Physics-informed machine learning in the determination of effective thermomechanical properties

We determine the effective (macroscopic) thermoelastic properties of two-phase composites computationally. To this end, we use a physics-informed neural network (PINN)-mediated first-order two-scale periodic asymptotic homogenization framework. A diffuse interface formulation is used to remedy the lack of differentiability of property tensors at phase interfaces. Considering the reliance on the standard integral solution for the property tensors on only the gradient of the corresponding solutions, the emerging unit cell problems are solved up to a constant. In view of this and the exact imposition of the periodic boundary conditions, it is merely the corresponding differential equation that contributes to minimizing the loss. This way, the requirement of scaling individual loss contributions of different kinds is abolished. The developed framework is applied to a planar thermoelastic composite with a hexagonal unit cell with a circular inclusion by which we show that PINNs work successfully in the solution of the corresponding thermomechanical cell problems and, hence, the determination of corresponding effective properties

Additive manufacturing of NiTi architected metamaterials

Additive manufacturing has revolutionized the creation of complex and intrinsic structures, offering tailored designs for enhanced product performance across various applications. Architected cellular or lattice structures exemplify this innovation, customizable for specific mechanical or functional requirements, boasting advantages such as reduced mass, heightened load-bearing capabilities, and superior energy absorption. Nonetheless, their single-use limitation arises from plastic deformation resulting from localized yield damage or plastic buckling. Incorporating NiTi shape memory alloys (SMAs) presents a solution, enabling structures to recover their original shape post-unloading. In this study, an NiTi architected metastructure, featuring auxetic behavior and a negative Poisson's ratio, was designed and fabricated via laser powder bed fusion (LPBF). The samples exhibit promising superelastic performance with recoverable deformation strains at room temperature. Comprehensive characterization processes evaluated the functional performance of the fabricated metastructures. The metastructure geometry promoted microstructure formation primarily along the wall thickness. Cycling compression tests, conducted at three applied force levels, demonstrated stable cyclic behavior with up to 3.8 % reversible deformation strain, devoid of plastic buckling or yielding damage. Furthermore, the NiTi metastructures displayed robust energy absorption capacity and damping behavior, underscoring their potential for reusable energy dissipators in various industries including aerospace, automotive, construction, and etc.</p

Computational Homogenization of Architectured Materials

Architectured materials involve geometrically engineered distributions of microstructural phases at a scale comparable to the scale of the component, thus calling for new models in order to determine the effective properties of materials. The present chapter aims at providing such models, in the case of mechanical properties. As a matter of fact, one engineering challenge is to predict the effective properties of such materials; computational homogenization using finite element analysis is a powerful tool to do so. Homogenized behavior of architectured materials can thus be used in large structural computations, hence enabling the dissemination of architectured materials in the industry. Furthermore, computational homogenization is the basis for computational topology optimization which will give rise to the next generation of architectured materials. This chapter covers the computational homogenization of periodic architectured materials in elasticity and plasticity, as well as the homogenization and representativity of random architectured materials

Prevention of Internal Cracks in Forward Extrusion by Means of Counter Pressure: A Numerical Treatise

In the context of forward bulk extrusion, where product defects are frequently observed, the effect of counter pressure on damage accumulation materializing a Continuum Damage Mechanics (CDM) approach is presented. A Lemaitre variant damage model accounting for unilateral damage evolution coupled with a multiplicative finite plasticity is utilized for this purpose. After a presentation of the crack governing mechanism, it is demonstrated that application of counter pressure introduces a marked decrease in the central damage accumulation, which in turn increases the formability of the material through keeping the tensile triaxiality in tolerable limits. It is also shown that, for a crack involving process, through systematic increase of the counter pressure, the crack sizes diminish; and at a certain level of counter pressure chevron cracks can be completely avoided

Identification of fully coupled anisotropic plasticity and damage constitutive equations using a hybrid experimental–numerical methodology with various triaxialities

A hybrid experimental–numerical methodology is presented for the parameter identification of a mixed nonlinear hardening anisotropic plasticity model fully coupled with isotropic ductile damage accounting for microcracks closure effects. In this study, three test materials are chosen: DP1000, CP1200, and AL7020. The experiments involve the tensile tests with smooth and notched specimens and two types of shear tests. The tensile tests with smooth specimens are conducted in different directions with respect to the rolling direction. This helps to determine the plastic anisotropy parameters of the material when the ductile damage is still negligible. Also, in-plane torsion tests with a single loading cycle are used to determine separately the isotropic and kinematic hardening parameters. Finally, tensile tests with otched specimens and Shouler and Allwood shear tests are used for the damage parameters identification validation tests

Identification of fully coupled anisotropic plasticity and damage constitutive equations using a hybrid experimental–numerical methodology with various triaxialities

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Gradient Enhanced Physically Based Plasticity: Implementation and Application to a Problem Pertaining Size Effect: Implementation and application to a problem pertaining size effect

A physically based plasticity model is implemented which describes work hardening of a material as a function of the total dislocation density. The local part of the model, which involves statistically stored dislocations (SSDs) only, is based on Bergström's original model. The nonlocal part is based on geometrically necessary dislocations (GNDs) which appear and evolve due to existence of large plastic strain gradients. The evolution of GNDs with respect to strain gradients is described based on the flow theory. The gradients are computed explicitly using the converged plastic strain field and the coupling is achieved using a staggered (weak) approach. Gradient computation is carried out using an effcient algorithm that makes use of plastic strain increments at integration points whose arrangement is not necessarily regular. The algorithm is applied on a void growth problem in which high strain gradients occur around the void due to stress concentrations