Sofia Damian, Ph.D. Candidate 39th cycle, University of Trento, DICAM
Many man-made architected and natural materials, such as hard and soft biological tissues, paper, concrete, and elastomeric solids, are characterized by a heterogeneous and strongly interlaced microstructure. Hence, due to the long-range interactions governed by an internal length scale at the microscopic level, the macroscopic mechanical behavior of the solids is nonlocal. The possibility of using those materials for a wide range of applications makes it essential to have the capability of predicting not only the elastic behavior but, moreover, the onset of damage, fracture, and delamination. In this light, during my Ph.D. we are focusing on modeling microstructured solids through a multiscale approach, considering their inherent size-dependency.
This will be achieved by combining Peridynamics (PD) and Structured Deformations (SD). The former is a recently developed nonlocal theory of continuum mechanics [5] which keeps track of the internal length scale, thus of the long-range interactions, through a specific parameter called horizon. On the other hand, the theory of Structured Deformations [2, 3, 4] allows one to consider a pair of length scales and to account for distributed discontinuities of the relative displacements, called disarrangements, at the submacroscopic level of a defect-free part of the material. Through the combination of those approaches, we aim to define a model capable of both capturing the nonlocal behavior and predicting damages in mechanical metamaterials.
During the first year of my Ph.D., in collaboration with the University of Naples “Federico II”, we are focusing on the PD theory. Starting from a dimensionally reduced PD model developed in [1], we investigate both the elastic and non-elastic behavior of a thin plate subject to various loading conditions. This is a key point of our research project as we obtain novel results in terms of damage prediction in solids with no need of pre-existing notches. Furthermore, the simulations performed on a plate with constant overall stiffness but different degrees of nonlocality allow us to examine how the geometrical redistribution of material inside a plate loaded with the same conditions gives significantly different behaviors in terms of internal actions and the onset of damage.
Our goal for the near future is to tackle the problem through SD by enhancing this theory with the opportunity to consider also nonlocal interactions. This would allow us to define a model capable of describing and predicting the behavior of mechanical metamaterials with novel and interesting features.
References
[1] Cavuoto, R., Cutolo, A., Dayal, K., Deseri, L., Fraldi, M.: Distal and non-symmetrical crack nucleation in delamination of plates via dimensionally-reduced peridynamics. J. Mech. Phys. Solids 172, 105189 (2023).
[2] Del Piero, G., Owen, D. R.: Structured deformations of continua. Arch. Rational Mech. Anal. 124, 99–155 (1993).
[3] Del Piero, G., Owen, D. R.: Integral-gradient formulae for structured deformations. Arch.
Rational Mech. Anal. 131, 121–138 (1995).
[4] Deseri, L., Owen, D. R.: Toward a Field Theory for Elastic Bodies Undergoing Disarrangements. J. Elast. 70(1), 197–236 (2003).
[5] Silling, S. A.: Reformulation of elasticity theory for discontinuities and long-range forces. J. Mech. Phys. Solids 48(1), 175-209 (2000).