Amphorae served as universal containers for wine, oil and salted fish products. They served for transport by sea and land of all the aforementioned and many other goods, during antiquity and partly in the Middle Ages. Amphorae were manufactured for thousands of years, with numerous variations of their shape, but all have had to meet the practical need for strength and fracture resistance during transport. They were produced in numerous locations throughout the Mediterranean, and the analysis of archaeological remains at the sites of production yields a wealth of information that directly or indirectly contributes to the knowledge of their mechanical properties.
Kilikoglou and Vekinis (2002) conducted an experimental study of the limiting deformations of amphorae to determine the yield limit of the material. The obtained limiting deformation values were then used to determine the endurance of the amphorae by the finite element method (FEM), for loads that regularly occur in use. For different thicknesses of amphorae walls and different types of ceramics, authors determined the limiting curve of material yield.
Radić Rossi et al. (2004) applied FEM in the analysis of the origin and function of the amphora’s spike. The following amphora types were analysed: Py 3B, Lamboglia 2, Dressel 20, and the hypothetical flat bottom type Py 3B. Common interpretations of the role of spikes include fixing the containers into the ground or sand, stacking them in the cargo space of the ship, and gripping when handling heavy vessels. Conducted analysis in the linear domain (ceramics as elastic material) showed that the spike hardens the amphora, protecting it from impact on uneven substrates. The authors concluded that the increase of amphorae strength and the increase in their reliability were the main reason for the existence of the amphorae spikes.
Four years later, Hein et al. (2008) published a systematic study of amphorae remains from excavations in ancient Halasarna on the Greek island of Kos. The authors analysed the chemical composition of dozens of samples divided into groups. They determined the proportions of individual chemical elements in the material, as well as scattering around the mean value of these proportions. Micro photographically, they analysed the presence of inclusions in the base material and concluded that the chemical composition of the mixture and the mechanical properties of the ceramics were stable throughout the production period of the amphorae at that location, from the 5th to the 1st century BC. At the same time, the shape of the amphorae changed during this period. Therefore, they modelled amphorae of different shapes, produced in the 4th to 1st century BC., and performed a strength analysis by finite element method. They concluded that the analysis provided clear evidence that, in the case of these amphorae, the development of their shape over time was the result of technological improvements: while the weight of the amphorae remained approximately the same, the capacity of the amphorae increased and the stresses under typical loads of their shoulders and bodies decreased. The test was limited to five different forms of amphorae from one location and to simple models, and was performed by analysis in the linear region, i.e. without the possibility of investigating the occurrence of cracks and fractures. Therefore, the authors suggested the need for additional, more complex numerical simulations.
Subsequently, Hein and Kilikoglou (2014) continued to investigate the strength of amphorae, that is, their tendency for fracturing, using FEM. They modelled several amphorae, arranged in multiple rows, as they would be placed in the cargo space of the ship, and analysed the stresses at the point of their contact. They concluded that fracture of the amphora could be expected if the contact force exceeded 1000N. The simulation did not take into account the friction coefficient or the breakage of the amphora. The authors concluded that the application of the FEM in archaeological research, through the simulation of the structural and mechanical response of the objects under consideration, has great potential, and pointed to the relatively small number of publications on the argument. With this ends the review of works that applied FEM in modelling and testing the amphorae models.
The ship, in the words of the famous German philosopher J. W. F. Hegel, "is a machine whose invention does the greatest honour to the boldness of man as well as to his understanding" (Hegel 1837). Archaeological remains tell us about ships of past times, and numerical modelling could help in their plausible reconstruction. In addition, in the places of shipwrecks, the ship’s cargo is often found without any or with modest remnants of the ship that carried it. The reconstruction of such events generally stops at the level of unproven assumptions.
A complete analysis and reconstruction of the sinking of a modern cargo ship was presented by Kery and Fisher (2012). Using modern engineering tools, they have developed a methodology for numerical analysis for the purpose of determining the cause of a shipwreck on a heavy sea. The methodology includes the analysis of the seaworthiness and the strength of the ship, for the various loads resulting from navigation in heavy seas. The methodology is equally applicable for the analysis of ancient shipwrecks, taking into account the structural differences between ancient and modern ships.
Kery and Stauffer (2015) analysed the processes of shipwreck taphonomy (geological and biological processes after the sinking of a ship) in the context of the action of sea currents, waves and other environmental conditions, on the decomposition and arrangement of ship residues and cargo with the passage of time. Modern engineering tools (Orcalflex software) have been used to model all the effects of environmental forces on a ship after its sinking below sea level, including impact on the seafloor and scattering of cargo during sinking. The paper, among other things, highlighted the problem of lack of data and research, regarding ancient shipwrecks.
Rudan and Radić Rossi (2017; in press) presented a complex analysis of the capsizing and sinking of an ancient ship loaded with cargo. The simulation involved a scenario in which a damaged ship, subject to the effects of wind and waves, was flooded, capsized, and finally sunk, until the cargo (amphorae) was dumped onto the seafloor. The simulation indicated the possibility of analysing different shipwreck scenarios, with the most likely scenario being one that, as a result of the simulation, gives an image of the shipwreck on the seafloor approximately equal to that at the site. The concept of such simulation was presented in the paper, without application to a specific shipwreck. It was concluded that systematic analysis of shipwrecks, taking into account archaeological, climatological and other scientific facts, makes it possible to define scenarios and carry out appropriate simulations. That can then lead to scientifically based confirmation of the cause of the shipwreck.
Murray et al. (2017) conducted experimental studies of the role of cutwater of the Mediterranean galley in the basin, using a 1:20 scale ship model. The results were compared with those for the classic bow of a merchant ship. They measured and compared the resistance of the ship at different speeds of navigation. Compared to experiments conducted at the Technical University of Athens, they concluded that the results confirmed the assumption that the cutwater had the function of increasing the hydrodynamic efficiency of the hull. The experiments did not rule out the possibility that such a bow could have also been used for offensive purposes, but they certainly confirmed its impact on increasing the speed of the ship.
Kerry (2017) presented the possibilities of modern methods of analysis in simulating ship behaviour in stormy conditions. In his work he performed modelling of nonlinear waves in combination with hurricane winds, which together cause a nonlinear response of the ship to the waves, often leading to capsizing and sinking of the ship. The methodology presented has been applied to four types of ships from different periods of history, including the generic model of a two-masted sailboat, which in many respects resembles ancient and medieval ships.
In the review article, Rudan and Radić Rossi (2018) also outlined a number of possibilities of applying modern engineering methods in nautical archaeology. Attention was drawn to the analysis of structures made of ceramics and wood, and the implementation of complex simulations of seaworthiness, capsizing and sinking of the ship by the finite element method, and the method of fluid-structure interaction. They pointed to the opportunities and importance of the numerical simulations performed in the research and interpretation of different scenarios of damage and fracture of ship structures and their load. They concluded that such interdisciplinary research requires the close collaboration of archaeologists and engineers. They also pointed out that there was a very limited number of publications on such research. The three cited articles, written by Rudan and Radić Rossi, are the result of the AdriaS - Archaeology of Adriatic Shipbuilding and Seafaring (IP-2014-09-8211) Project, funded by the Croatian Science Foundation.
Helfman et al. (2019) used FEM to compare two basic designs of wooden ships: those built with the shell-first, and those built with the skeleton-first technique. A simple linear static FEM analysis was performed, as a continuation of the research from Helfman et al. (2018). Their recent research has shown that there are three critical interdependent factors that determine the relative strength of structure for these two ship construction techniques: the number of transverse frames, the number of longitudinal reinforcements, and their relative position.
References:
Hegel, J. W. F. 1837. Vorlesungen über die Philosophie der Weltgeschichte. Eduard Gans, Berlin.
Hein, A., Georgopoulou, V., Nodarou, E., Kilikoglou, V. 2008. Koan amphorae from Halasarna - investigations in a Hellenistic amphora production centre. Journal of Archaeological Science 35: 1049-1061
Hein, A., Kilikoglou, V. 2014. Breaking pots – simulating design failures of transport amphorae by using the finite element method (FEM). 1st CAA GR Conference, Rethymno, Crete, Greece.
Helfman, N., Nishri, B., Cvikel, D. 2018. A comparative structural analysis of shell-frst and frame-based ship hulls of the 1st millennium AD. Naval Engineering Journal 130: 91–103.
Helfman, N., Nishri, B., Cvikel, D. 2019. Finite Element Analysis of Shell‑First and Longitudinally Reinforced Frame‑Based Wooden Ships. Journal of Maritime Archaeology 14: 291–309.
Kery, S. 2017. Marine Forensics: The Art and Science of Simulating Ships in Storm Conditions. Interservice/Industry Training, Simulation, and Education Conference (I/ITSEC): 1-16.
Kery, S. M., Fisher, B. 2012. A Forensic Investigation Of The Breakup And Sinking Of The Great Lakes Iron Ore Carrier Edmund Fitzgerald, November 10th 1975, Using Modern Naval Architecture Tools And Techniques. International Marine Forensics Symposium, National Harbor MD: 1-36.
Kery, S., Stauffer, J. 2015. Hydrodynamics Related to Shipwreck Taphonomy. MTS/IEEE Oceans, Washington DC: 1-21.
Kilikoglou, V., Vekinis, G. 2002. Failure Prediction and Function Determination of Archaeological Pottery by Finite Element Analysis. Journal of Archaeological Science 29: 1317–1325.
Murray, W. M., Ferreiro, L. D., Vardalas, J., Royal, J. G. 2017. Cutwaters Before Rams: an experimental investigation into the origins and development of the waterline ram. The International Journal of Nautical Archaeology 46.1: 72-82.
Radić Rossi, I., Senjanović, I., Rudan, S., Indof, J. 2004. Podrijetlo i funkcija šiljatoga dna amfora. Prilozi Instituta za arheologiju u Zagrebu 21: 91.-107.
Rudan, S., Radić Rossi, I. 2017. Numerical Simulation of the Sinking Ship Scenario, Based on the Archaeological Records, abstract. Under the Mediterranean: 100 years on … The Honor Frost Foundation Conference of ‘Mediterranean Maritime Archaeology’ Nicosia, 20-24 October 2017.
Rudan, S., Radić Rossi, I. 2018. Application of the State-Of-The-Art Engineering Methods in Nautical Archaeology. Pomorski zbornik – Journal of Maritime and Transportation Science, Special edition 2.2: 113-122.
Rudan, S., Radić Rossi, I. 2020. Numerical simulation of a sinking ship scenario based on archaeological records / Numerička simulacija potonuća broda na temelju arheoloških zapisa. Archaeologia Adriatica 14: 139-157.