Abstract

Paper presents a Comparison of Ramberg-Osgood and Bilinear Stress-Strain Material Relation of Duplex Stainless Steel CHS Columns in Compression Utilizing Two Different Implicit Numerical Solvers: ANSYS and FEM Solver of SCIA Engineer

Abstract

Due to the advancements in additive manufacturing and increased applications of additive manufactured structures, it is essential to fully understand both the elastic and plastic behavior of cellular materials, which include the mathematically-driven triply periodic minimal surfaces (TPMS). The elastic and plastic behaviors have been well established for many TPMS structures. These structures are however rather computationally expensive to model explicitly when used in meta-materials and hence the need to develop an accurate yield function in order to model their plastic behavior in a homogenized approach. In this study, the effect of different loading conditions is numerically investigated on the effective yield strength of IWP ligament based (IWP-L) TPMS.

Abstract

We develop the integral approach for the analysis of nonlocal ductile damage in metals. The starting point is the previously proposed phenomenological model of finite strain plasticity. The original damage model is delocalized by the averaging operator, applied to damage-related quantities like porosity and continuity. Depending on the implemented delocalization procedure, at least one internal length parameter in introduced into the formulation. As a result, the damage localization is controlled by the presence of length-like parameters, thus regularizing the boundary value problem. Owing to the regularization, numerically robust and physically sound simulations of crack initiation and propagation are possible. Unphysical localization of strain and damage into a zero thickness layer is effectively prevented. From the theoretical standpoint, the basic properties of the new material model are analysed. Model’s thermodynamic consistency, objectivity, and w-invariance are established. Efficient numerical algorithms are proposed. To test the robustness of the integral-based approach, low-order meshless smoothed particle simulations are carried out. As a demonstration problem, we simulate crack initiation and propagation in a compact tension specimen. The resulting force-displacement curves, apparent fracture toughness, energy dissipation, and patterns of damage distribution provide insight into the mechanical phenomena, captured by the framework. The impact of the modelling assumptions on the predicted structural strength is clarified: Isotropic and anisotropic averaging is discussed; the delocalization is applied on various configurations; continuity is introduced as a dual damage variable to minimize the unrealistic diffusion of damage.

Abstract

In a classical way the Cauchy stress tensor is expressed in function of instantaneous internal variables as the strain, the strain rate and the temperature. If good predictions of the response of materials are obtained under quasi-static loadings, inaccurate estimations are finding for some severe dynamic conditions where high plastic strain, high strain rate or temperature gradients and microstructures changes occur during the plastic flow. To describe the metals work hardening under specific loadings, the traditional laws reduce the influence of the material deformation history only through the cumulated plastic strain defined from the time integral of the generalized strain rate. From a thermodynamic point of view the material stress is rather related to the dissipated plastic strain energy responsible for any change in the material thermomechanical state. This work propose then a new formalism to define a material constitutive equation from an equivalent stress expressed as a function of the dissipated plastic deformation energy. This new approach takes into account the microstructure changes which govern a lot of the physical mechanisms responsible for plastic flows: work-hardening, dynamic softening and phase transformation. This formulation remains valid for large paths of material deformation and for all the spectrum of loading conditions: from static, transient until rapid dynamic ones. Variational energetic approaches were first mentioned by R. HILL [1] indicating that the work-hardening phenomenon depends on the plastic strain energy. Recently a new formalism introduced by M. YOSHINO et al. [2] define for a first time a named reference stress as a function of plastic strain energy. From a thermodynamics point of view a reliable energy approach must be based on the principle that any system finds its time evolution by minimizing the losses energies and minimising the generated entropy [3]. One of the main objectives of this work is to find in an energetic framework the proposed general constitutive laws [4] defining the equivalent stress as a mixture between a hardening and a saturation term via the material fraction undergoing dynamic softening (recovery, recrystallization or phase transformation) described by an Avrami law expressed in terms of plastic strain. Firstly will be finding the energetic form of the usual hardening formulations proving the equivalency between the new formulation and the traditional ones. The obtained new constitutive model will be discussed comparing to a numerical implementation on the incremental elastic-plastic Prandtl-Reuss equations resolution. References: [1] R. Hill, The Mathematical theory of plasticity, Oxford, The Clarendon Press, (1950). [2] M. Yoshino et T. Shirakashi, Flow-stress equation including effects of strain-rate and temperature history, Int. J. Mech. Sci., 39 (12) :1345-1362 (1997). [3] A. Bejan, Advanced Engineering Thermodynamics, 2nd ed. Wiley, New York, (1997). [4] A. Gavrus, Constitutive equation for description of metallic materials behavior during static and dynamic loadings taking into account important gradients of plastic deformation, Key Engineering Materials, 504-506:697–702 (2012).

Abstract

Paraboloidal plastic yield criterion appropriately conveys the nonlinear elastoplastic behaviour of the polymers. The elastoplastic stress and strain relationship for the paraboloidal yield criteria is devised using the radial return mapping algorithm. For the numerical implementation of the devised relationship, an exact solution method using the classical loading-unloading conditions is presented. It avoids the erstwhile iterative scheme and improves efficiency of the solution technique. The non-iterative mathematical implementation is verified with the polymer experimental results in tension, compression and shear for simple and real-sized geometries under large strain conditions using the Abaqus solver tool to prove its functionality and computational efficiency.

Abstract

In this work, the Authors describe some of the still open and unsolved questions related to the constitutive modeling of snow with reference to Elasto-Plastic approaches. Furthermore, some suggestions on possible computational solutions through Finite Element tools are highlighted. The goal is twofold: first, we try to summarize the current state-of-the-art of FE analysis on snow; and second, we suggest some possible research directions and computational solutions to improve the existing mechanical models.

Abstract

Thermoplastic polymers nowadays are drawing attention in the automotive industrial thanks to their low cost, lightweight, and sustainability. They can be simply reshaped through the thermoforming process by heating up above their melting temperatures. Most thermoplastic polymers are semicrystalline ones that are composed of micro-spherulite structures with amorphous and crystalline regions. The amorphous region refers to the randomly distributed polymer chains whereas these chains are well-ordered lamellae in crystalline regions. These two phases interact with each other and result in a highly non-linear material response with the famous "double yield phenomenon". Therefore, to accurately predict the rate- and temperature- dependent semicrystalline polymers (SCPs) is still a challenge. Besides temperature increases due to the plastic dissipation under high-speed loading, inversely leading to the thermal softening and degrading the material performance. In this work, We proposed a thermomechanical modeling strategy for SCPs with a double yield phenomenon. Material characterization only requires few essential tests and the predicted results are promising.