Evaluation of typical concrete material models used in hydrocodes for high dynamic response simulations
Introduction
Concrete is an important material in civil and defence constructions. Yet concrete material has very complicated nonlinear behaviour that is difficult to be fully described for general stress conditions by a simple constitutive model. When concrete is subjected to extreme loads such as blast load from the detonation of explosive charges, or a hyper-velocity impact of missiles and fragments, the modelling of concrete can be further complicated due to rate effects, overloading and large deformations.
With the advancement in the computing power, it is now possible to perform numerical simulation for the response of concrete structures subjected to severe shock and impact loads, including the modelling of the loading sources if necessary (e.g., simulation of the airblast and structural response in a coupled manner). A number of commercial hydrocodes such as AUTODYN [1], and LS-DYNA [2] are available for the general simulation of structural nonlinear dynamic responses. However, in order for such simulations to produce reliable results regarding the response of a concrete structure, a sound material model capable of representing the essential mechanical processes of the material under varying stress and loading rate conditions is vital.
Concrete by nature is a heterogeneous material. Hence, modelling concrete at a meso-scale level, i.e., considering the heterogeneity of the material composition using, for example, the discrete element method (DEM) [3], is advantageous in depicting detailed mechanical processes of the material. However, the enormous computational demand associated with a meso-scale model could become prohibitive in solving practical problems. Therefore, in general applications, concrete is often treated as homogeneous by the so-called macro-scale material models.
Numerous studies have been carried out in the last 15 years for the development and improvement of the macro-scale concrete models for high-pressure applications, e.g., [4], [5], [6], [13], [14], [15], [16], [17], [18], [19]. Various material models have been proposed, from relatively simple to more sophisticated ones, and their capabilities in describing the actual nonlinear behaviour of the material under different loading conditions vary. Besides, because of the general complexity of the models, the determination of the model parameters (i.e., the model parameterisation) also plays an important role in the actual performance of these models. This requires a sufficient understanding of the modelling formulation and the associated considerations.
In this paper, a brief review of some typical models for concrete and concrete-like brittle materials is given first. A detailed examination of two widely used concrete models, namely, the RHT model [17] available in AUTODYN and the Concrete Damage Model [18], [19] in LS-DYNA is presented next. The similarities and distinctive features of these two models are analyzed, and their actual behaviour is examined through numerical tests in generating the stress–strain relationships under various stress conditions. Some potential issues with the present form of the RHT model are highlighted. Within the framework of its current formulation, a modified parameter setting is proposed to improve the behaviour of the RHT model, especially concerning the post-peak softening process under both tensile and compressive stress conditions.
In the last part of this paper, the RHT model with the default and the currently proposed parameter settings and the Concrete Damage Model are applied to simulate a physical test on a reinforced concrete slab under explosion loading. The simulation results are compared with the experimental observations. Conclusions are then drawn on the basis of both the material model exploration and the concrete slab simulations.
Section snippets
Review of typical concrete material models used in hydrocodes
A number of models for concrete-like materials have been developed. These models generally share in common some basic features of brittle materials such as pressure hardening, strain hardening and strain rate dependency. However, for simplicity some models adopt highly restrictive assumptions, consequently their applicability is limited to a certain class of problems. In cases where the loading environment of the material is very complex and cannot be pre-defined, more robust material models
Overview of RHT model
The RHT model [6], [17] was developed as an enhancement to the JH concrete model by the introduction of several new features. In this model, the strain hardening and the third invariant dependence were taken into account. An independent fracture strength surface was incorporated to allow for a more appropriate modelling of the material softening response. In addition, the concrete hydrostatic tensile strength was made rate dependent. These aspects are elaborated in the following paragraphs.
The Concrete Damage Model
The Concrete Damage Model was first developed for DYNA3D [4], [5], [18] and now is available in LS-DYNA as material #72. Apart from its comprehensiveness covering a number of important factors that are pertinent to the dynamic behaviours of concrete, in the latest versions of this model [18], [19] several outstanding issues as noted in Section 3 are addressed quite satisfactorily.
Application of RHT model and Concrete Damage Model in simulation of concrete slab under explosive loading
In order to further demonstrate the behaviour of the two concrete models when applied in the analysis of concrete structures under complex high dynamic loading conditions, the material models are used to simulate a physical experiment on a reinforced concrete slab under blast loading. The simulated results are then compared with the experimental observations. More details about the computational model can be found in [26].
The test concrete slab has a net dimension of 2 m (length) × 1 m (width) ×0.1 m
Conclusions
This paper presents a review and evaluation study of several concrete material models available in some commonly used hydrocodes. These material models represent different levels of sophistication and, therefore, different capabilities in representing the behaviour of the brittle material under different stress and loading rate conditions. Two of the most comprehensive models, namely the RHT model in AUTODYN and the Concrete Damage Model in LS-DYNA, are examined in greater detail. Numerical
References (26)
- et al.
Discrete element modeling of concrete submitted to dynamic loading at high strain rates
Comput Struct
(2004) - et al.
A plasticity concrete material model for Dyna3D
Int J Impact Eng
(1997) AUTODYN v4.2 user manual
(2001)LS-DYNA keyword user's manual, version 970
(April 2003)- et al.
A new concrete material model for DYNA3D. TM-94-14.3, report to the Defense Nuclear Agency
(October 1994) - et al.
A new concrete material model for DYNA3D—release II: shear dilation and directional rate enhancements. TM-96-2.1, report to the Defense Nuclear Agency
(January 1996) - Riedel W, Thoma K, Hiermaier S. Penetration of reinforced concrete by BETA-B-500—numerical analysis using a new...
A simple constitutive description for cellular concrete
(1972)- Shugar TA, Holland TJ, Malvar LJ. Applications of finite element technology to reinforced concrete explosive...
- et al.
An assessment of the cap model: consistent return algorithms and rate-dependent extensions
J Eng Mech
(1988)