cracks. This unified model can describe the behavioral characteristics of reinforced concrete in cyclic tension-compression conditions, i.e. multiple tensile crack orientations, progressively rotating crack damage, and compressive crushing of concrete. The proposed constitutive model was implemented to finite element analysis, and it was verified by comparison with existing experimental results from reinforced concrete shear panels and walls under cyclic load conditions.

• Earthquakes and Structures
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• v.10 no.5
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• pp.1089-1109
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• 2016

Modified two-surface model (M2SM) is one of the steel elasto-plastic hysteretic constitutive models that consider both analysis accuracy and efficiency. However, when M2SM is used for complex strain history, sometimes the results are irrational due to the limitation of stress-strain path judgment. In this paper, the defect of M2SM was re-modified by improving the judgment of stress-strain paths. The accuracy and applicability of the improved method were verified on both material and structural level. Based on this improvement, the nonlinear time-history analysis was carried out for a deck-through steel arch bridge with a 200 m-long span under the ground motions of Chi-Chi earthquake and Niigata earthquake. In the analysis, we compared the results obtained by hysteretic constitutive models of improved two-surface model (I2SM) presented in this paper, M2SM and the bilinear kinematic hardening model (BKHM). Results show that, although the analysis precision of displacement response of different steel hysteretic models differs little from each other, the stress-strain responses of the structure are affected by steel hysteretic models apparently. The difference between the stress-strain responses obtained by I2SM and M2SM cannot be neglected. In significantly damaged areas, BKHM gives smaller stress result and obviously different strain response compared with I2SM and M2SM, and tends to overestimate the effect of hysteretic energy dissipation. Moreover, at some position with severe damage, BKHM may underestimate the size of seismic damaged areas. Different steel hysteretic models also have influences on structural damage evaluation results based on deformation behavior and low cycle fatigue, and may lead to completely different judgment of failure, especially in severely damaged areas.

• Computers and Concrete
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• v.7 no.2
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• pp.159-167
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• 2010

This paper demonstrates numerical techniques for complex large-scale modeling with microplane constitutive theories for reinforced high strength concrete, which for these applications, is defined to be around the 7000 psi (48 MPa) strength as frequently found in protective structural design. Applications involve highly impulsive loads, such as an explosive detonation or impact-penetration event. These capabilities were implemented into the authors' finite element code, ParaAble and the PRONTO 3D code from Sandia National Laboratories. All materials are explicitly modeled with eight-noded hexahedral elements. The concrete is modeled with a microplane constitutive theory, the reinforcing steel is modeled with the Johnson-Cook model, and the high explosive material is modeled with a JWL equation of state and a programmed burn model. Damage evolution, which can be used for erosion of elements and/or for post-analysis examination of damage, is extracted from the microplane predictions and computed by a modified Holmquist-Johnson-Cook approach that relates damage to levels of inelastic strain increment and pressure. Computation is performed with MPI on parallel processors. Several practical analyses demonstrate that large-scale analyses of this type can be reasonably run on large parallel computing systems.

• Computers and Concrete
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• v.30 no.4
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• pp.257-267
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• 2022

Two different types of rubber aggregates (40 mesh rubber powder and 1-4 mm rubber particles respectively) were devised to substitute fine aggregates at 10%, 15%, 20% and 30% by volume in self-compacting concrete to investigate their basic mechanical properties. The results show that with the increase of rubber content, the reduction of compressive strength, splitting tensile strength and static modulus of elasticity gradually increase, and energy dissipation performance gradually increase. The rubber addition significantly reduces brittleness and decelerates damaged process. Whilst, the effect of rubber particles is greater when they are finer. Considering the mechanical properties, the optimal rubber content is 10%. It is recommended that the rubber volume content in rubberized concrete (RC) should not be higher than 20%. In addition, a constitutive model under uniaxial compression was proposed basing on the strain equivalent principle of Lemaitre and the damage theory, which was in good agreement with the test curves.

• Steel and Composite Structures
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• v.17 no.2
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• pp.185-198
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• 2014

Carbon-manganese steel A42 (French standards) is used in steam generator pipes of nuclear center and subject to low cycle fatigue (LCF) loads. In order to obtain the material LCF behavior, the tests are implemented in a hydraulic fatigue machine. The LCF plastic deformation and cyclic stress in macroscope have been influenced by the accumulated low cycle fatigue damage. The constitutive kinematic and isotropic hardening modeling is modified with coupling fatigue damage to describe the fatigue behavior. The improved model seems to be good agreement with the test results.