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Plier vs. courber vs. fléchir

The French words plier, courber, and fléchir all translate to the English verb "to bend", but they describe distinctly different types of bending. The choice depends on whether the object is folded at a sharp angle, bent into a smooth arc, or flexed under weight and pressure.

Plier

The word plier generally means to bend something by creating a sharp angle, a crease, or a fold. It is the standard verb for folding paper or fabric, bending a joint like an arm or knee, and is used metaphorically to describe submitting or yielding to someone else's will.
Il faut plier la feuille de papier en quatre.
(You must fold the sheet of paper in four.)
Elle n'arrive plus à plier son bras à cause de la douleur.
(She can no longer bend her arm because of the pain.)
Le vent était si fort qu'il faisait plier les arbres.
(The wind was so strong that it made the trees bend.)
L'armée a refusé de plier face à l'ennemi.
(The army refused to bend in the face of the enemy.)
Ce tuyau en plastique est difficile à plier sans le casser.
(This plastic pipe is difficult to bend without breaking it.)

Courber

The verb courber refers to bending something into a smooth curve, arc, or rounded shape without creating a sharp fold or crease. It is commonly used when talking about wires, branches, roads, or a person's back.
L'artisan doit courber le fil de fer pour fabriquer un cintre.
(The craftsman must bend the wire to make a hanger.)
Le vieil homme marche en regardant le sol, le dos complètement courbé.
(The old man walks looking at the ground, his back completely bent.)
La branche se courbe sous le poids des pommes.
(The branch bends under the weight of the apples.)
La rivière courbe doucement vers le sud.
(The river bends gently to the south.)
Il a dû courber la tête pour passer la porte basse.
(He had to bend his head to pass through the low door.)

Fléchir

The word fléchir means to flex or to bend slightly under weight, pressure, or tension, implying a degree of elasticity. In sports or medical contexts, it refers to flexing a muscle or joint. Metaphorically, it means to waver, weaken, or give in under pressure.
Les haltérophiles doivent fléchir les jambes avant de soulever le poids.
(Weightlifters must bend their legs before lifting the weight.)
La poutre en bois commence à fléchir sous le poids du toit.
(The wooden beam is starting to bend under the weight of the roof.)
Ses genoux ont fléchi de terreur quand il a entendu le bruit.
(His knees bent with terror when he heard the noise.)
Malgré les menaces constantes, le témoin n'a pas fléchi.
(Despite the constant threats, the witness did not bend.)
La courbe de l'inflation commence enfin à fléchir.
(The inflation curve is finally starting to bend downwards.)

Summary

To choose the correct translation for "to bend", consider the physical outcome of the action. Use plier when the action creates an angle or a fold, like bending a knee or folding paper. Use courber when you are forming a smooth curve or arc, such as bending wire or having a bowed back. Finally, use fléchir when describing an object sagging or flexing under pressure, the athletic action of flexing a joint, or a person weakening in their resolve.