Elasto-plastic constitutive model of aluminum alloy foam subjected to impact loading

A multi-parameter nonlinear elasto-plastic constitutive model which can fully capture the three typical features of stress-strain response, linearity, plasticity-like stress plateau and densification phases was developed. The functional expression of each parameter was determined using uniaxial compression tests for aluminum alloy foams. The parameters of the model can be systematically varied to describe the effect of relative density which may be responsible for the changes in yield stress and hardening-like or softening-like behavior at various strain rates. A comparison between model predictions and experimental results of the aluminum alloy foams was provided to validate the model. It was proved to be useful in the selection of the optimal-density and energy absorption foam for a specific application at impact events.

An elasto-plastic constitutive model of moderate sandy clay based on BC-RBFNN

Application research of neural networks to geotechnical engineering has become a hotspot nowadays.General model may not reach the predicting precision in practical application due to different characteristics in different fields.In allusion to this,an elasto-plastic constitutive model based on clustering radial basis function neural network(BC-RBFNN) was proposed for moderate sandy clay according to its properties.Firstly,knowledge base was established on triaxial compression testing data;then the model was trained,learned and emulated using knowledge base;finally,predicting results of the BC-RBFNN model were compared and analyzed with those of other intelligent model.The results show that the BC-RBFNN model can alter the training and learning velocity and improve the predicting precision,which provides possibility for engineering practice on demanding high precision.

An elasto-plastic and viscoplastic damage constitutive model for dilatancy and fracturing behavior of soft rock squeezing deformation

Soft rock squeezing deformation mainly consists of pre-peak damage-dilatancy and post-peak fracture-bulking at the excavation unloading instant,and creep-dilatancy caused by time-dependent damage and fracturing.Based on the classic elastoplastic and Perzyna over-stress viscoplastic theories,as well as triaxial unloading confining pressure test and triaxial unloading creep test results,an elastoplastic and viscoplastic damage constitutive model is established for the short-and long-term dilatancy and fracturing behavior of soft rock squeezing deformation.Firstly,the criteria for each deformation and failure stage are expressed as a linear function of confining pressure.Secondly,the total damage evolution equation considering time-dependent damage is proposed,including the initial damage produced at the excavation instant,in which the damage variable increases exponentially with the lateral strain,and creep damage.Thirdly,a transient five-stages elasto-plastic constitutive equation for the short-term deformation after excavation that comprised of elasticity,pre-peak damage-dilatancy,post-peak brittle-drop,linear strain-softening,and residual perfectly-plastic regimes is developed based on incremental elasto-plastic theory and the nonassociated flow rule.Fourthly,regarding the timedependent properties of soft rock,based on the Perzyna viscoplastic over-stress theory,a viscoplastic damage model is set up to capture creep damage and dilatancy behavior.Viscoplastic strain is produced when the stress exceeds the initial static yield surface fs;the distance between the static yield surface fs and the dynamic yield surface fd determines the viscoplastic strain rate.Finally,the established constitutive model is numerically implemented and field applied to the-848 m belt conveyer haulage roadway of Huainan Panyidong Coal Mine.Laboratory test results and in-situ monitoring results validate the rationality of the established constitutive model.The presented model takes both the transient and time-dependent damage and fracturing into consideration.

Nonlinear constitutive models of rock structural plane and their applications

Structural planes play an important role in controlling the stability of rock engineering,and the influence of structural planes should be considered in the design and construction process of rock engineering.In this paper,mechanical properties,constitutive theory,and numerical application of structural plane are studied by a combination method of laboratory tests,theoretical derivation,and program development.The test results reveal the change laws of various mechanical parameters under different roughness and normal stress.At the pre-peak stage,a non-stationary model of shear stiffness is established,and threedimensional empirical prediction models for initial shear stiffness and residual stage roughness are proposed.The nonlinear constitutive models are established based on elasto-plastic mechanics,and the algorithms of the models are developed based on the return mapping algorithm.According to a large number of statistical analysis results,empirical prediction models are proposed for model parameters expressed by structural plane characteristic parameters.Finally,the discrete element method(DEM)is chosen to embed the constitutive models for practical application.The running programs of the constitutive models have been compiled into the discrete element model library.The comparison results between the proposed model and the Mohr-Coulomb slip model show that the proposed model can better describe nonlinear changes at different stages,and the predicted shear strength,peak strain and shear stiffness are closer to the test results.The research results of the paper are conducive to the accurate evaluation of structural plane in rock engineering.

An Elasto-plastic Damage Constitutive Theory Based on Pair Functional Potentials and Slip Mechanism

The deformation work rate can be expressed by the time rate of pair functional potentials which describe the energy of materi- als in terms of atomic bonds and atom embedding interactions. According to Cauchy-Born rule, the relations between the micro- scopic deformations of atomic bonds and electron gas and macroscopic deformation are established. Further, atomic bonds are grouped according to their directions, and atomic bonds in the same direction are simplified as a spring-bundle component. Atom embedding interactions in unit reference volume are simplified as a cubage component. Consequently, a material model com- posed of spring-bundle components and a cubage component is established. Since the essence of damage is the decrease and loss of atomic bonding forces, the damage effect can be reflected by the response functions of these two kinds of components. For- mulating the mechanical responses of two kinds of components, the corresponding elasto-damage constitutive equations are de- rived. Considering that slip is the main plastic deformation mechanism of polycrystalline metals, the slip systems of crystal are extended to polycrystalline, and the slip components are proposed to describe the plastic deformation. Based on the decomposition of deformation gradient and combining the plastic response with the elasto-damage one, the elasto-plastic damage constitutive equations are derived. As a result, a material model iormulated with spring-bundle components, a cubage component and slip components is established. Different from phenomenological constitutive theories, the mechanical property of materials depends on the property of components rather than that directly obtained on the representative volume element. The effect of finite deformation is taken into account in this model. Parameter calibration procedure and the basic characteristics of this model are discussed.

STRUCTURAL DAMAGE MODEL OF UNSATURATED EXPANSIVE SOIL AND ITS APPLICATION IN MULTI-FIELD COUPLE ANALYSIS ON EXPANSIVE SOIL SLOPE

Focused on the sensitivity to climate change and the special mechanical characteristics of undisturbed expansive soil, an elasto-plastic damage constitutive model was proposed based on the mechanics of unsaturated soil and the mechanics of damage. Undisturbed expansive soil was considered as a compound of non-damaged part and damaged part. The behavior of the non-damaged part was described using non-linear constitutive model of unsaturated soil. The property of the damaged part was described using a damage evolution equation and two yield surfaces, i.e., loading yield （LY） and shear yield （SY）. Furthermore, a consolidation model for unsaturated undisturbed expansive soil was established and a FEM program named UESEPDC was designed. Numerical analysis on solid-liquid-gas tri-phases and multi-field couple problem was conducted for four stages and fields of stress, displacement, pore water pressure, pore air pressure, water content, suction, and the damage region as well as plastic region in an expansive soil slope were obtained.