Introduction of a spherical indenter into a half-space with a functionally graded elastic coating

The Stressed-Strained State of an Elastic Half-Spacewith a Soft Functionally Graded Coating Penetratedby a Flat-Base Punch

“…Âî ìíîãèõ ðàáîòàõ íàïðÿaeåííîå ñîñòîÿíèå óïðóãîãî ñëîÿ (ïîëóïðîñòðàíñòâà) ïðè êîíòàêòíîì âçàèìîäåéñòâèè èññëåäóåòñÿ â ïðåäïîëîaeåíèè, ÷òî ðàñïðåäåëåíèå êîíòàêòíûõ äàâëåíèé ïîä øòàìïîì çàðàíåå èçâåñòíî è ïðèáëèaeåííî ñîîòâåòñòâóåò ðàñïðåäåëåíèþ êîíòàêòíûõ äàâëåíèé â çàäà÷å Ãåðöà [2,3]. Îäíàêî â ðàáîòå [1] ïîêàçàíî, ÷òî äëÿ òîíêèõ ïîêðûòèé èñïîëüçîâàíèå ðåøåíèÿ Ãåðöà äàåò áîëüøóþ ïîãðåøíîñòü, òàê êàê äëÿ ìàòåðèàëîâ ñ ïîêðûòèÿìè, îñîáåííî äëÿ ìàòåðèàëîâ ñ òîíêèìè ïîêðûòèÿìè, ðàñïðåäåëåíèå êîíòàêòíûõ äàâëåíèé ïîä ñôåðè÷åñêèì øòàìïîì â îáùåì ñëó÷àå ñóùåñòâåííî îòëè÷àåòñÿ îò ðàñïðåäåëåíèÿ Ãåðöà [4].…”

The frictionless axial interaction of a rigid disk with a two-layered functionally graded transversely isotropic medium

“…Aizikovich et al [19] studied the deformation of a gradient coating layer on a half-space under the action of arbitrary axisymmetric loading. Also, Aizikovich et al [20] considered the arbitrary and suffciently smooth function for variation of material properties in the study of a functionally graded coating on a half-space under the action of a spherical indenter. Liu et al [21] studied the axisymmetric frictionless contact of FGM, dividing the FGM layer to series of sub-layers and assuming the linear variation of the shear modulus in each layer and reducing the formulation to a Cauchy singular integral equation, and also analyzed the contact of a smooth rigid punch with a functionally graded coating on a homogeneous half-space with the approximate solution of a singular integral equation [22].…”