Material length scales in gradient-dependent plasticity/damage and size effects: theory and computation

Structural materials display a strong size-dependence when deformed non-uniformly into the inelastic range: smaller is stronger. This effect has important implications for an increasing number of applications in structural failure, electronics, functional coatings, composites, micro-electro-mechanical systems (MEMS), nanostructured materials, micro/nanometer fabrication technologies, etc. The mechanical behavior of these applications cannot be characterized by classical (local) continuum theories because they incorporate no ‘material length scales’ and consequently predict no size effects. On the other hand, it is still not possible to perform quantum and atomistic simulations on realistic time and structures. It is therefore necessary to develop a scale-dependent continuum theory bridging the gap between the classical continuum theories and the atomistic simulations in order to be able to design the size-dependent structures of modern technology. Nonlocal rate-dependent and gradient-dependent theories of plasticity and damage are developed in this work for this purpose. We adopt a multi-scale, hierarchical thermodynamic consistent framework to construct the material constitutive relations for the scale-dependent plasticity/damage behavior. Material length scales are implicitly and explicitly introduced into the governing equations through material rate-dependency (viscosity) and coefficients of spatial higher-order gradients of one or more material state variables, respectively. The proposed framework is implemented into the commercially well-known finite element software ABAQUS. The finite element simulations of material instability problems converge to meaningful results upon further refinement of the finite element mesh, since the width of the fracture process zone (shear band) is determined by the intrinsic material length scale; while the classical continuum theories fail to address this problem. It is also shown that the proposed theory is successful for the interpretation of indentation size effects in micro/nano-hardness when using pyramidal and spherical indenters and gives sound interpretations of the size effects in micro-torsion of thin wires and micro-bending of thin beams. Future studies should be directed toward incorporation of the size effects into design procedures and code recommendations of modern engineering structures (e.g. for MEMS, NEMS, coatings, thin films), fiber composites (e.g. for aircrafts and ships), etc

A finite deformation coupled plastic-damage model for simulating fracture of metal foams

Metal foams are a novel class of lightweight materials with unique mechanical, thermal, and acoustical properties. The low ductility of metal foams hinders the possibilities of applying secondary forming techniques to shape metal foam sandwich panels into desired industrial components. An important factor is the limited studies on their macroscopic damage and fracture behavior under complex loading conditions. There exist numerous mechanistic micromechanics models describing the fracture behavior of metal foams at the strut level, but very few work have been done on modeling their macroscopically coupled plasticity-damage constitutive behavior. The objective of this study is to develop a continuum finite deformation elasto-plastic-damage mechanics-based constitutive model for metal foams. The constitutive model is implemented in a user-defined material subroutine (UMAT) in the finite element software ABAQUS/Standard. The elasto-plastic part is implemented using backward-Euler return algorithm within Deshpande–Fleck constitutive framework. Continuum damage mechanics framework is formulated for the development of damage evolution equations. These damage evolution equations take into consideration the various key degradation mechanisms that lead to the macroscopic fracture of metal foams under various loading conditions. The model is calibrated and validated based on experimental data on aluminum foams under different loading paths, strain rates, and temperatures

Effect of Lode Parameter and Stress Triaxiality on the Effective Plastic Yield Properties of Triply Periodic IWP Ligament-Based Minimal Surface

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

A deep learning energy-based method for classical elastoplasticity

The deep energy method (DEM) has been used to solve the elastic deformation of structures with linear elasticity, hyperelasticity, and strain-gradient elasticity material models based on the principle of minimum potential energy. In this work, we extend DEM to elastoplasticity problems involving path dependence and irreversibility. A loss function inspired by the discrete variational formulation of plasticity is proposed. The radial return algorithm is coupled with DEM to update the plastic internal state variables without violating the Kuhn-Tucker consistency conditions. Finite element shape functions and their gradients are used to approximate the spatial gradients of the DEM-predicted displacements, and Gauss quadrature is used to integrate the loss function. Four numerical examples are presented to demonstrate the use of the framework, such as generating stress-strain curves in cyclic loading, material heterogeneity, performance comparison with other physics-informed methods, and simulation/inference on unstructured meshes. In all cases, the DEM solution shows decent accuracy compared to the reference solution obtained from the finite element method. The current DEM model marks the first time that energy-based physics-informed neural networks are extended to plasticity, and offers promising potential to effectively solve elastoplasticity problems from scratch using deep neural networks

A physically based gradient plasticity theory’,

Abstract The intent of this work is to derive a physically motivated mathematical form for the gradient plasticity that can be used to interpret the size effects observed experimentally. The step of translating from the dislocation-based mechanics to a continuum formulation is explored. This paper addresses a possible, yet simple, link between the TaylorÕs model of dislocation hardening and the strain gradient plasticity. Evolution equations for the densities of statistically stored dislocations and geometrically necessary dislocations are used to establish this linkage. The dislocation processes of generation, motion, immobilization, recovery, and annihilation are considered in which the geometric obstacles contribute to the storage of statistical dislocations. As a result, a physically sound relation for the material length scale parameter is obtained as a function of the course of plastic deformation, grain size, and a set of macroscopic and microscopic physical parameters. Comparisons are made of this theory with experiments on micro-torsion, micro-bending, and micro-indentation size effects

Influence of carbon nanotubes on printing quality and mechanical properties of 3D printed cementitious materials

This paper presents the impact of incorporating carbon nanotubes (CNTs) into the 3D printing of cementitious materials, along with the effective dispersion of CNTs. Compared to the control mix, adding CNTs with superplasticizer significantly enhanced the printing quality by reducing the error in height of two-layers from 38% to 30% and an 81% enhancement in the buildability. Moreover, rheology properties revealed shear-thinning behaviour with lower viscosity, resulting in improved flowability. The progressive increase in CNT concentrations up to 0.2% yielded a noteworthy improvement in the mechanical properties. At 28 days, the incorporation of 0.2% CNTs resulted in a significant increase in the flexural strength, compressive strength, and Young's modulus by 99%, 72%, and 43%, respectively, compared to the mix containing silica fume. Microstructural investigation of the CNT-cement matrix revealed nanoscale crack bridges formed by CNTs, reinforcing the cementitious material and improving its mechanical properties.</p

IMECE2005-81384 A DISLOCATION BASED GRADIENT PLASTICITY THEORY WITH APPLICATIONS TO SIZE EFFECTS

ABSTRACT The intent of this work is to derive a physically motivated mathematical form for the gradient plasticity that can be used to interpret the size effects observed experimentally. This paper addresses a possible, yet simple, link between the Taylor&apos;s model of dislocation hardening and the strain gradient plasticity. Evolution equations for the densities of statistically stored dislocations and geometrically necessary dislocations are used to establish this linkage. The dislocation processes of generation, motion, immobilization, recovery, and annihilation are considered in which the geometric obstacles contribute to the storage of statistical dislocations. As a result a physically sound relation for the material length scale parameter is obtained as a function of the course of plastic deformation, grain size, and a set of macroscopic and microscopic physical parameters. The proposed model gives good predictions of the size effect in micro-bending tests of thin films and microtorsion tests of thin wires